sensors Article
An Improved BAQ Encoding and Decoding Method for Improving the Quantized SNR of SAR Raw Data Wei Ji 1,2,3 , Xiaolan Qiu 1,2, * , Xuejiao Wen 1,2 and Lijia Huang 1,2 1
2 3
*
Key Laboratory of Technology in Geo-Spatial Information Processing and Application System, Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China;
[email protected] (W.J.);
[email protected] (X.W.);
[email protected] (L.H.) Institute of Electronics, Chinese Academy of Sciences, Beijing 100190, China School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China Correspondence:
[email protected]; Tel.: +86-138-1171-1782
Received: 23 October 2018; Accepted: 26 November 2018; Published: 1 December 2018
Abstract: When the original echo data of SAR are saturated for quantization, the performance of the commonly used block adaptive quantization (BAQ) algorithm will be degraded, which will degrade the imaging quality. This article proposes an improved Llody-Max codec method, which only needs to change the codec look-up table to get better quantization performance when the original echo is saturated. The simulation results show that the proposed method can reduce the quantization power loss, improve the echo signal-to-noise ratio (SNR), and reduce the influence of quantization saturation on the scattering mechanism of polarized SAR data, which have good practical application value. Keywords: synthetic aperture radar (SAR); raw data compression; block adaptive quantization (BAQ); anti-saturation; signal-to-noise ratio (SNR)
1. Introduction Synthetic aperture radar (SAR) system technology has been developing towards high resolution, wide swaths, high revisit frequency, multi-frequency, multi-polarization, and so on. The application of SAR has turned from qualitative applications to quantitative applications. Therefore, the improvement of SAR quantitative accuracy has become one of the key aspects in development. The quality of SAR raw echo data is a prerequisite for good SAR image quality. Due to a large amount of SAR raw echo data and the limitation of transmission bandwidth, data rate, and so on, the SAR raw data are usually compressed [1–3]. Therefore, quantization and compression will affect the quality of echo and further the SAR images. There have been quite a lot of studies on SAR raw data compression algorithms [4–6]. Considering the complexity of the algorithm, compression time, hardware conditions, and other factors, the block adaptive quantization (BAQ) algorithm is mainly adopted in SAR satellites for its simplicity and efficiency. For example, it has been used in the American Magellan SAR [7], ESA’s Sentinel-1 [8], Canada’s Radarsat-2 [9], Germany’s TanDEM-X [10], Chinese GF-3 SAR [11], and so on. The BAQ algorithm can adaptively quantify the echo with variant power intensity, and get the best quantization SNR for the Gauss distributed echo. However, when the echo is saturated the performance of BAQ will be degraded. To enhance the performance, and also to reduce the data rate, many improved BAQ methods have been proposed. For example, the flexible dynamic block adaptive quantizer algorithm used by Sentinel-1 is proposed in the literature [8], which is a data compression algorithm that automatically selects a BAQ quantizer out of a set of five quantizers, based on an estimation of the local SNR estimated
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estimated blocks on the acquired data. In these two methods, the overall performances are improved under limited data rate, but the performance of the saturated data cannot be improved. The literature blocks on the acquired data. In these two methods, the overall performances are improved under [10] describes a novel azimuth-switched quantization (ASQ) technique, which provides the capability limited data rate, but the performance of the saturated data cannot be improved. The literature [10] of synthesizing fractional quantization rates without impacting the complexity and computational describes a novel azimuth-switched quantization (ASQ) technique, which provides the capability of load of the quantization scheme. The method has been carried out in the frame of the TanDEM-X synthesizing fractional quantization rates without impacting the complexity and computational load of mission, and it is shown that performance and resources can be dynamically scaled with a very fine the quantization scheme. The method has been carried out in the frame of the TanDEM-X mission, and it discretization. Zhao et al., in the literature [12], propose a method for selecting a quantization strategy is shown that performance and resources can be dynamically scaled with a very fine discretization. based on the judgment of echo data saturation. In the case of low saturation, the traditional BAQ Zhao et al., in the literature [12], propose a method for selecting a quantization strategy based on the compression [7] is used, and in the case of high saturation, the saturation data is coded and decoded judgment of echo data saturation. In the case of low saturation, the traditional BAQ compression [7] separately. This method can get better quantization SNR for the saturated data, but it has to increase is used, and in the case of high saturation, the saturation data is coded and decoded separately. the saturation judgment, which will increase the amount of computation on the system. Qiu et al. This method can get better quantization SNR for the saturated data, but it has to increase the saturation propose a method in the literature [13], which obtains the variance of the input signal by calculating judgment, which will increase the amount of computation on the system. Qiu et al. propose a method the quantization output power, and then dynamically changes the quantized boundary code value. in the literature [13], which obtains the variance of the input signal by calculating the quantization So, it can improve the performance when the data is saturated, but the improvement is not as output power, and then dynamically changes the quantized boundary code value. So, it can improve significant because it is limited by the coding system. Qi et al. propose a quantization method, based the performance when the data is saturated, but the improvement is not as significant because it is on the optimal nonlinear scalar quantizer and a power compensation decoder, in the literature [14]. limited by the coding system. Qi et al. propose a quantization method, based on the optimal nonlinear The method is based on the relationship between signal saturation, uniform quantified peaks, scalar quantizer and a power compensation decoder, in the literature [14]. The method is based on standard deviation (before and after) uniform quantization, and signal amplitude mean, and they the relationship between signal saturation, uniform quantified peaks, standard deviation (before and designed a new look-up table and a power compensator. Our studies on this method found that the after) uniform quantization, and signal amplitude mean, and they designed a new look-up table and a encoding and decoding methods can be further optimized, and the quantization performance can be power compensator. Our studies on this method found that the encoding and decoding methods can further improved. be further optimized, and the quantization performance can be further improved. This article proposes an improved BAQ encoding and decoding method for improving the This article proposes an improved BAQ encoding and decoding method for improving the signal-to-noise ratio of SAR raw data. Through the analysis of uniform quantization and coding signal-to-noise ratio of SAR raw data. Through the analysis of uniform quantization and coding processes, this article redesigns the standard deviation and the amplitude mean value look-up table processes, this article redesigns the standard deviation and the amplitude mean value look-up table of the uniform quantized signal. The decoding method is redesigned according to the principle of of the uniform quantized signal. The decoding method is redesigned according to the principle of minimum-quantization noise loss. This method significantly improves compression performance, minimum-quantization noise loss. This method significantly improves compression performance, compared with the traditional BAQ compression algorithm [7] and other methods [12–14]. This compared with the traditional BAQ compression algorithm [7] and other methods [12–14]. This method method does not need to make any changes to the quantization hardware system, and only needs to does not need to make any changes to the quantization hardware system, and only needs to replace the replace the look-up table. There is no increment in the complexity and computation of the algorithm. look-up table. There is no increment in the complexity and computation of the algorithm. The rest of The rest of the article is arranged as follows: In Section 2, the improved BAQ compression algorithm the article is arranged as follows: In Section 2, the improved BAQ compression algorithm is described. is described. Section 3 gives the performance analysis results, through simulation and practical Section 3 gives the performance analysis results, through simulation and practical experiments to experiments to verify the effectiveness of the method. Section 4 concludes the article. verify the effectiveness of the method. Section 4 concludes the article. 2. The Improved BAQ Encoding and Decoding Method 2. The Improved BAQ Encoding and Decoding Method The traditional BAQ method first divides the input signal into blocks, then uniformly quantizes, The traditional BAQ method first divides the input signal into blocks, then uniformly quantizes, normalizes, and non-uniformly quantizes the data for each block, and then decodes it to get the normalizes, and non-uniformly quantizes the data for each block, and then decodes it to get the output signal, as shown in Figure 1. When N bit non-uniform quantization was performed on the output signal, as shown in Figure 1. When N bit non-uniform quantization was performed on original SAR echo, the quantitative dynamic range was [ − 2 N − 1 , 2NN−− 11] , Nand all values larger than the original SAR echo, the quantitative dynamic range was [−2 , 2 −1 ], and all values larger N −1 N −1 N −1 1−1 −1 +quantified −1 −( −0.5 smaller than ( −than were as (2 −as and , respectively. (2 − 2 +(− 1) 2 N 0.5)(2 N 2 N )− 1 and + 0.5)(− than (21)N −and ) and smaller 1) were quantified 2 N −1 + 0.5), N −1 N − 1 respectively. when the absolute value of the signal isthan greater 2 , quantization saturation 2 than , quantization saturation occurs. So, when theSo, absolute value of the signal is greater occurs. Quantization saturation in a truncation effect, leading lossofofeffective effective quantization Quantization saturation resultsresults in a truncation effect, leading to to thethe loss intervals, intervals, which which ultimately ultimately leads leads to to power power loss loss and and affects affectsthe thequality qualityof ofthe theimage. image.
Input signal
Divide data into blocks
Uniformity quantization
Output signal
Decoding
Normalization and nonuniformity quantization
Figure Figure 1. 1. The flowchart of traditional traditional BAQ BAQ method. method.
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As the Lloyd-Max quantizer (adopted by the traditional BAQ method) requires the quantization As the the Lloyd-Max Lloyd-Max quantizer quantizer (adopted (adopted by by the the traditional traditional BAQ BAQ method) method) requires requires the the quantization quantization As signal to conform to the standard Gaussian distribution, it is necessary to normalize the signal after signal to conform distribution, it isit necessary to normalize the signal after signal conform to tothe thestandard standardGaussian Gaussian distribution, is necessary to normalize the signal uniform quantization. In the actual system, in order to reduce the amount of computation, a preuniform quantization. In the actual system, in order to reduce the amount of computation, a preafter uniform quantization. In the actual system, in order to reduce the amount of computation, designed mean standard deviation look-up table is adopted, to find the standard deviation according mean mean standard deviation look-uplook-up table is adopted, to find the according adesigned pre-designed standard deviation table is adopted, to standard find the deviation standard deviation to the mean value and then realize normalization. Quantization saturation can lead to a mismatch of to the mean and then normalization. Quantization saturation can lead to acan mismatch according to value the mean valuerealize and then realize normalization. Quantization saturation lead to of a the mapping relationship between the mean value and standard deviation of signal amplitude in the mapping relationship the mean value standard deviation of signal amplitude in mismatch of the mapping between relationship between the and mean value and standard deviation of signal traditional BAQ methods, as shown in Figure 2. If the original variance is used for normalization, traditional in BAQ methods,BAQ as shown in Figure 2. If the original2.variance is used for normalization, amplitude traditional methods, as shown in Figure If the original variance is used although the unsaturated part still satisfies the standard Gaussian distribution, the absence of although the unsaturated still satisfies part the still standard Gaussian distribution, thedistribution, absence of for normalization, althoughpart the unsaturated satisfies the standard Gaussian effective quantization interval will be caused, due to the truncation effect. Therefore, the standard effective quantization will beinterval caused,will duebetocaused, the truncation effect. Therefore, theTherefore, standard the absence of effectiveinterval quantization due to the truncation effect. deviation adopted by the traditional method can no longer be used in the case of quantitative deviation adopted by the traditional can no longercan beno used in the the standard deviation adopted by themethod traditional method longer be case used of in quantitative the case of saturation, but should be solved again according to the truncated signal [14], as shown by the red saturation, but should but be solved according to the truncated signal [14], as shown the red quantitative saturation, shouldagain be solved again according to the truncated signal [14], asby shown by curve in Figure 2. curve Figure the redincurve in 2. Figure 2.
Figure 2. The relationship between the signal standard deviation and mean value of signal amplitude, Figure Figure 2. 2. The relationship relationship between between the the signal standard standard deviation deviation and and mean mean value of signal amplitude, before and after uniform quantization. before and after uniform quantization. before and after uniform quantization.
In the the caseof of non-uniformquantization, quantization, taking BAQ example, when signal after In 8:38:3 BAQ as as anan example, when thethe signal after 8 bit88 In thecase case ofnon-uniform non-uniform quantization,taking taking 8:3 BAQ as an example, when the signal after bit uniform quantization is not saturated, normalized peak datawill will fallininthe the eighthquantization quantization uniform quantization is not saturated, thethe normalized peak data bit uniform quantization is not saturated, the normalized peak data willfall fall in theeighth eighth quantization interval, so that all quantization intervals are effective, as shown in Figure 3a. When the signal after after interval, interval, so so that that all all quantization quantization intervals intervals are are effective, effective, as as shown shown in in Figure Figure 3a. 3a. When When the the signal signal after bit uniform uniform quantization is is saturated, the the data will will be truncated. truncated. If normalized normalized by the the standard 888 bit bit uniform quantization quantization is saturated, saturated, the data data will be be truncated. If If normalized by by the standard standard deviation in the traditional method, it will cause the normalized peak data to fall into a certain deviation deviation in in the the traditional traditional method, method, it it will will cause cause the the normalized normalized peak peak data data to to fall fall into into aa certain certain quantization interval, resulting in an invalid part of the quantization interval. As shown in Figure 3b, quantization interval, resulting in an invalid part of the quantization interval. As shown in Figure quantization interval, resulting in an invalid part of the quantization interval. As shown in Figure 3b, 3b, the peak peak value falls falls into the the seventh interval interval after normalization, normalization, resulting in in the invalidation invalidation of the the the the peak value value falls into into the seventh seventh interval after after normalization, resulting resulting in the the invalidation of of the first and and eighth quantization quantization intervals. Then, Then, if the original original method is is also adopted adopted for encoding encoding and first first and eighth eighth quantizationintervals. intervals. Then, ifif the the original method method is also also adopted for for encoding and and decoding, it will inevitably lead to large quantization noise and cannot achieve a good quantization decoding, it will inevitably lead to large quantization noise and cannot achieve a good quantization decoding, it will inevitably lead to large quantization noise and cannot achieve a good quantization effect. Therefore, Therefore, it is necessary necessary to recalculate recalculate the standard standard deviation for for normalization, as as well as as the effect. effect. Therefore, itit is is necessary to to recalculate the the standard deviation deviation for normalization, normalization, aswell well as the the threshold and quantization level of each quantization interval. threshold and quantization level of each quantization interval. threshold and quantization level of each quantization interval.
(a) (a)
(b) (b)
Figure Figure 3. 3. Quantization Quantization interval interval distribution distribution for for 8:3 8:3 BAQ BAQ coding: coding: (a) (a) eight eight quantization quantization intervals intervals are are Figure 3. Quantization interval distribution for 8:3 BAQ coding: (a) eight quantization intervals are valid; valid; (b) (b) six six quantization quantizationintervals intervalsare arevalid. valid. valid; (b) six quantization intervals are valid.
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In order to achieve a better compression effect, this article makes two improvements: First, we redesign the mean standard deviation look-up table for normalization; Second, we improve the threshold and quantization level of the individual quantization intervals for the Lloyd-Max quantizer, which is the core of BAQ. The improved method for the mean standard deviation look-up table is as follows: In practice, satellite coding is based on the average, to find the corresponding standard deviation and quantization threshold of the table for normalization. For convenience, this article improves the original normalization method. The signals without saturation (after uniform quantization) are still normalized with the original standard deviation, and the signals with saturation (after uniform quantization) are normalized with the standard deviation described by the red curve in Figure 2. When decoding, the unsaturated case can be decoded according to the original mode, and the saturated case can be decoded, according to the corresponding table when encoding. The improved method for the Lloyd-Max quantizer is as follows: The probability distribution of the signal after uniform quantization can be expressed as:
R −∞ δo( x ); x ≤ − M f 1 ( x ) = ( − M f 2 (µ n)dµ)· 2 1 x f2 (x) = √ exp − 2σ2 ; − M < x < M , R2πσ ∞ f 3 ( x ) = ( M f 2 (µ)dµ)·δ( x ); x ≥ M
(1)
where σ is the standard deviation of the signal after uniform quantization, M is the value at the saturation threshold, and δ( x ) is the impulse function, which represents the probability value at the “truncated” point, and is equal to the probability that the unsaturated signal goes from truncation to positive infinity. According to the definition, the distortion of the quantized signal is: D=
N Z x i +1
∑
i =1 x i
( x − yi )2 f ( x )dx,
(2)
where xi is the threshold level, yi is the quantization level, and x N +1 is defined as positive infinity. By calculating the partial derivatives of xi and yi in the Equation (2), the minimum value of the quantized signal distortion can be obtained. y i + y i −1 , i = 2, · · · , N 2
(3)
( x − yi ) f ( x )dx = 0, i = 1, · · · , N
(4)
xi = Z x i +1 xi
To further consider the impact of saturation, we need to re-solve the required xi to get the minimum quantization loss yi 0 , corresponding to xi . Equation (4) is shifted and sorted:
R x i +1 x
yi 0 = R ixi+1 xi
x f ( x )dx f ( x )dx
, i = 1, · · · , N.
(5)
According to the above recursion, we can get xi and yi 0 with the smallest quantization loss in the saturation case. Taking the 8:3 BAQ as an example, the specific solution steps for the threshold level xi and quantization level yi 0 of the improved Lloyd-Max quantizer are as follows: (1)
(2)
For the 8:3 BAQ, N equals 4 and we need to set x1 and y1 , where x1 is zero and the range of y1 is known to be between 0.1 and 0.3, based on prior knowledge. We perform iterative calculations according to Equations (3) and (4) to obtain x2 , x3 , x4 , y2 , y3 , and y4 , corresponding to different values of y1 . Calculate the corresponding y1 0 , y2 0 , y3 0 , and y4 0 , according to Formula (5), for each group x1 , x2 , x3 , and x4 .
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(2) Calculate the corresponding y1′ , y2′ , y3′ , and y4′ , according to Formula (5), for each group x1 y1′ , y2′ , y3′ , and y4′ , according to Formula (5), for each group x1 (2) Calculate the corresponding , x 2 , x3 , and x4 . Sensors 2018, and x 2 , 18, x3 ,4221 x4 . (3) ,According to Formula (2), the quantization distortion is calculated for each group x , x 5 of , 12 x, 1
2
3
(3) According to Formula (2), the quantization distortion is calculated for each group x1 , x 2 , x3 , x 4 , y1′ , y2′ , y3′ , and y4′ . Then, select the set of solutions corresponding to the smallest (3) According distortion is calculated for each group ′ ,Formula ′ quantization 2 , x3 , x4 , 1 , xsmallest y3′ , and(2), ythe the set of solutions to xthe x 4 , y1′ , yto 2 distortion: 4 . Then, quantization Namely, the select optimal threshold level andcorresponding the optimal quantization level. y1 0 , y2 0 , y3 0 , and y4 0 . Then, select the set of solutions corresponding to the smallest quantization distortion: Namely, the optimal threshold and the optimal quantization level. (4) quantization For the different input signals, repeat the above steps tolevel obtain different optimal threshold levels distortion: Namely, the optimal threshold level and the optimal quantization level. (4) For the different input signals, repeat the above steps to obtain different optimal threshold levels f xto. obtain different optimal threshold levels optimal quantization levels, under (4) and For the different input signals, repeat thedifferent above steps f x and and optimal optimal quantization quantization levels, levels, under under different different f ( x ). . The flowchart is as follows (Figure 4): The flowchart is as follows (Figure 4):
() ()
Figure 4. Flowchart for calculating the threshold and quantization level. Figure 4. 4. Flowchart Flowchart for for calculating calculating the the threshold threshold and and quantization quantization level. level. Figure
(1) (1) (1) (2) (2) (2) (3) (3) (3) (4) (4) (5) (5) (5)
The overall method of this article is as follows: The overall method of this article is as follows: The overall method of this article is as follows: Divide a pulse of the SAR raw echo into blocks. Take M sampling points of one block (M is Divide a pulse of the SAR raw echo into blocks. Take M sampling points of one block (M is Divide a pulse raw echo into blocks. Take M sampling points of one block (M is generally taken of as the 1024SAR or 512). generally taken as 1024 or 512). generally taken as 1024 or 512). The SAR raw echo is sampled and N bit uniformly quantized, where N is generally 8; The SAR SAR raw rawabsolute echo is is sampled sampled and Nthe bitIuniformly uniformly quantized, where N is generally generallyrespectively, 8; The echo and bit quantized, is 8; The average amplitude ofN and Q signals in eachwhere block N is calculated, The average absolute amplitude of the I and Q signals in each block is calculated, respectively, The average amplitude of the and Q the signals in each block is calculated, respectively, denoted as A.absolute According to the value ofIA, find corresponding standard deviation in the new denoted as A. According to the value of A, find the corresponding standard deviation in the new new denoted A. According to the value A, find the corresponding standard deviation in the standardasdeviation look-up table for of normalization; standard deviation look-up table for normalization; standard deviation look-up table for normalization; For the normalized data, non-uniform quantization coding is performed, according to the For the data, non-uniform quantization coding is performed, according to the optimal For the normalized normalized data, non-uniform coding is performed, according to the optimal threshold level corresponding toquantization each standard deviation obtained by the method in threshold level corresponding to each standard deviation obtained by the method in this article; optimal threshold level corresponding to each standard deviation obtained by the method in this article; decoding, to the standard deviation, the corresponding decoding this article; During decoding,according according to corresponding the corresponding standard deviation, the corresponding method is adopted, so as to achieve the purpose of data recovery. During decoding, according to the corresponding standard deviation, the corresponding decoding method is adopted, so as to achieve the purpose of data recovery. decoding method is adopted, so as to achieve the purpose of data recovery. The The flowchart flowchart is is as as follows follows (Figure (Figure 5): 5): The flowchart is as follows (Figure 5):
Input signal Input signal
Divide data into blocks Divide data into blocks
Output signal Output signal
3. Analysis and Results
Uniform quantization Uniform quantization
Decode with improved Lloyd-Max Decode withquantizer improved Lloyd-Max quantizer
According to the new correspondence According to the table, new normalize the signal correspondence table, normalize the signal Coding Encode with Coding improved LloydEncode with -Max quantizer improved Lloyd-Max quantizer
Read parameters Read parameters Decoding Decoding Figure 5. 5. Flowchart of of the the overall overall method. method. Figure Figure 5. Flowchart of the overall method.
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In order to prove the effectiveness of this method, this article compares the results of the proposed method and the existing methods, from the aspects of echo quantized signal-to-noise ratio, quantization power loss, and polarization scattering mechanism retention ability.
3. Analysis Analysis and and Results Results 3. In order order to to prove prove the the effectiveness effectiveness of of this this method, method, this this article article compares compares the the results results of of the the In proposed method method and and the the existing existing methods, methods, from from the the aspects aspects of of echo echo quantized quantized signal-to-noise signal-to-noise ratio, ratio, proposed quantization power loss, and polarization scattering mechanism retention ability. quantization power loss, and polarization scattering mechanism retention ability. Sensors 2018, 18, 4221
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3.1. Quantization Quantization Loss Loss and and Quantization Quantization SNR SNR 3.1. 3.1. Quantization Loss andGaussian-distributed Quantization SNR First, we we simulate simulate data at at different different input input powers powers and and then then uniformly uniformly First, Gaussian-distributed data quantize the data. Next,Gaussian-distributed we average average the the uniformly uniformly quantizedinput data powers and find find thethen look-up table First,the wedata. simulate data at quantized different and uniformly quantize Next, we data and the look-up table (described in Section 2), to get the standard deviation corresponding to the average value to quantize theindata. Next,2), weto average thestandard uniformlydeviation quantizedcorresponding data and find the table (described (described Section get the tolook-up the average value to normalize. Then, wethe encode and deviation decode the the normalized data data as described described in Section Section 2. Finally, Finally, we in Section 2), to get standard corresponding to the average value to normalize. Then, normalize. Then, we encode and decode normalized as in 2. we find and compare the SNR and quantized power loss of the processed data. Compared with the we encode and decode normalized data aspower described 2. Finally, we find and compare the find and compare the the SNR and quantized loss in ofSection the processed data. Compared with the original BAQ [7] and and several existing anti-saturation methods [13–15], the results results areand shown in SNR andBAQ quantized power loss of the processed data. Compared with the original BAQ [7] several original [7] several existing anti-saturation methods [13–15], the are shown in Figures 66anti-saturation and 7. 7. existing methods [13,14], the results are shown in Figures 6 and 7. Figures and 35 35
Original method Original method Qiu's method Qiu's method Qi's method Qi's method Our method Our method
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Power (dB) PowerLoss Loss (dB)
25 25 20 20 15 15 10 10 5 5 0 0 -5 -5-10 -10
0 0
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30 40 50 30 40 (dB) 50 Input Power Input Power (dB)
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Figure 6. Comparison of input power and quantization power loss. Figure Figure 6. Comparison Comparison of of input input power power and quantization power loss. 16 16 14 14 12 12
SNR (dB) SNR (dB)
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Original method Original Qi's method method Qi's method Qiu's method Qiu's Our method method Our method
Original method Original Qi's method method Qi's method Qiu's method Qiu's Our method method Our method
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(b) (b)
Figure 7. (a) Comparison of input power and SNR; (b) comparison of saturation and SNR. Figure 7. (a) Comparison of input power and SNR; (b) comparison of saturation and SNR.
It can thethe quantitative power loss of It can can be be seen seen from fromFigure Figure666that, that,with withthe theincrease increaseofof ofinput inputpower, power, quantitative power loss It be seen from Figure that, with the increase input power, the quantitative power loss the method in this article is always minimal, and the advantage of this method is more obvious when of the the method method in in this this article article is is always always minimal, minimal, and and the the advantage advantage of of this this method method is is more more obvious obvious of the input power is 40–60 is db.40–60 Fromdb. Figure 7a,Figure we intuitively see that, after the echo datathe saturation in when the input power From 7a, we intuitively see that, after echo data when the input power is 40–60 db. From Figure 7a, we intuitively see that, after the echo data this method, the quantized SNR is optimal, which is 3–4 dB higher than the average of the original saturation in in this this method, method, the the quantized quantized SNR SNR is is optimal, optimal, which which is is 3–4 3–4 dB dB higher higher than than the the average average of of saturation method [7]. method Compared with Qiu’s method [14],method it has an average of 2–3 dB improvement. Compared the original [7]. Compared with Qiu’s [14], it has an average of 2–3 dB improvement. the original method [7]. Compared with Qiu’s method [14], it has an average of 2–3 dB improvement. with Qi’s method, it method has an average of 1–2 dB improvement. When the SNR is greater than 12 dB, Compared with Qi’s Qi’s [15], it it has has an average average of 1–2 1–2 dB dB improvement. improvement. When the SNR SNR is greater greater Compared with method [15], an of When the is the input power range of this method is 8–41.7 dB, and 8–37.1 dB for the other methods, nearly 4 dB than 12 12 dB, dB, the the input input power power range range of of this this method method is is 8–41.7 8–41.7 dB, dB, and and 8–37.1 8–37.1 dB dB for for the the other other methods, methods, than more for this method. In order to more intuitively embody the anti-saturation function of the proposed method, the data saturation and quantization signal-to-noise ratio are statistically analyzed. As shown in Figure 7b, we can see that the SNR of the proposed method is greater than or equal to the existing anti-saturation method at different saturations. Saturation refers to the ratio of the number of data points exceeding the range of [−2 N −1 , 2 N −1 ] to the total, in the process of uniform quantization.
analyzed. As shown in Figure 7b, we can see that the SNR of the proposed method is greater than or equal to the existing anti-saturation method at different saturations. Saturation refers to the ratio of the number of data points exceeding the range of [ − 2 N − 1 , 2 N − 1 ] to the total, in the process of uniform quantization. 7 of 12 From Figure 8, we obtain the effective quantization interval, threshold, and quantization level of the four methods when the input power is 45 dB. There are only four effective quantization intervals the 8, original method and Qiu’s method, interval, six effective quantization intervals for Fromfor Figure we obtain the effective quantization threshold, and quantization levelQi’s of method, and eight effective quantization intervals forare ouronly method. the four methods when the input power is 45 dB. There four effective quantization intervals for In summary, the simulation results, this result is consistent with theand previous the original methodaccording and Qiu’s to method, six effective quantization intervals for Qi’s method, eight analysis.quantization This methodintervals has better effective foranti-saturation our method. performance.
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(a)
(b)
(c)
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Figure Figure 8.8. Effective Effective quantization quantization interval, interval, threshold, threshold, and and quantization quantization level level when when the the input input power power is is 45 45 dB: dB: (a) (a)Original Originalmethod; method;(b) (b)Qiu’s Qiu’smethod; method;(c) (c)Qi’s Qi’smethod; method;(d) (d)our ourmethod. method.
In summary, according to the simulation results, this result is consistent with the previous analysis. 3.2. Influence on Polarization Scattering Mechanism This method has better anti-saturation performance. SAR raw data compression can reduce on-board downlink data rate effectively. However, SAR rawInfluence data compression induces distortions on polarimetric information of quad-polarimetric SAR 3.2. on Polarization Scattering Mechanism data. In order to analyze the influence of different quantization compression methods on the SAR raw data compression can reduce on-board downlink data rate effectively. However, characteristics of polarimetric SAR, we selected the unsaturated polarization data of GF-3 in the San SAR raw data compression induces distortions on polarimetric information of quad-polarimetric Francisco area and added quadratic phase to simulate the echo. We controlled the saturation of the SAR data. In order to analyze the influence of different quantization compression methods on the data by controlling the input power, and then made quantization compression with the traditional characteristics of polarimetric SAR, we selected the unsaturated polarization data of GF-3 in the San BAQ method, Qi’s method, Qiu’s method, and the method in this article, and analyzed their Francisco area and added quadratic phase to simulate the echo. We controlled the saturation of the data polarization characteristics. The images after the quantization compression processing and power by controlling the input power, and then made quantization compression with the traditional BAQ loss difference are shown in Figures 9 and 10. method, Qi’s method, Qiu’s method, and the method in this article, and analyzed their polarization characteristics. The images after the quantization compression processing and power loss difference are shown in Figures 9 and 10.
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It can can be be seen seen intuitively, intuitively, in Figure 10, that the power loss of the Qi’s quantization compression It in Figure Figure 10, 10, that that the the power power loss loss of of the the Qi’s Qi’s quantization quantization compression compression It can be seen intuitively, in method is large, and the image relative brightness appears obviously reduced. By adopting Qiu’s method is is large, large, and and the the image image relative relative brightness brightness appears appears obviously obviously reduced. reduced. By By adopting adopting Qiu’s Qiu’s method quantization compression method, the power loss is reduced and the visual effect of the image is quantization compression method, the power loss is reduced and the visual effect of the image is quantization compression method, the power loss is reduced and the visual effect of the image is relatively improved. improved. With With the the quantization quantization compression compression method method in in this this article, article, the the power power loss loss is is relatively relatively improved. With the quantization compression method in this article, the power loss is minimized and the visual effect of the image is closer to the original image. It can be seen, in Figure 10, minimized and and the the visual visual effect effect of of the the image image is is closer closer to to the the original original image. image. It It can can be be seen, seen, in in Figure Figure minimized thatthat the the power gaingain of our method alsoalso has has relatively good results. 10, power of our method relatively good results. 10, that the power gain of our method also has relatively good results. This article article then then compares compares the the target target scattering scattering characteristics characteristics of of three three quantitative quantitative compression compression This This article then compares the target scattering characteristics of three quantitative compression methods, including sea, forest, and building area, as shown in Figure 9a. In the H-alpha methods, including including sea, sea, forest, forest, and and building building area, area, as as shown shown in in Figure Figure 9a. 9a. In In the the H-alpha H-alpha plane, plane, plane, alpha methods, alpha alpha represents the scattering angle, and H represents the scattering entropy. We can classify the represents the scattering angle, and H represents the scattering entropy. We can classify the target represents the scattering angle, and H represents the scattering entropy. We can classify the target target based on its position in the H-alpha plane. The H-alpha plane graph and the interval histogram based on on its its position position in in the the H-alpha H-alpha plane. plane. The The H-alpha H-alpha plane plane graph graph and and the the interval interval histogram histogram of of based of the three methods are shown in Figures 11–13. the three methods are shown in Figures 11–13. the three methods are shown in Figures 11–13.
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From From the the scattering scattering characteristics characteristics of of the the target, target, the the scattering scattering characteristics characteristics of of the the proposed proposed method method are are superior superior to to the the other other two two methods methods in in the the sea, sea, forest, forest, and and building building areas, areas, and and closer closer to to the the target target scattering scattering characteristics characteristicsof ofthe the original original image. image. In In summary, summary,this this method method is is superior superior to to the the other other two two methods, methods, in in both both visual visual effect effect and and target target scattering scattering characteristics, characteristics, for for saturated saturated data data processing. processing.
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4. Conclusions This article proposes an anti-saturation coding and decoding method for BAQ, commonly used in satellite-borne SAR. The simulation data and actual data show that the performance of this method is better than that of the traditional and existing anti-saturation methods, and this method does not need to modify the hardware system on the satellite, which can play a good role in correcting the saturation echo. It reduces the quantization power loss, improves the image SNR, and has important engineering application value. Author Contributions: Investigation, X.W. and L.H.; Methodology, X.Q. and W.J.; Formal analysis, W.J.; Writing review and editing, W.J. Funding: This work was funded by NSFC No. 61331017. Acknowledgments: We thank S.W. for helping us revise the article. Conflicts of Interest: The authors declare no conflict of interest.
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