A comparison of several algorithms for SAR raw data ...

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 33, NO. 5, SEPTEMBER 1995

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A Comparison of Several Algorithms for SAR Raw Data Compression Ursula Benz, Member, IEEE, Klaus Strodl, and Albert0 Moreira, Member, IEEE

Abstract-This paper proposes new algorithms for synthetic aperture radar (SAR) raw data compression and compares the resulting image quality with the quality achieved by commonly used methods. The compression is carried out in time and frequency domain, with statistic, crisp, and fuzzy methods. The algorithms in time domain lead to high resolution and a good signal-to-noise ratio, but they do not optimize the performance of the compression according to the frequency envelope of the signal power in both range and azimuth directions. The hardware requirements for the compression methods in the frequency domain are significant, but a higher performance is obtained. Even with a data rate of 3 bitdsample, a satisfactory phase accuracy is achieved which is an essential parameter for polarimetric and interferometric applications. Preliminary analysis concerning the suitability of the proposed algorithms for different SAR applications shows that the compression ratio should be adaptively selected according to the specific application.

I. INTRODUCTION

S

YNTHETIC aperture radar (SAR) is a very efficient instrument for obtaining a better understanding of the earth’s environment. SAR data represent an important source of information for a large variety of scientists around the world. Modem spacebome SAR systems have an on-board hardware consisting basically of a transmitting and receiving unit and analog-to-digital ( A D )conversion, followed by a realtime data downlink and/or a storage facility. One of the major constraints in the design and operation of current spacebome SAR systems is the nonavailability of a downlink with a high data rate. Usually, SAR raw data are represented in Cartesian format. The data rate of each channel is proportional to the pulse repetition frequency (PRF), the number of sampled values in each received echo, and the number of quantization bits in each sample. There are some possibilities to reduce the data rate, but these will deteriorate the system performance. For example, a reduction of PRF will increase azimuth ambiguities unless a corresponding longer azimuth antenna is used. In this case, the azimuth resolution would be degraded. Also, the system bandwidth can be decreased at the cost of a reduced range resolution. By simply reducing the number of quantization bits, the digitization noise will increase, thereby deteriorating the impulse response function (IRF), the image dynamic range, and the radiometric accuracy. Manuscript received December 1, 1994; revised May 2, 1995. The authors are with the German Aerospace Research Establishment (DLR), Institute for Radio Frequency Technology, D-82230 Oberpfaffenhofen, Germany. IEEE Log Number 9413907.

Thus, efficient algorithms for SAR raw data compression become an important tool in fulfilling the requirements of advanced SAR systems. Until now, the block adaptive quantizer (BAQ) has been selected for on-board data compression due to its simplicity for coding and decoding (e.g., SIR-C [7] and Magellan [ 141). Signal-to-distortion noise ratios (SDNR) of 14.8 dB, 8.7 dB, and 2.4 dB are achieved for data compressions of 3 bits/sample, 2 bits/sample, and 1 bidsample, respectively. The real-time implementation of an on-board encoding algorithm provides several advantages: Reduced data rate for downlink. In this case, less power is required for transmission to the ground station, andor more information channels (e.g., polarimetric and multifrequency applications) can be incorporated in the downlink. More raw data storage on-board before transmission to ground stations. This allows SAR imaging during longer orbit segments, where no downlink is available. Reduced amount of stored data (on-board and/or onground). Due to the high entropy of SAR raw data, data compression always causes a loss of information, i.e., compression is associated with image quality degradation. Depending on the user’s requirements for a given application, a tolerable degree of image deterioration should be accepted. In some cases, as for interferometric applications, a smaller reduction factor for the data compression is allowed in order to maintain the phase accuracy of the complex image data. On the other hand, if a global monitoring (e.g., use of the wide swath mode of the ENVISAT platform’s ASAR instrument 121) or detection of man-made target is to be performed, then a much higher degree of data reduction is possible. The trade-off between the image quality requirements for each application and the complexity of the data compression algorithm is an important point in system design. The optimal control system must be designed to optimize the compression ratio and to choose a suitable compression algorithm. The aim of this paper is twofold. First, current data compression algorithms are described and compared with newly proposed approaches. Second, performance of the algorithms is outlined and it is shown that the data rate (i.e., compression ratio) should be an adaptive parameter in a SAR system. Section I1 reviews digitization errors and their effects on SAR image quality. The model used is based on system and communication theory. It is shown that the quantization and digitization errors have basically white-noise characteristics and are decorrelated with the signal.

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complex raw data

An important topic in raw data compression is the estimation of an achievable reduction ratio leading to an acceptable degradation in reconstruction of the ground reflectivities. In general, degradation caused by the encoding and decoding process can be expressed in the same way as the errors due to the usual digitization process. In the following text, this assumption will be used for the error analysis. Fig. 1 shows the basic data flow in SAR systems with data compression and the used notation in this paper. B. Theoretical Analysis of Digitization Errors

Fig. I .

Overview of the data flow and the used notation.

Section I11 briefly describes the BAQ algorithm and then presents two new algorithms: the block adaptive vector quantizer (BAVQ) and the fuzzy block adaptive quantizer (FBAQ). The BAVQ achieves improved performance due to the use of vector quantization. It also requires a much simpler hardware than the standard vector quantizer (VQ). The FBAQ allows automatic selection of the number of bits, depending on the area imaged. Additionally, FBAQ permits on-line recognition of system errors and malfunctioning. Section IV presents an algorithm based on data reduction in the transform domain. The fast Fourier transform (FFT) in connection with the block adaptive quantizer (FFT-BAQ) allows for coding to be adapted to the signal-to-noise ratio (SNR) variation in the transform domain. This approach leads to the best performance for a given data rate. Section V presents the results of image processing and compares the image qualities of the different algorithms. For simplicity, a constant data rate of 2 bitslsample is initially chosen for image comparison, and then the results are extended for other data rates. Section VI concludes by showing the suitability of each algorithm for the various applications. 11. QUANTIZATION ERRORSAND THE EFFECTON IMAGE QUALITY A. Basic Model for Datu Compression The inclusion of a model based on communication theory is convenient since data compression in this field has been widely used for many years. The illumination can be considered as a convolution of the complex ground reflectivities with the transmitted pulse. Each echo of the illuminated terrain is received with a delay given by the range between the scatterer and the antenna, and summed at the receiver. Thus, according to the central limit theorem, the output of the receiver is a continuous random signal with Gaussian distribution [ 2 11. This summation can be considered as a convolutional encoding of the data sequence. The convolutional encoding represents the first part of the source encoding. It is followed by analog-to-digital (A/D) conversion, which forms the second part. The last step in source encoding is the raw data compression. Here, the aim is to reduce the redundancy of the data and to remove insignificant information. Finally, different processing algorithms decode the data sequence in order to reconstruct the complex ground reflectivities.

Digitization errors n D consist of two parts: quantization nQ and saturation (clipping) noise nc. The error nQ caused by the quantization step is uncorrelated with the signal s, if the quantization step is small with respect to the clipping level. Each quantizer has a specific range of values, which is usually smaller than the range of input values. Input values above the saturation level are clipped. The output signal S of the quantizer consists of the input signal s. the quantization nQ. and the saturation noise nc, as follows: s" = s n Q nc. (1)

+

+

One way to measure the performance of a quantizer is the mean square error (MSE). The MSE is defined as the expected value E of the squared difference between the input signal s and the mapped output .S: ,I1

X(s M 1

E ( s - s")2 =

-

-

2 )2

~

where M is the number of input samples. The MSE is usually normalized by the input signal power of. Thus, the normalized MSE (NMSE) is the quotient of MSE and of.The power 0:. is the sum of the squared input signals s, so that the NMSE is given by

%I

-E(. 111 1

-

NMSE =

5)2

(3)

The SNR is indirectly proportional to the NMSE and is a common parameter for the image quality analysis:

SNR=

1 ~

NMSE .

(4)

Another important quality measure is given by the comparison of quantizer input and output power. For a zero mean, Gaussian-distributed, stationary and ergodic signal, the power which is given by its variance (squared standard deviation 02), can be also calculated by the autocorrelation function of the signal. If all three components of 5 in ( I ) are independent, the output power is the sum of the input power, the quantization and the saturation noise power [18]:

where og and CT,~are the standard deviations of the input and output signal, respectively. As mentioned above, 71c is correlated with the signal and, for few quantization steps, even n~ is correlated. This means that signal power is transferred

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into noise components. This effect, for both correlated and uncorrelated noise components, can be taken into consideration with a constant b:

The input power a: is decreased by (1 - b)’. This loss of the quantizer is represented by a = (1- b ) . Thus, the output power consists of the input power multiplied by the squared loss a’ added to the correlated noise components. The correction factor k of the quantizer can be defined as k = 1/a and must be evaluated and used for the amplitude compensation of the output signal in order to reduce the loss. The degree of correlation between the output and the input signals is calculated using their cross correlation: Af nr 1 1 s . .s* = (I. . s ’ s* R,,,,,(O) = M M M +1 C(nq + IbC) . s * . 1

M

The processing of raw data consists basically of twodimensional matched filtering with a limited bandwidth B. Considering the SAR processor as a linear filter, the SNR for image data can be defined by the ratio of the mean signal power at the output Po to the noise power N o . No consists of two parts, the system noise power N s and the digitization noise power N D ; which are assumed to be constant.

SNR =

P O

( N sf ~ V D )

(9)

’

To measure the quality of different compression algorithms, the signal-to-digitization noise ratio (SDNR) in the image is used. Hence, the system noise N s in (9) is removed. Using the matched filter transfer function in the frequency domain ( H (f ) = S*( f ) ) . we obtain the following description for the signal to digitization noise ratio [5]:

SDNR[dB] = 10 . log

(7)

The results of simulations of a 1-bit, 2-bit, and 3-bit quantizer lead to maximum values for the second term of (7) (normalized by the input signal power) of about 0.023, 0.013, and 0.008, respectively. Hence, with a good approximation, the last term of (7) can be neglected so that the loss a can be calculated by

The loss a equals 0.63 for 1 bivsample, 0.89 for 2 bitskample, 0.96 for 3 bitskample, and 1 for 5 bitskample.

\ n


SNR. For pratical SAR systems, real multiplications. In the following text, the trade-off between hardware coma SDNR equal to 25 dB fulfills this condition. This means that at least 4 bits are necessary. In this case, the standard BAQ plexity and the algorithm’s performance is analysed. As far as the BAVQ is concerned, it can be seen that the encoding leads to a SDNR of approximately 20 dB. However, the approach described in Section I1 for amplitude hardware of the BAVQ algorithm can be implemented with calibration of the image data can be used so that a smaller reduced complexity due to the simplified vector quantization number of bits is satisfactory for many applications. Addi- (only an additional ROM, a latch unit, and control circuits tionally, an offset level corresponding to the digitization noise are required). Considering that the performance of the promust be subtracted from the intensity image for improving the posed BAVQ algorithm can even be improved if more scalar image calibration. This procedure is the same as in case of the values (e.g., 6) are used for generation of the codebooks, system noise. With this procedure, the measured radiometric the compression using the BAVQ leads to a better trade-off resolution of the processed images with the FFT-BAQ is between hardware complexity and performance than the BAQ changed by less than 0.1 dB. The calibration accuracy is better algorithm. than 0.2 dB. These results are much better when compared The real-time implementation of the FBAQ requires only with the standard BAQ algorithm, which has a calibration one additional ASIC (e.g., a special fuzzy coprocessor [SI). accuracy of ca. 0.7 dB. Although the performance of the FBAQ is similar to that of For applications in which complex image data are needed, the BAQ, the similar hardware realization with an additional a higher SDNR value is necessary due to the required phase software implementation can be used as a control system to accuracy. The procedure for amplitude calibration has no adapt the data rate to the imaged terrain characteristics [4]. effects on the phase accuracy. In the analysis carried out in [ 2 ] , The computational requirement for the FFT-BAQ is very a standard deviation of the phase error of f12.8” and k4.02” high. The number of integrated circuits (ASIC’s and/or DSP’s)

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in Table I11 for the FFT-BAQ is given for a real-time implementation of a data compression system with an input data rate of 100 Mbits/s. In a first trade-off analysis, the improved performance of the FFT-BAQ in comparison to the BAQ would not justify the additional hardware requirement. However, the FFT-BAQ can be slightly modified in order to form the first part of a two-dimensional SAR processing. Thus, on-board data compression can be carried out with the best performance for a given data rate and the requirements for on-ground SAR processing are reduced. In this case, the additional on-board hardware for the FFT-BAQ is justified. The results of this paper form the basis for the development of a (fuzzy) control system, which is able to choose an adequate compression ratio according to the user’s requirement, sensor operation mode, and raw data characteristic. The development of this control system is an important point for future research.

REFERENCES N. Ahmed and K. R. Rao, Orthogonal Transforms for Digital Signal Processing. New York: Springer-Verlag, 1975. S. Buckreuss, J. Moreira, H. Rinkel, and G. Waller, “Advanced SAR interferometry study,” DLR Mitteilung 94-10, Inst. Radio Freq. Technol., DLR, Wessling, Germany, 1994. U. Benz, A. Moreira, K. Strodl, and F. Blaeser, “A block adaptive vector quantization for optimized SAR raw data reduction,” in Proc. ERIM, Strassbourg, Sept. 1994, vol. 2, pp. 379-390. U. Benz, “A fuzzy block adaptive quantizer (FBAQ) for synthetic aperture radar,” in Proc. Fuu-IEEE, Orlando, FL, June 1994, pp. 1583-1 585. U. Benz, A. Moreira, and K. Strodl, “A comparison of several algorithms for on-board SAR raw data compression,” DLR Internal Rep., July 1994. C. Y. Chang, J. G. Bowers, W. C. Fang, and J. C. Curlander, “Functional design of data compression algorithms,” Jet Propulsion Lab., California Inst. of Technol, Pasadena, Internal Rep., July 1989. J. C. Curlander and R. McDonough, “Synthetic aperture radar, systems and signal processing,” in Wiley Series in Remote Sensing. New York: Wiley, 1991. S. Dieterle, “Optimization of a fuzzy block adaptive quantizer (FBAQ) for real-time SAR raw data reduction,” Diplomarbeit, DLR/LNSA, Inst. Radio Freq. Technol., DLR, Wessling, Germany, 1994. F. E. Douglas and K. R. Rao, Fast Transforms: Algorithms, Analyses, Applications. London: Academic, 1982. Th. Eiting, “Anwendung von Sequenztransformationen auf SAR-Daten zur Datenreduktion,” Diplomarbeit, DLR/FH-Munich, Inst. Radio Freq. Technol., DLR, Wessling, Germany, 1994. R. M. Gray, “Vector quantization,” IEEE ASSP Mag., pp. 4-29, Apr. 1984. R. Horn, “E-SAR-The experimental airborne L/C-band SAR system of DFVLR,” in Proc. IGARSS, Sept. 1988, pp. 1025-1026. B. Kosko, Neural Networks and Fuzzy Systems, A Dynamical Systems Approach To Machine Intelligence. Englewood Cliffs, NJ: PrenticeHall, 1992. R. Kwok, “Block adaptive quantization of Magellan SAR data,” IEEE Trans. Geosci. Remote Sensing, vol. 27., no. 4, pp. 375-383, July 1989. G. Kuduvalli, M. Dutkiewicz, and I. Cumming, “Synthetic aperture radar signal data compression using block adaptive quantization,” in 1994 Science Information Management and Data Compression Workshop, Greenbelt, MD, Sept. 19941 pp. 43-55.

[16] Y. Linde, A. Buzo, and R. Gray, “An algorithm for vector quantizer design,” IEEE Trans. Commun., vol. COM-28, no. 1, pp. 84-95, Jan. 1980. [I71 J. Max, “Quantizing for minimum distortion,” IEEE Trans. IRE, vol. 6, pp. 7-12, Mar. 1960. [ 181 T. Misra and A. Moreira, “Simulation and performance evaluation of the real-time subaperture RTS processor for the E-SAR system of DLR,” Inst. Radio Freq. Technol., DLR, Wessling, Germany, DLR Internal Rep. IB 551-2/91, Feb. 1991. [I91 A. Moreira and F. Blaeser, “Fusion of block adaptive and vector quantizer for efficient SAR data compression,” in Proc. IGARSS ’93, Tokyo, pp. 1583-1585. [20] A. Moreira, D. Hounam, and K. Strodl, “ASAR ambiguity study,” Final DLR Rep., ESAESTEC, Dec. 1994. [21] G. W. Zeoli, “A lower bound on the data rate for synthetic aperture radar,” IEEE Trans. Inform. Theory, vol. IT-22, no. 6, pp. 708-715, 1976.

Ursula Benz (M’94-A’95) was born in Passau, Germany, in 1963. She received the Diploma degree in electrical engineering in 1991 from the Fern Universitaet Hagen, Germany. Since 1991, she has been with the German Aerospace Research Establishment (DLR) in Oberpfaffenhofen, Germany. She is involved in the design and development of signal processing algorithms and hardware for the DLR airborne SAR. Her current research interest is in the field of SAR data compression and analysis using statistics and fuzzy logic.

Klaus Strodl was born in Munich, Germany, in 1965. He received the Diploma degree in electrical engineering in 1991 from the Technical University of Munich, Germany. From 1992 to 1993 he was with the SAR and image processing department of Daimler Benz Aerospace, Dornier in Immenstaad, Germany. At the end of 1993 he joined the Signal Processing Group of the Institute of Radio Frequency Technology at the German Aerospace Research Establishment (DLR), Oberpfaffenhofen, Germany. His current activities are digital signal processing and data encoding techniques for SAR s) (stems.

Alberto Moreira (M’92) was born in Sao Jose Campos, Brazil, in 1962. He received the B.S.E.E. and the M.S.E.E. degrees, in 1984 and 1986, respectively, from the Aeronautical Technological Instititute (ITA), Brazil, and the Eng. Dr. degree from the Technical University of Munich, Germany, in 1993. From 1985 to 1986, he worked at ITA as a Research Assistant and Consultant. In 1986 he ioined the German Aerospace Research Estaglishment (DLR), Oberpfaffenhofen, Germany, where he is currently Head of the Signal Processing Group He is presently responsible for the concept and development of an arborne, high-precision, real-time SAR processor. His areas of interest include digital signal processing algorithms, data compression, interferometry, and advanced SAR concepts.