Satellite Image Restoration Using RLS Adaptive Filter and Enhancement by Image Processing Techniques Muhammad Sajid
Dr. Khurram Khurshid
Department of Electrical Engineering Institute of Space Technology Islamabad, Pakistan
[email protected]
Department of Electrical Engineering Institute of Space Technology Islamabad, Pakistan
[email protected]
Abstract— Satellite images in course of capturing and transmitting are frequently degraded due to channel effects or uncertain conditions. These effects introduce different noise patterns such as, Additive White Gaussian Noise, Salt & Pepper Noise and Mixed Noise. Therefore, retrieved images are highly noise corrupted because the image contents are more attenuated or amplified. The selection of optimum image restoration and filtering technique depends to have knowledge about the characteristics of degrading system and noise pattern in an image. In this paper, Recursive Least Square (RLS) adaptive algorithm is used for image restoration from highly noise corrupted images. The implementation of proposed methodology is being carried out by estimating the noise patterns of wireless channel through configuring System Identification with RLS adaptive algorithm. Then, these estimated noise patterns are eliminated by configuring Signal Enhancement with RLS algorithm. The restored images are functioned for further denoising and enhancement techniques. The image restoration and further processing algorithms are simulated in MATLAB environment. The performance is evaluated by means of Human Visual System, quantitative measures in terms of MSE, RMSE, SNR & PSNR and by graphical measures. The experimental results demonstrate that RLS adaptive algorithm efficiently eliminated noise from distorted images and delivered a virtuous evaluation without abundant degradation in performance. Keywords—Additive White Gaussian Noise (AWGN); Salt & Pepper Noise (SPN); Recursive Least Square (RLS); Human Visual System (HVS)
I. INTRODUCTION Image restoration and filtering is the significant field of digital image processing, which is used to restore the degraded or distorted image contents [1, 2]. The goal of de-noising is to remove noise by preserving important image details and to acquire good quality image [3]. The optimal choice of restoration filter is important and shows a vital role for images de-noising. Satellite images when captured and transmitted in wireless channel usually degraded due to noisy channel effects [4]. The image degradation is caused by channel noise and random atmospheric turbulence [5, 6]. As a result, the channel contents are either attenuated or amplified during transmission. In wireless channel, different noise patterns, i.e. Additive White Gaussian Noise, Impulse Noise and Mixed Noise should exist and distorted the satellite images [1, 7].
Therefore, the retrieved images are highly noisy because the contents of output image are either more attenuated or amplified. The retrieved images require de-noising before using in different applications. During image restoration there is always a compromise among noise elimination and maintaining true image contents [2]. If both images and noise contents are accessible, it becomes easy to design a filter in order to improve SNR. When the contents are not entirely recovered, and then required suitable models for estimating the real information. Generally, the models are inaccurate or time fluctuating [6]. Therefore, use of adaptive filters must fulfill the particular requirements. During few decades of progression, the researchers have developed and implemented different well-organized techniques for image restoration and de-noising. The adaptive filtering is one of most suitable technique especially for noise cancellation in signal and image processing applications [8]. The performance of adaptive filter is shown to be selfadjusted, thus extensively used. The ultimate goal is to regulate the adaptive filter parameters for achieving minimum mean square error between the filter output and desired signal [9, 10]. In this paper, we have presented RLS adaptive algorithm for optimum restoration of satellite images. The RLS algorithm iteratively executes an exact minimization of the gradient square of desired estimated error signal. Our proposed methodology is implemented by configuring the RLS algorithm with System Identification approach for noise estimation and then Signal Enhancement for noise removal. The algorithms for image restoration, further de-noising and enhancement are simulated in the MATLAB platform. Finally, the performance is examined by means of fidelity criterion, i.e. Human Visual System (HVS), quantitative and graphical measures. Our goal is to achieve improved value of Signal to Noise Ratio (SNR) & Peak Signal to Noise Ratio (PSNR). II.
PROPOSED METHODOLOGY FOR IMAGE RESTORATION
The channel noise is more intensive type of noise among the all. Any deficiency in AWGN channel, results the direct addition of white noise with constant spectral density and Gaussian distribution [1]. The practical noise level classification in communication channel demonstrates that SNR is said to be better at ≥ 20dB, so the noise level is low.
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The SNR becomes worse when valued at ≥ 10dB, which is high noise condition [1]. In this paper, only AWGN channel effects are being considered when image is transmitted in wireless channel. Furthermore, image signal gets corrupted with impulse noise and mixed noise after threshold at the receiver. The mixed noise is combination of AWGN and SPN [1]. The model for proposed scheme is shown in Fig. 1, which effectively describes the image restoration, its de-noising and enhancement scheme.
B. Recursive Least Square (RLS) Adaptive FIR Filter The RLS algorithm is recognized as to follow fast convergence rate, when the range of Eigen value is large for the correlation matrix of input signal. This algorithm gives outstanding performance when operational in time variable conditions [10, 12]. The objective of this algorithm is to select the filter coefficients in such a way that the output signal y(k) will match accurately with desired signal in least square estimate [13]. These advantages are achieved at the cost of increased computational limitations and other instability factors [8, 10]. The RLS algorithm is implemented by computing known initial conditions and then updating the previous estimate based on information kept in the recent data samples [10]. Which is done by estimating the least square of filter coefficients w(n-1) at iteration n-1, by calculating the estimate of coefficients at iteration n by means of recently available information [8]. The Eq.1 describes the input vector x(k) with N filter order. 1 …
(1)
The objective function for LS algorithms is specified by ∑
(2)
∑
(3)
… is the filter Where coefficients, ε(i) = a-posteriori output error and λ= forgetting factor, ranges from 0 λ ≤ 1. The expression for filter coefficients w(k) is given in Eq.4. (4)
Fig. 1. Model for Proposed Scheme.
A. Introduction to Adaptive Filter The adaptive filter is held as a computational device and operated when the fixed specifications are not recognized or not fulfilled by the discrete time filters [10]. The adaptive filters have ability to track variations in the signal or parameters of time-varying system to meet the performance factors. The adaptive filter efforts to model output signal for correlation with its input signal iteratively in real time [9, 10]. The performance is upgraded automatically by adjusting the filter coefficients and impulse response of respective input through algorithm [10, 11]. The efficiency of adaptive filter mainly depends on design techniques and adaptation algorithm [9, 12]. The general configuration of an adaptive FIR filter is shown in Fig. 2. Desired Signal Input x(k)
+ Adaptive Filter
-
∑
d(k) Output
y(k) e(k) Adaptive Algorithm
Fig. 2. General Configuration of an Adaptive Filter.
Where, represents the inverse correlation matrix of defines the deterministic cross input signal and correlation matrix among the input and desired signal. Computational Initialization of RLS Algorithm 1 Where, δ should be the inverse estimate of input signal. 1
1
0
0
…0
≥ 0 1 PD k
λPD k
1
d k x k
If required then evaluate y k
wT k x k
ε k
d k
y k
C. Channel Estimation & Image De-noising Channel estimation is a technique to describe the effects of physical channel on the input system. When channel is supposed to be linear, the channel estimate or approximates the impulse response of the system. An efficient channel estimator is one that satisfies the conditions for error minimization [14]. In this paper, our ultimate goal is to
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achieve minimum mean square error (MMSE) by eliminating noise effects using RLS adaptive algorithm. The proposed methodology for image restoration is categorized in two steps shown in Fig. 3.
The expression for minimum MSE is stated in Eq.8 (8) The main function of this configuration is to provide a system output feedback to the adaptive filter and then modifying the filter by using RLS adaptive algorithm in order to achieve the least square estimate [10, 15]. III. EXPERIMENTAL RESULTS In this paper, the proposed methodology for image restoration, its de-noising and enhancement is tested and implemented in MATLAB R2012b (8.0) software by acquiring the original gray scale data- based satellite images.
Fig. 3. Proposed Methodology for Image Restoration.
1.
Channel Estimation by System Identification The wireless channel conditions changes rapidly with the passage of time. We need to estimate the channel patterns which resembles somehow with the patterns, which were embedded as channel noise in the desired image signal d(k). The estimation of these patterns is achieved by configuring System Identification with RLS algorithm iteratively as shown in Fig. 3(A). This technique is used for modeling of an unknown system. The same input image x(k) is excited from both unknown system and adaptive algorithm. d(k) shows the desired image of represents the unknown system shown by Eq. 5, observed channel noise, it degrades desired signal at the output of unknown system. (5) (6) Where, y(k) is the adaptive filter output and difference between d(k) and y(k) gives error signal written in Eq.6. The filter coefficients are represented by w(k). These coefficients are being regulated in order to reduce the error iteratively. When objective function is minimized, then the coefficients of adaptive filter are matched with that of unknown noise patterns [15].
Satellite Image –1: Laguna Del Maule, a volcanic field shown in Fig. 4A [16]. On April 9, 2003, this image was acquired from Advanced Space-borne Thermal Emission & Reflection Radiometer (ASTER) on NASA’s Terra Satellite using infrared, red, & green wavelength of light. This image is in JPEG format with dimensions of 720 x 480 pixels. Satellite Image–2: Houston Texas USA is shown in Fig. 5A [17]. On October 5, 2007, this image was acquired from Worldview-1 Satellite having 0.4 meter resolution and dimensions of 1800 x 1800 pixels. The experimental results are based on fidelity criterion of the proposed methodology. This benchmark consists of subjective, objective and graphical measures for the evaluation of image quality. The subjective criterion is done by means of Human Visual System (HVS) and provides less precision [2]. A. Image Restoration from 50 time AWGN. Fig. 4(A) & 5(A) represents the data-based satellite images as an input. These images are corrupted by adding AWGN with 50 times more noise power as shown in Fig. 4(B) & 5(B). The important parameters of RLS adaptive algorithm are required to select through consecutive testing, i.e. forgetting factor, λ = 0.98; filter coefficients = 2; regularization factor, δ = 0.001 and No. of iterations = 10. The satellite images restoration is achieved from RLS adaptive algorithm shown in Fig. 4(C) & 5(C).
2.
Image De-noising: by Signal Enhancement After achieving the estimated noise patterns, image de-noising is done by means of Signal Enhancement configured with RLS algorithm shown in Fig. 3(B). The are efficiently removed embedded noise patterns from desired image signal x(k) by correlating with estimated noise pattern or e(k). The signal enhancement scheme has two input signals [13]. The desired image signal is contaminated with Gaussian noise represented by, . The estimated noise or e(k) is treated as the input of RLS adaptive algorithm, . which is uncorrelated with x(k) but correlated with The error signal is written in Eq. 7. (7)
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B. Image De-Noising And Enhancement After achieving fine restoration results, these satellite images are used for further processing, i.e. de-noising and enhancement by means of image processing (IP) techniques successively. In image de-noising process, impulse noise and mixed noise is eliminated by using spatial filtering algorithms.
Fig. 4. Satellite Image –1 Restoration using RLS Algorithm, its De-noising and Enhancement.
• Median filter is the robust nonlinear filter, in which output pixel is calculated by median value of neighbor pixels. The restored images are now fed to median filter, which effectively removes salt and pepper noise while preserving sharp edges of image, [6] as shown in Fig. 4(D) & 5(D). • Averaging filter is used for noise reduction and smoothing of sharp edges. It is signified as a low pass filter, by changing every pixel to mean value, weighted average or the intensity of nearest neighbor, as a result noise density is minimized [6]. The average filtered images are exposed in Fig. 4(E) & 5(E). It produces blurring effect in an image. The resultant satellite images after de-noising process are shown appropriate visual quality. Ultimately, the de-noised images are employed for enhancement, i.e. sharpness and contrast improvement. • Laplacian filter highlights the edges and other cutoffs. The images retrieved from laplacian filter are enhanced by giving fine details and sharpness as shown in Fig. 4(F) & 5(F). • Histogram Equalization is used to improve poor intensity distributions. This method is applied for sharpening in order to achieve the uniform distribution of intensity shown in Fig. 4(G). C. Performance Evaluation The objective criterion is computed quantitatively by means of MSE, RMSE, SNR and PSNR parameters. • Mean Square Error (MSE) is the squared error loss. ∑
∑
,
,y
(9)
Where, f (x, y) is an original image, , be the restored image, x and y describes the discrete coordinates of image and M×N represents image size. • Root Mean Square Error (RMSE) is defined as. ∑
∑
,
,
(10)
• Signal to Noise Ratio (SNR) is stated as. ∑ ∑
∑ ∑
, ,
,
(11)
• Peak Signal to Noise Ratio (PSNR) is expressed in logarithmic decibel scale. 10 log
Fig. 5. Satellite Image –2 Restoration using RLS Algorithm, its De-noising and Enhancement.
(12)
The graphical criterion computes the statistical summary in order to achieve most significant features of resultant images. It provides further dimensions to mimic the HVS for image
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quality assessment. Fig. 6 & 7 demonstrates the graphical analysis in term of MSE. It gives the difference between original and resultant images for each stage of proposed scheme. MSE also describes the error magnitude against each image pixel, which is minimized efficiently during restoration and de-noising process to some extent. Hence, it is obvious from graphical criterion that the ultimate goal is achieved by successive reduction in MSE or squared error loss.
Fig. 6. Graphical Analysis of SatelliteImage–1Restoration, De-noisingand Enhancement.
Fig. 7. Graphical Analysis of Satellite Image–2 Restoration, De-noising and Enhancement.
Table 1 & 2 shows the quantitative parameters, i.e. MSE, RMSE, SNR & PSNR are computed for the performance evaluation of RLS adaptive restoration, de-noising and enhancement methods. The noise level for each stage is calculated by means of MSE & RMSE and the retrieved image quality is examined by SNR & PSNR. It is already mentioned in section II that the noise level is held to be lower, when SNR is valued at • 20dB. Consequently, we have achieved the SNR values for RLS restored images shown in Fig. 4(C) and 5(C) is 83dB and 125dB respectively. In this paper, the overall behavior of our methodology validates that the noise level is successively diminished by improving the values of SNR &
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PSNR and the values for MSE & RMSE are minimized effectively during the whole process. TABLE I. Images
Satellite Image 1
TABLE II. Images
Satellite Image - 2
QUANTITATIVE ANALYSIS FOR SATELLITE IMAGE – 1 Restoration & Enhancement Techniques RLS Restored image Median filtered image Avg. filtered image Laplacian filtered image Histogram Equalized image
Quantitative Parameters MSE
RMSE
SNR
PSNR
217.04
0.025
82.84
57.02
297.69
0.029
58.86
53.86
407.18
0.034
42.42
50.73
545.82
0.04
33.59
47.80
626.17
0.043
34.89
46.43
RLS Restored image Median filtered image Avg. filtered image Laplacian filtered image
References [1]
[2]
[3]
QUANTITATIVE ANALYSIS FOR SATELLITE IMAGE – 2 Restoration & Enhancement Techniques
and performed better than using conventional filters for the elimination of AWGN. Thus, the resultant images after denoising have shown better visual effects and preserve the sharp edges. The RLS adaptive algorithm have shown to achieve the improved value of Signal to Noise Ratio (SNR) and reduced value of Mean Square Error (MSE) at higher rate of convergence but at the compromise of large computational complexity and memory requirement.
Quantitative Parameters
[4]
MSE
RMSE
SNR
PSNR
119.24
0.006
125.0
63.01
132.99
0.006
110.18
61.92
232.62
0.008
62.20
56.33
374.74
0.011
41.13
51.56
D. Performance Comparison with Other Filtering Techniques The performance evaluation of Arithmetic Mean Filter (AMF), Geometric Mean filter (GMF) and Median filter for de-noising of satellite images is presented [18]. The data based satellite images are used for implementation and simulations. These images are degraded with various types of noises such as Gaussian, Salt & Pepper and Speckle noise and achieving filtration results. Here, PSNR is the only criteria or benchmark designated for performance evaluation of above de-noising filters. Finally, the experimental results and performance comparison shows that RLS adaptive algorithm approach gives better image filtration results and higher values of PSNR. IV. CONCLUSION
[5] [6]
[7]
[8]
[9]
[10] [11]
[12]
In this paper, RLS adaptive algorithm is implemented for the removal of Gaussian noise from satellite images. The adaptive process detects abnormalities in the wireless channel and then eliminates these deformities effectively. The data-based satellite images are used for simulation and then computing MSE, RMSE, SNR and PSNR for the RLS adaptive restoration and also for further image processing methods. The MATLAB simulation results validate that the proposed approach efficiently eliminated noise from corrupted satellite images and delivered the fine evaluation without generous reduction in performance measures. Hence, it is concluded that the RLS adaptation for image restoration is more efficient
[13] [14]
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