Improved Kuan Filter and Wavelet Based SAR Image Despeck ... image. The despeckled image is then...

Improved Kuan Filter and Wavelet Based SAR Image Despeck-

ling and Compression

Sikiru Yommy Aiyeola1, Rahmon Ariyo Badru2, Olufunke Janet Alao3, Tofade Christopher Temidayo4, Wasiu

Akande Ahmed5, Alapa Frederick6 1,2,3,4,6National Space Research and Development Agency (NASRDA), Abuja, Nigeria; 5School of Instrumentation Science and Opto-Electronics

Engineering, Beihang University, Beijing, China

Email: [email protected]

ABSTRACT

Synthetic aperture radar (SAR) image compression is very essential in minimizing storage and transmission costs in bandwidth-limited channels. In this paper, we present a SAR image compression approach in which speckle noise removal precedes com-pression. The image compression is improved by first eliminating speckle noise from the image. We start by using the k-nearest neighbour (K-NN) algorithm to improve the Kuan filter. The improved Kuan filter is then used to remove speckle noise from the SAR image. The despeckled image is then compressed with the discrete wavelet transform, followed by further encoding of the wavelet coefficients using the set partitioning in hierarchical trees (SPIHT) scheme with the removal of the slightly complex arith-metic coding scheme to reduce computational time. The objectives of the present research include; removal of speckle noise from SAR image, accomplishing efficient SAR image encoding, and exploring enormous advantages of wavelet transform. From the results obtained the proposed approach favorably compared with the conventional wavelet-SPIHT approach, judging by the val-ues of the performance evaluation metrics obtained. Keywords : Synthetic Aperture Radar (SAR), SAR image compression, speckle noise, k-nearest neighbour (KNN) algorithm, Kuan filter, set partitioning in hierarchical Trees (SPIHT), wavelet transform.

1 INTRODUCTION

Synthetic Aperture Radar (SAR) images are an important

means of gathering information about the earth surface by sci-

entists. However, while the amount of data obtained is increas-

ing speedily, the speed of transmission to the ground receiving

station, and storage capacity, are not increasing rapidly. Hence,

algorithms for encoding and decoding image data that will en-

sure excellent compression while at the same time give good

quality reconstructed image need to be developed [1]. But in

SAR images, the quality of the reconstructed image is always

degraded due to the presence of speckle noise. The speckle phe-

nomenon, is caused by coherent radiation during SAR image

processing, and in order to get high quality reconstructed SAR

image, the image must be despeckled prior to further pro-

cessing. Researchers in the image processing community have

embraced the use of wavelet transforms due to their high en-

ergy compaction capability and multiresolution analysis for ef-

fectively analysing images [2], [3]. Wavelets are a mathematical

tool suitable for image compression [4]. Wavelet transform al-

gorithm creates a pyramid containing the low resolution ap-

proximation and the details of the original image at different

scales [5]. It decorrelates an image both in space and frequency,

and has the capability to concentrate the image energy into a

few low and high frequency coefficients [6]. Among the well-

known SAR image despeckling filters are Lee, Kuan, and Frost,

but with these filters however, difficulties arise when denoising

and edge preservation are simultaneously required [7]. Lee,

Kuan, Frost, and others are spatial domain filters [8], [9], [10],

[11]. In this paper, we propose a SAR image compression ap-

proach in which the despeckling precedes compression. We use

the k-nearest neighbour algorithm to significantly improve the

performance of Kuan filter. The use of SPIHT without the arith-

metic coding also reduces the computational time of the ap-

proach. This paper is organized as follows: Section 2 discusses

the objectives of the present research, Section 3 discusses

speckle noise in SAR images, and Section 4 discusses Kuan fil-

ter, In Section 5 the K-Nearest Neighbour Algorithm is dis-

cussed, while Section 6 discusses Wavelet Transform, SPIHT

Algorithm is discussed in Section 7, Section 8 presents the per-

formance Evaluation Metrics, while Sections 9, 10, and 11 re-

spectively present the Proposed Approach, Experimental Re-

sults and Conclusion.

2 OBJECTIVES OF THE PRESENT RESEARCH

(a) Since speckle noise affects the result of any SAR image en-coding method, it is therefore essential to first deal with this phenomenon before the image is encoded. (b) To accomplish the goal of perfectly encoding SAR images using two dimensional discrete wavelet transform. (c) The aim is to explore the enormous advantages of wavelet transform for image encoding. Wavelet-based image compres-

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International Journal of Advancements in Research & Technology, Volume 7, Issue 9, September-2018 ISSN 2278-7763 44

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sion schemes have gained popularity due to their ability to re-duce the blocking artifacts that are commonly experienced in JPEG-based image compression. Wavelet transform also has the ability to achieve multiresolution analysis, which leads to better energy compaction with good quality reconstructed images.

3 SPECKLE NOISE IN SAR IMAGES

When a surface is illuminated by a radar and such surface is rough compared to the wavelength of the radar, the echoes em-anating from the surface comprises of waves that are reflected from a number of scatterers contained in what is called a reso-lution cell. As a result of the roughness of this surface, the sep-aration between the scatterers and receiver differs, hence the re-ceived echoes are no more coherent in phase, even though they are still coherent in frequency. If the received waves sum up constructively, the strength of the received signal is strong, if on the other hand, they are out of phase during their reception, the received signal’s strength is weak. The formation of SAR image is due to coherent processing of radar pulses that return in suc-cession at the receiver. This process results in pixels with vary-ing intensities. This variation in intensities is what results in the granular appearance seen in SAR images, and that is referred to as speckle noise. This noise modifies the intensities of the im-aged surface [12]. Figure 1 shows a SAR image with speckle contamination.

3.1 Speckle Noise Model

Speckle noise is a characteristic of SAR images. It is a random noise which impacts SAR image negatively [13]. Speckle noise is multiplicative. Degraded SAR image can be modelled by the equation below:

𝐼𝐷(𝑚, 𝑛) = 𝐼𝑜(𝑚, 𝑛) ∗ 𝑁(𝑚, 𝑛) (1)

where 𝐼𝐷(𝑚, 𝑛) is the degraded image with speckle noise,

𝐼𝑂(𝑚, 𝑛) is the original image, 𝑁(𝑚, 𝑛) is the speckle noise.

4 KUAN FILTER

Kuan filter is a well-known SAR image despeckling filter that

had been used by the image processing community. To apply

this filter, the following representations are made:

𝑊𝑓= Filter window centered at the pixel with coordinates (𝑟, 𝑐)

𝐶𝑊𝑓= Center pixel in 𝑊𝑓

𝐾 = Weighting function, given by: 𝐾 =1−

𝐶𝑢2

𝐶𝑒2⁄

1+𝐶𝑢2

𝜇𝑊𝑓= Local mean within the filter window, 𝑊𝑓

𝜎𝑊𝑓= Standard deviation of 𝑊𝑓

A despeckled pixel can be expressed as follows:

𝑌(𝑟, 𝑐) = 𝜇𝑊𝑓+ 𝐾(𝐶𝑊𝑓

− 𝜇𝑊𝑓) (2) (2)

𝐶𝑒 =𝜎𝑊𝑓

𝜇𝑊𝑓

and the noise variance coefficient is given by:

𝐶𝑢 = 1√𝑁𝐿𝑜𝑜𝑘

⁄

The NLook value controls the amount of smoothing that can be

applied to an image, by simply varying the noise variance coef-

ficient. The higher the NLook, the more the image details that

are preserved. On the other hand, by reducing the NLook better

smoothing is achieved [14].

5 K-NEAREST NEIGHBOUR ALGORITHM

It is a non-parametric search algorithm used for classifying objects

and it is based on closest training examples. It is a technique for

locating the points in a group of data that are closest to the object

of interest. If in a given-dimensional space, we represent a group

of 𝑦 reference positions by 𝑅 = {𝑟1, 𝑟2, 𝑟3, … 𝑟𝑦} and 𝑦 represents a

group of query positions 𝑄 in the same space, then 𝑄 =

{𝑞1, 𝑞2, 𝑞3, … 𝑞𝑦}. The 𝑘 closest point determination requires

searching for the k nearest points to each position q in the reference

group R. Euclidean and other distance determination methods can

be used for this purpose [15]. Figure 2 shows an example with k=3.

The blue dots represent some reference positions, while the green

cross represents the query position. This algorithm is used in pat-

tern recognition [16], [17]. We can find the Euclidean distance be-

tween the points 𝑅 and 𝑄 from:

𝑫𝑬 = √(𝒓𝟏 − 𝒒𝟏)𝟐 + (𝒓𝟐 − 𝒒𝟐)𝟐 + ⋯ + (𝒓𝒚 − 𝒒𝒚)𝟐 (3)

The basic steps required in the K-NN algorithm classification are illustrated in this paper, [18].

Fig. 1. SAR Image with speckle contamination

Fig. 2. An example of K-Nearest Neighbour (K-NN) Classification

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6 WAVELET TRANSFORM

A wavelet is a “small wave” which has its energy compacted in time and this provides a means for analyzing non-stationary and transient phenomena. Wavelet transform has been used in data compression [19]. A function f(t) can be analyzed, or pro-cessed if it is expressed as a linear decomposition by:

𝑓(𝑡) = ∑ 𝑎𝑠𝜓𝑠𝑠 (𝑡) (4)

where the integer s is an index of for the summation, and a_s is the expansion coefficients and ψ𝑠(𝑡) is the set of real-valued function of t called the expansion set. Wavelets are generated from a mother wavelet by scaling and translation. Two-dimen-sional representation of wavelets is achieved from the func-tion 𝑓(𝑡) [20].

ψ𝑎,𝑏(𝑡) = 2𝑎

2⁄ 𝜓(2𝑎𝑡 − 𝑏), 𝑎, 𝑏 ∈ 𝑍 (5)

7 SPIHT ALGORITHM

The SPIHT is an important wavelet coefficients coding scheme. It was brought into the image coding community in the year 1996. In this algorithm, the wavelet coefficients obtained from the wavelet transformation of the image are first encoded and then transmitted using multiple passes [2]. SPIHT uses most significant bit (msb) approach for sorting the transform coeffi-cients from the wavelet decomposition and it employs the list of significant pixels (LSP), list of insignificant sets (LIS) and list of insignificant pixels (LIP) in the coding process.

7.1 SPIHT Coding Steps

A. Step One In each of the multiple passes undergone during the SPIHT en-coding, only the coefficients that are equal or greater in magni-tude than the threshold are encoded. The threshold (Thresh) for each pass is computed as follows: 𝑇ℎ𝑟𝑒𝑠ℎ = 2𝑃−𝑁 (6) where, N=0, 1,2,3,4 ...,P N= the pass number, and P is obtained as follows: 𝑃 = ⌊𝑙𝑜𝑔2𝑚𝑎𝑥𝑖𝑚𝑢𝑚(𝑐𝑜𝑒𝑓𝑓(𝑖, 𝑗))⌋ (7)

𝑐𝑜𝑒𝑓𝑓(𝑖, 𝑗) is the coefficient at coordinate (i,j)in the image. B. Step Two: Sorting Pass When N=n, where n is an integer. The pixel that satisfies the condition 𝑇(𝑛) ≦ |𝑐𝑜𝑒𝑓𝑓(𝑖, 𝑗)| < 2𝑇(𝑛) is regarded to as being significant. The significant pixel’s position and sign bit are then encoded. C. Step Three: Refinement Pass The third step of the SPIHT coding is the refinement pass. Dur-ing this pass, the pixels that satisfy the following condition |𝑐𝑜𝑒𝑓𝑓(𝑖, 𝑗) ≧ 2𝑇(𝑛)| are refined by encoding the 𝑛𝑡ℎ most sig-nificant bit (that is those pixels that had their coordinates trans-mitted during the previous sorting pass).

D. Step Four Increment N by one, and go back to the sorting pass (step B).

8 PERFORMANCE EVALUATION METRICS

We use the mean squared error (MSE), the peak signal-to-noise ratio (PSNR) and the feature preserving index (FPI) as the per-formance evaluation metrics.

𝑀𝑆𝐸 =

1

𝑋𝑌∑ ∑ (𝐼[𝑥, 𝑦] − 𝐼[𝑥, 𝑦])2𝑌−1

𝑦=0𝑋−1𝑥=0 (8)

where the original image is 𝐼[𝑥, 𝑦] and 𝐼[𝑥, 𝑦] is the decom-

pressed image. The peak signal-to-noise-ratio is given as: 𝑃𝑆𝑁𝑅 = 10𝑙𝑜𝑔10(2𝑁 − 1)2/𝑀𝑆𝐸 (9) where the pixels are represented using N number of bits,

while the feature preserving index is given as:

𝐹𝑃𝐼 =∑ (2.𝑅𝑓−𝑅𝑓1−𝑅𝑓2)𝑛

1

∑ (2.𝑅−𝑅1−𝑅2)𝑛1

(10)

where the original pixel value on the linear feature is repre-sented by R, while 𝑅1 and 𝑅2 give the values of the surrounding pixels on both sides of the feature. . 𝑅𝑓,𝑅𝑓1 and 𝑅𝑓2 respectively give the filtered values of the pixels [22]. The higher the value of the FPI, the better a filter to preserves linear features in an image [23].

9 PROPOSED APPROACH

We present a method of encoding SAR images which gives a compressed image of good quality. In this method, attempt is made to remove speckle noise from the SAR image by using an improved Kuan filter. The KNN classification algorithm is used to improve the performance of this filter for use in removing speckle noise from the image before its compression using the discrete wavelet transform. A window size of KxK is chosen and the method is such that instead of using all the neighbour pixels to calculate the filtering parameters, one can select a number of neighbour pixels to ensure that the best results are obtained in terms of performance evaluation metrics values. The number of neighbour pixels specified is k. For this experi-ment, we used a sliding window size of 3x3, and out of the 9 elements, we chose 6 to calculate the filtering parameters. The resulting image is then compressed using the 2-D Discrete Wavelet Transform. This is followed by the use SPIHT algo-rithm to further encode the wavelet coefficients. Figure 3 shows an illustration of the despeckling approach using 3x3 sliding window. The blue dots represent the image pixels as an exam-ple and the center pixel of the sliding window is the red dot.

Fig. 3 Illustration of the center pixel sliding window

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10 EXPERIMENTAL RESULTS

The experiment is carried out on a sample SAR image contam-inated with speckle noise of variance 0.03. The image is com-pressed with wavelet transform without speckle noise removal which is the conventional way of compressing SAR images. We then use our two-stage approach on the image. First, we des-peckled the image with the improved Kuan filter and second, we compressed the image using wavelet transform and further encoded the wavelet coefficients with SPIHT scheme, but with the removal of the slightly complex arithmetic coding stage. Displayed in Figure 4 are three SAR images with (a) being the original image, (b) is the image that is encoded without dealing with the inherent speckle noise and (c) result of the proposed approach. The values of the performance evaluation metrics clearly show the superiority of our proposed approach. Figure 5 shows the plots of the performance evaluation metrics against wavelet decomposition levels. The values of the performance evaluation metrics are contained in Table 1. The highlighted values are those obtained for our approach. The values of MSE, PSNR FPI, and computational time for the third level of decom-position have been tabulated. And for all the levels of decom-position, our approach shows better performance.

TABLE 1 PERFORMANCE EVALUATION RESULTS FOR THE SAR IMAGE FOR

ONE OF THE DECOMPOSITION LEVELS

Evaluation Metrics Compression without

Despeckling

Proposed

MSE 0.1028 0.0672

PSNR (dB) 19.7630 23.4559

FPI 0.6812 0.7581

Time (seconds) 5.2458 2.8483

dB = decibel.

(a) (b)

(c)

Fig. 4 (a) SAR image with speckle of variance 0.03 (b) Image com-pressed only (c) (proposed)

Despeckling and Compression

(a)

1 2 3 4 5 6 70

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Decomposition Levels

MS

E

Proposed

Compress only

(b)

1 2 3 4 5 6 75

10

15

20

25


PS

NR

Proposed

Compress only

(c)

1 2 3 4 5 6 70

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9


FP

I

Proposed

Compress only

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11 CONCLUSION

In this paper, we have introduced a new approach for SAR im-

age compression where speckle noise is first dealt with, due to

its adverse effects on the quality of reconstructed image. Our

approach employed the use of k-nearest neighbour algorithm

to improve the performance of Kuan filter for better speckle

noise removal. The despeckled image is then compressed using

the discrete wavelet transform. For the despeckling we used a

window size of 3x3 and the filtering parameters were obtained

using only 6 out of the 9 elements of the sliding window. We

observed that when we attempted to use larger window sizes,

blur was introduced into the despeckled image. Usually, when

too large window sizes are used blur is introduced into the des-

peckled image. Hence, we had to limit our window size to 3x3.

In this work, speckle noise was been removed to prepare the

SAR image for better compression using discrete wavelet trans-

form (DWT) and from the values of the evaluation metrics, it

can be concluded that our approach outperformed the conven-

tional SAR image compression method using wavelet trans-

form.

ACKNOWLEDGMENT

We wish to express our profound appreciation to the manage-ment of the National Space Research and Development Agency (NASRDA), Abuja, Nigeria.

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