Improved Kuan Filter and Wavelet Based SAR Image Despeck ... image. The despeckled image is then...
Transcript of 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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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 signalβs 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:
πΌπ·(π, π) = πΌπ(π, π) β π(π, π) (1)
where πΌπ·(π, π) is the degraded image with speckle noise,
πΌπ(π, π) is the original image, π(π, π) 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:
ππ= Filter window centered at the pixel with coordinates (π, π)
πΆππ= Center pixel in ππ
πΎ = Weighting function, given by: πΎ =1β
πΆπ’2
πΆπ2β
1+πΆπ’2
πππ= Local mean within the filter window, ππ
πππ= Standard deviation of ππ
A despeckled pixel can be expressed as follows:
π(π, π) = πππ+ πΎ(πΆππ
β πππ) (2) (2)
πΆπ =πππ
πππ
and the noise variance coefficient is given by:
πΆπ’ = 1βππΏπππ
β
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 π¦ reference positions by π = {π1, π2, π3, β¦ ππ¦} and π¦ represents a
group of query positions π in the same space, then π =
{π1, π2, π3, β¦ ππ¦}. The π 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 π and π from:
π«π¬ = β(ππ β ππ)π + (ππ β ππ)π + β― + (ππ β ππ)π (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 βsmall waveβ 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:
π(π‘) = β ππ ππ π (π‘) (4)
where the integer s is an index of for the summation, and a_s is the expansion coefficients and Οπ (π‘) 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 π(π‘) [20].
Οπ,π(π‘) = 2π
2β π(2ππ‘ β π), π, π β π (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: πβπππ β = 2πβπ (6) where, N=0, 1,2,3,4 ...,P N= the pass number, and P is obtained as follows: π = βπππ2πππ₯πππ’π(πππππ(π, π))β (7)
πππππ(π, π) 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 π(π) β¦ |πππππ(π, π)| < 2π(π) is regarded to as being significant. The significant pixelβs 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 |πππππ(π, π) β§ 2π(π)| are refined by encoding the ππ‘β 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.
πππΈ =
1
ππβ β (πΌ[π₯, π¦] β πΌ[π₯, π¦])2πβ1
π¦=0πβ1π₯=0 (8)
where the original image is πΌ[π₯, π¦] and πΌ[π₯, π¦] is the decom-
pressed image. The peak signal-to-noise-ratio is given as: ππππ = 10πππ10(2π β 1)2/πππΈ (9) where the pixels are represented using N number of bits,
while the feature preserving index is given as:
πΉππΌ =β (2.π πβπ π1βπ π2)π
1
β (2.π βπ 1βπ 2)π1
(10)
where the original pixel value on the linear feature is repre-sented by R, while π 1 and π 2 give the values of the surrounding pixels on both sides of the feature. . π π,π π1 and π π2 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
Decomposition Levels
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
Decomposition Levels
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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