Sar Image Despeckling Using Bandelet Transform with Firefly Algorithm

Removal of noise from image is often the first step in image processing and remains a challenging problem inspite of the sophistication of recent research. Among all noise, speckle noise existing in Satellite images, Medical images and Synthetic Aperture Radar (SAR) images is definitely to be removed since the details of the image are corrupted. The analysis of despeckling SAR image based on Bandelet transform with Firefly Algorithm (FA) is carried out in this paper. The transform domain despeckling is preferably adapted because of its improved efficiency. It begins with shrinking and stretching the Bandelet co-efficients of the coherent SAR image, the quality improved image with feature enhancement is integrated. Then to get the best oriented quality parameter of the despeckled image, an evolutionary computation technique FA is applied. The procedure is continued using fundamental Wavelet transform with FA and the results are compared for the conclusion to get the best despeckled image. KEYWORDS— SAR image, Bandelet Transform, Firefly Algorithm (FA), Speckle Suppression Index (SSI) and Peak Signal to Noise Ratio (PSNR). INTRODUCTION Synthetic Aperture Radar (SAR) is widely used to obtain the image of the earth in high resolution. To recover the sharp and clear image from the noisy image caused due to image acquisition conditions, despeckling is applied. In incoherent imaging system like digital camera produces an image with Gaussian additive noise. But in contrast, coherent imaging methods like SAR imaging produce multiplicative speckle noise. SAR images are used to interpret information and have many applications like Bio-mass estimation, Sea ice monitoring, Crop estimation, Flood control, Oil spill monitoring and Soil moisture content measurement. But a SAR image is inherently affected by speckle noise, which reduces the efficiency of the post processing steps in image processing and makes it more difficult to interpret. As it implies that the speckle noise reduces the intensity level of image and tends to blur the image by reducing its fine details [1] the goal of despeckling process is to suppress the multiplicative noise while preserving all the scene features such as textures and edges. As the power of the signal increases the speckle noise also increases by the same amount. Therefore speckle is a multiplicative noise and it can be explained with a standard deviation equal to its pixel reflectivity value. The speckle noise model can be represented in an Eq. 1 as, f(i ,j) = g( i, j) * n ( i, j) (1) where f (i, j) is the measured pixel level, g (i ,j) is the desired pixel reflectivity, n (i ,j) is the multiplicative noise and here i, j represent the indices of the spatial location. SAR signal is applied with logarithmic compression, which transforms the multiplicative noise into additive white Gaussian noise. This is given by Eq. 2 as, log [f (i ,j)] = log [g (i ,j) ] + log [n (i,j) ] (2) and rewritten as, D(i,j) = X(i,j)+Y(i,j) (3) where log [f(i ,j)] is denoted as D (i, j) and the terms log [g(i ,j)] and log [n(i ,j)] are denoted as X (i, j) and Y (i, j) respectively. Also the logarithmic conversion is used, that the additive noise can be easily removed. About two decades, researchers developed many techniques to filter the speckle noise and retain the image details. One method is that employs multiple look processing in frequency domain [2] thereby averaging statistically dependent looks on the same scene. This technique enhances the radiometric resolution at the expense of blurring. Later on the classical spatial filters like Median filter, Lee filter, Kaun filter, Frost filter and other despeckling algorithms were used to filter the noise effectively with less computation complexity. In these types of filtering the image details are not effectively preserved resulting in blurred edges. Also, single scale representation of a signal either in time or frequency is inefficient as it is difficult to differentiate signal from noise and also these kinds of filters are not suitable for non-stationary scene signal. However it is still an unsolved problem and there is no comprehensive method that solve all the constraints taken into consideration. These limitations are overcome by using transform based filtering of speckle. Previously the concept of filtering by using Wavelet transform [3]-[5], Curvelet Transform [6][8] and the combination of these two domains [9] were performed. The Wavelet transform is fundamental and powerful tool that acts on the denoising of SAR images because of its properties of time-frequency localization, multi-resolution, sparsity and decorrelation. It exhibits good performance in despeckling but some artifacts occur during filtering and also it is not directional. Another disadvantage in Wavelet domain is that it identifies only point discontinuities and not able to diagnose the direction of any line shaped discontinuity in the image. The extension of this is carried over by Curvelet transform. [10]-[11] The Curvelet transform is used to provide optimal sparse approximations of piecewise smooth image but offers limited localization in the spatial domain because of its band limited nature. The other multi-scale analysis is experimented with Ridgelet transform [12] The Ridgelet transform is only suitable for discontinuities along straight line and not optimal for complex images where the edges were mainly along curves. The Contourlet transform with its special characteristics of multi-resolution, multidirectional and speedy operation, address the problem of applying Wavelet transform, Curvelet transform and Ridgelet transform in despeckling of SAR images. Savithri et al., International Journal of Advanced Engineering Technology E-ISSN 0976-3945 Int J Adv Engg Tech/Vol. VII/Issue II/April-June,2016/364-370 The Contourlet transform includes Laplacian Pyramid [13] to capture the point of discontinuities followed by Directional Filter Banks to link the point of discontinuities into linear structure. Also sparse representation for two dimensional piecewise smooth signal that resemble images is produced by Contourlet transform. Including orthogonal and non orthogonal Bandelets [14]-[15] have greater adaptability than other Ridgelet, Curvelet and continuous Wavelet transforms. The number of its optional directions outperforms other geometric analysis tools, which can be used effectively approximate the edges. TRANSFORM DOMAIN Transform domain speckle removal process with edge preservation overcome the limitations existed in the previous techniques with Spatial filtering.. A. Wavelet transform Wavelet transform is the inheritance and development of traditional Fourier transform. Wavelet transform is a basic and powerful tool acts on the despeckling of SAR images because of its properties of time and frequency localization, multiresolution, sparsity and decorrelation. Wavelet transform method is practically very flexible and very much suitable in image denoising and enhancement. The application of wavelet transform is essential in image processing and classified into three classes as continuous, discrete and multiresolution based discrete wavelet transform[16]-[17]. Continuous wavelet transform The Continuous Wavelet Transform (CWT) is subjected to the uncertainty principle of Fourier analysis. If a signal with some event in it, the assignment of exact time and frequency response scale of that event cannot be made. Hence the scalogram of CWT of the signal, an event marks an entire region in the timescale plane. Discrete wavelet transform The Discrete Wavelet Transform (DWT) is a most popular method used in image resolution enhancement. In this the impossibility of analyzing the input signal with all wavelet coefficients is overcome by decomposing the input sequence into low-pass and high-pass sub bands each of which consists half the number of samples in the original sequence Multiresolution discrete wavelet transform Multiresolution is the method efficiently extract the details of an input signal at various resolution level. The computational complexity is reduced in this method by the usage of pyramidal algorithm. B. Contourlet transform The preservation of the edges should be definitely made while despeckling of SAR images. The smoothing of SAR images can be better performed using transform like Wavelet, Curvelet, Bandelet and Contourlet methods. The Contourlet transform exploits smoothness of contour effectively by considering variety of directions following the contours. It is observed that in the basic wavelet transform only the point discontinuities are represented by square supports but the Contourlet transform represents the multiscale geometric analysis. Fig. 1 shows the Contourlet transform consists of two steps which is the sub band decomposition and the directional transform [18]-[19]. Fig. (1) illustrates the construction of Contourlet transform by the Laplacian Pyramid (LP) and the Directional Filter Banks (DFB). The input image consisting of frequency components like LL(Low Low), LH(Low High), HL(High Low) and HH(High High) is applied to LP which generates a low pass output(LL) and bandpass outputs (LH,HL and HH). Then the Contourlet co-efficient are resulted by passing the passband output to DFB. To obtain more Contourlet co-efficients the low pass output from the LP is applied to another LP till the fine details of the image are resulted. Hence the LP capture point discontinuities and DFB links point discontinuities into linear structure of smooth contour. Fig. 1 Illustration of Contourlet Transform C. Bandelet Transform In image processing or image representation the geometry regularity is the challenging one. Edges with sharp image transition are very difficult to be represented in an image. To achieve better representation some geometric regularity of the functions are applied but not possibly obtained using Wavelet or Fourier basis. On further development, Bandelet basis was introduced for the optimal geometric representation of digital images in discrete domain. To estimate the geometric regularity, digital image information is achieved by “Multiresolution analysis”, thereby decomposing the digital image using Bandelets and making directional analysis on orthogonal Wavelet coefficients. By the use of wavelet bank with directional orthogonal filters, the orthogonal wavelet coefficients are computed. In directional analysis, the orthogonal directional projection and one dimensional wavelet transform along the direction of the geometry are realized [20]. Each geometric direction leads to a different transform so that an optimal set of filter could be found by the application of optimization technique. In Bandelet transform, 2D wavelet transform on the data and then 1D wavelet transform along geometry are implemented [21]. The signal possesses both orthogonality and symmetry which store energy to an amount as much as possible in the application of image processing. The Harr wavelet is used in Bandelet since it pertain both these properties simultaneously. FIREFLY ALGORITHM Firefly Algorithm (FA) [22]-[23] was developed by Xin-She Yang at Cambridge University in 2007. FA is an optimization algorithm inspired by the behavior and motion of fireflies. Numerous firefly species occupied in the sky produce short and rhythmic flashes in the moderate temperature region. Mostly specific species produce specific pattern. A kind of pattern formed by Savithri et al., International Journal of Advanced Engineering Technology E-ISSN 0976-3945 Int J Adv Engg Tech/Vol. VII/Issue II/April-June,2016/364-370 attraction of male and female species depends upon many factors like the rhythm of the flashes, flash rate and the flash time. Fireflies communicate with each other only at a limited distance normally few hundred meters at night. The light is observed by air and becomes weaker, also the intensity of light decreases as the distance from the light source increases. Firefly Algorithm follows rules as,  All the fireflies are unisex that means that one firefly is attracted to other firefly irrespective of their sex.  Attractiveness and brightness are proportional to each other and so for any two flashing fireflies, the firefly with less brightness tend to move to reach the one which is brighter also decrease with their distance decreases. If the brightness of all fireflies is same they will move randomly.  The objective functions determine brightness of a firefly.  The brightness is proportional to the value of the objective function for a maximization problem. The variation in light intensity and formulation of attractiveness are the main important points in Firefly algorithm since the attractiveness of a firefly is determined by its objective function.  Some initialization has to be made in the FA algorithm including, 1) γ: the light coefficient of absorption 2) d: the particular distance from the light source 3) s: the domain space. The attraction of firefly i, to another brighter firefly j, is expressed as,