Statistical Modelling of Log Transformed Speckled Image Prabhishek Singh Research Scholar, Department of Information Technology Babasaheb Bhimrao Ambedkar University, Lucknow, Uttar Pradesh, India prabhisheksingh88@gmail.com Dr. Raj Shree Assistant Professor, Department of Information Technology Babasaheb Bhimrao Ambedkar University, Lucknow, Uttar Pradesh, India rajshree.bbau2009@gmail.com Abstract— In remote sensing imagery, synthetic aperture radar (SAR) images are affected by the speckle noise whose granular appearance degrades the quality of active SAR images and also disturbs its visual appearance hence it becomes difficult to automatically interpret the SAR data. Speckle noise is multiplicative in nature. Despeckling SAR images is a critical task as most of the restoration models are dedicated to the additive noise; therefore it is needed to transform this multiplicative nature of speckle noise into additive noise. This is performed by applying log transformation on the speckled image which changes its nature and also removes the signal dependency of the speckle noise. There are some drawbacks of applying log transformation but still it provides satisfactory results which are all discussed in this paper. Major focus behind this paper is to experimentally analyze the implementation of logarithmic transformation in the speckled SAR images and realize that how the statistical properties of the speckled image get changed using probability intensity distribution. Speckle noise is mainly found in SAR images and ultrasound images. This paper purely focused on SAR images. Matlab programming is used to realize the practical implementation. Keywords--- SAR image; speckle noise; log transform; Matlab I. INTRODUCTION Image despeckling is a field of image processing which deals with despeckling an original SAR image from a speckled SAR image. Image restoration can be defined as the process of removal of degradation in an image through linear or non-linear filtering. SAR is the form of Radar that is mounted on the satellites and aircrafts that capture the high resolution images of the broad areas of the earth surface. While capturing such images it has to deal with various weather conditions, day and night, so a special treatment is needed to handle such images because in such case chance of noise intrusion is higher. The kind of noise that attacks in such scenario is called as the Speckle noise. SAR images are different from optical images. SAR images are formed by the coherent interaction of the transmitted microwave with targets (terrain). This coherent interaction causes random constructive and destructive interference resulting in salt and pepper noise throughout the image. Hence later it suffers from the effects of speckle noise. It is a granular noise that inherently exists in and degrades the quality of the active SAR image. It is a multiplicative noise. Fig 1 shows original SAR image. Fig 2 shows speckled image with the 20% intrusion of speckle noise. Figure 1. Original SAR Image [1] Figure 2. Speckled Image (Speckle Noise=0.2) In terms of mathematical image processing there are two basic noise models: additive noise model and multiplicative noise model. Additive noise model is systematic in nature and is in use since last many years. Most of the filtering techniques developed for additive noise models and there are only standard filters dedicated to multiplicative noise. Therefore additive noise are easily modeled and it easy to reduce and remove [2]. Whereas multiplicative noise is dependent on the image, complex to model and hence not an easy task to reduce. Various additive noise are Pink noise, Black noise, Gaussian noise, Flicker noise, Brown noise or Brownian noise, Contaminated Gaussian noise, Power-law International Journal of Computer Science and Information Security (IJCSIS), Vol. 14, No. 8, August 2016 426 https://sites.google.com/site/ijcsis/ ISSN 1947-5500