Steering Kernel Regression via Laplacian for Image Denoising in Spatial Domain

ABSTRACT: Recently digital imaging devices are used in many applications and they often suffer from some degradation, such as noise, blurring, aliasing effects, and more due to environment limitations. Captured images are mostly not of favorable quality and need to be enhanced by software. One of the significant reasons of the performance degradations for most methods is the presence of noise. Noise removal, therefore, is one of the most important tools for many applications. In this thesis, we focus on this issue as one of the main important problem of image processing. We discuss about the various sources of noise corrupting image and illustrate the statistical behavior of noise and discuss about how to eliminate the effects of the noise from our images. The classic kernel regression (KR) is a statistical framework that enables us to regard a variety of image restoration problems as regression, and it has a few beneficial properties instead of other regression methods. We have modified the classic kernel regression (KR) with steering matrices which are estimated by the singular value decomposition of the second derivatives of pixels that we apply, which makes our method relying not only the spatial properties (the sample location and density), but also the photometric properties of these samples (i.e., pixel value). Thus, the effective size and shape of the regression kernel are adapted locally to the underlying image structure. Steering kernel regression (SKR) method has been shown to provide excellent denoising result. Steering kernels adapt to the local pixel intensity statistics and geometry. SKR employs the gradient for finding the structure of local region by applying the first order structure tensor, but in this work we propose to use an adaptive kernel, which is based on the second derivative of pixels and find the structure tensor of hessian matrix (which related to the second derivative) for each pixel to make the structure tensor more robust in the face of noise to maintain the image details. Since edges in an image have significant profile, we apply second derivative because gradient produces thick edges while second order derivative (Laplacian) produces finer edges also magnitude of gradient can be used to detect presence of edge at point, but sign of second derivative can be used to determine whether edge pixel itself lies on the dark or bright side of edges. The motivation behind structure tensor is a fact that image contains directional structure such as edges and the motivation behind second derivative is to obtain finer edges. Quantitative and perceptual evaluations from simulations have been shown that proposed framework indicates an average PSNR improvement compared to other framework, and compared with the conventional SKR method an average 0.3 dB PSNR increase is obtained. Comparisons show the superiority of this method over other descriptors. Keywords: Denoising, kernel function, kernel regression, Steering matrix, Taylor series, structure tensor. …………………………………………………………………………………………………………………………