Least Square based Image Denoising using Wavelet Filters

Background/Objectives: Noise in a digital image, is unwanted information that degrades the quality of an image. The main aim of the proposed method is to denoise a noisy image based on least square approach using wavelet filters. Methods/ Statistical Analysis: One dimensional least square approach proposed by Selesnick is extended to two dimensional image denoising. In our proposed technique of least square problem formulation for image denoising, the matrix constructed using second order filter coefficients is replaced by wavelet filter coefficients. Findings: The method is experimented on standard digital images namely Lena, Cameraman, Barbara, Peppers and House. The images are subjected to different noise types such as Gaussian, Salt and Pepper and Speckle with varying noise level ranging from 0.01db to 0.5db. The wavelet filters used in the proposed approach of denoising are Haar, Daubechies, Symlet, Coiflet, Biorthogonal and Reverse biorthogonal. The outcome of the experiment is evaluated in terms of Peak Signal to Noise Ratio (PSNR). The analysis of the experiment results reveals that performance of the proposed method of least square based image denoising by wavelet filters are comparable to denoising using existing second order sparse matrix. Applications/Improvements: Digital images are often prone to noise; hence, proceeding with further processing of such an image requires denoising. This work can be extended in future to m-band wavelet filters.