Reconstruction of Wavelet Coefficients

Abstract

A comparative study of different methods of reconstruction of wavelet coefficients is presented. The following are the different techniques for the reconstruction of wavelet coefficients. To start with, we show how to design and construct Daubechies four coefficient wavelet system which are orthogonal and compactly supported wavelets. Then we outline the multi resolution analysis of wavelets using Mallat transform. Multi resolution analysis can be illustrated by the decomposition and reconstruction of wavelet system using Laplacian Pyramid. To construct wavelet systems with finite support and regularity using orthonormal and interpolariting units, only multicomponent wavelets are possible. When image function is expressed in terms of scaling functions and wavelet functions of higher resolution, we need to consider only few wavelet coefficients and wavelet coefficients are dominant only near edges. The wavelet coefficient near edges can be estimated using wavelet transform maxima and statistical inference of coefficients using Markov tree model. An alternate method is the reconstruction of wavelet coefficients using total variation minimisation. If we use thresholding, so that when we neglect wavelet coefficients having values less than a threshold value there is ringing across edges. Hence we propose an improved algorithm of reconstruction of wavelet coefficients using zero padding and cycle spinning. PSNR of images with wavelet based interpolation and denoising by cycle spinning is moderately high.