А locally adaptive wavelet filtering algorithm for images

Abstract

The algorithms based on the decomposition of a noisy image in an orthogonal basis of wavelet functions have been widely used to filter images (especially contrasting ones) over the past four decades. In this case, most wavelet filtering algorithms are of a threshold nature, namely: the decomposition coefficient smaller in an absolute value of a certain threshold value is reset to zero; otherwise the coefficient undergoes some (most often nonlinear) transformation. A certain (and very significant) drawback of threshold algorithms is that all coefficients of a certain decomposition level are processed with one identical threshold value (i.e., a constant value for all de-composition coefficients). This does not allow taking into account the “individual energy” of each decomposition coefficient for its more optimal processing. Therefore, we propose its own filtering factor for each coefficient, built on the basis of the optimal Wiener filtering and where a filtering parameter is introduced to compensate for incomplete a priori information on the value of the processed decomposition coefficients. In order to select a filtering parameter, a statistical approach has been proposed that makes it possible to estimate the optimal value of this parameter with acceptable accuracy. The performed computational experiment has shown the developed algorithm effectiveness for wavelet filtering of images.