Image Denoising by using Non-Tensor Product Wavelets Filter Banks

In image denoising, where a tradeoff between noise suppression and the preservation of actual image discontinuities must be made, solutions are sought which can "detect" important image details and accordingly adapt the degree of noise smoothing. The techniques of image denoising fall into two categories: spatial domain methods and transform domain methods. The term spatial domain refers to the image plane itself, and approaches in this category are based on direct manipulation of pixels in an image. Transform domain processing techniques are based on modifying the Fourier or wavelet transform of an image. The major problem of these traditional methods is as follows: The representation couldn\´t contain basis elements oriented at a variety of directions, much more than the few directions that are offered by tensor product wavelets. To conquer the above headache trouble, a new approach to image denoising by using a non-tensor product bivariate orthogonal wavelet filter banks is presented. The core of our new method is that using centrally symmetric orthogonal matrices to compute filter banks. Our investigations demonstrate that there are three characteristics in this new approach: First, it is easily to understand and implement that using iterative method to compute orthogonal filter banks; Second, three high frequency subbands could present more directional features than tensor product wavelets; And the last is that different filter banks could emphasize different directional information. We employ those new filter banks to the denoising of some standard images embedded in white noise, the experimental results show that our new approach is superior to other methods in terms of denoising effectiveness.