Wavelets-based Signal Sparse Representation And Its Application In Image Denoising

As known, compressed sensing theory (CS), put forward by E. Candes, T. Tao and D. Donoho etc., promoted development of computer and information science greatly in recent years. It pointed out that sampled by much lower sampling bandwidth than what Nyquist-Shannon sampling theorem characterized, natural signals can be recovered com-pletely. Motivated by compressed sensing theory, the signal sparsity and its representation are of interest in several applications.In this paper, by introducing multi-resolution and wavelet transform to achieve the sparse representation of signal, we shall improve the R-O-F model, which can be solved by convex optimization. More precisely, we shall utilize Bregman iterative algorithm and Split Bregman iterative algorithm to solve the corresponding convex problems. More details, including the relevant theories and algorithms, will be characterized in this paper. To illustrate our results, several experimental results in image denoising will be exhibited at the end of this paper, which show that by using the new method for signal sparse representation, the performance of R-O-F model is also improved.On the occasion, the theoretical research and experiments of this paper make a useful attempt in signal sparse representation and provide a reference for the following theory and algorithm based on signal sparse representation.