A new denoising method based on wavelet transform and sparse representation

Wavelet threshold denoising is a powerful method for suppressing noise in signals and images. However, this method uses a coordinate-wise processing scheme, which ignores the structural properties in the wavelet coefficients. We propose a new denoising method using sparse representation which is a powerful mathematical tool developed only recently. Instead of thresholding wavelet coefficients individually, we minimize the number of coefficients in the sparse representation frame work under certain conditions. The denoised signal is reconstructed by solving an optimization problem. We show that, by using an iterative algorithm, the solution to the optimization problem can be obtained uniquely and the estimates are unbiased, i.e., the statistical means of the estimates are equal to the ideal wavelet coefficients. Our experiments on test signals show that this new denoising method is effective and efficient for a wide variety of signals including those with a low signal-to-noise ratio.