Improving Inverse Wavelet Transform by Compressive Sensing Decoding with Deconvolution

By virtue of compressive sensing (CS) that can recover sparse signals from a few linear and non-adaptive measurements, we propose an alternative decoding method for inverse wavelet transform when only partial coefficients are available. Classic CS decoding such as $l_1$-minimization indeed provides better reconstruction of sparse signals than inverse wavelet transform. Since many natural images are not sparse, we propose to further improve CS decoding from the Bayesian point of view. Specifically, as wavelet transform can be described as convolution, we present an iterative deconvolution method for CS decoding in the case of partial wavelet coefficients. Experimental results demonstrate the efficiency of our method. We conclude that such findings indicate promising applications in compression.