Exploiting Wavelet-Domain Dependencies in Compressed Sensing

This paper presents a method for improving wavelet-based Compressed Sensing (CS) reconstruction algorithms by exploiting the dependencies among wavelet coefficients. During CS recovery, a simple measure of significance for each wavelet coefficient is calculated using a weighted sum of the (estimated) magnitudes of the wavelet coefficient, its highly correlated neighbors, and parent. This simple measure is incorporated into three CS recovery algorithms, Reweighted L1 minimization algorithms (RL1), Iteratively Reweighted Least Squares (IRLS), and Iterative Hard Thresholding (IHT). Experimental results using one-dimensional signals and images illustrate that the proposed method (i) improves reconstruction quality for a given number of measurements, (ii) requires fewer measurements for a desired reconstruction quality, and (iii) significantly reduces reconstruction time.