Wavelet-Based Compressed Sensing Using Low Frequency Coefficients

Signal models such as wavelet trees, block sparsity and statistical models are integrated into compressed sensing (CS) recovery algorithms in order to improve recovery accuracy and decrease the number of measurements. However, there are many constraints in practical applications. This paper introduces a new simple and efficient model based on the fact that low frequency coefficients are more important than others in wavelet domain. Furthermore, a degradation algorithm is designed to convert two-dimensional images to one-dimensional signals. This process makes the representations of images more sparse under a fixed wavelet basis. The proposed model and the degradation algorithm are successfully incorporated into two CS algorithms, including iteratively reweighted l1 minimization (IRL1) and iterative hard thresholding (IHT). Extensive experiments demonstrate that the proposed algorithms are significantly effective to improve recovery accuracy.