Band-Wise Adaptive Sparsity Regularization for Quantized Compressed Sensing Exploiting Nonlocal Similarity

The theory of compressive sensing (CS) has attracted considerable research interests from signal and image processing communities. And in practice, because of the considerations of data storage and transmission, scalar quantization is necessary to be implemented on the CS measurements. In this paper, we propose an adaptive bandwise sparsity regularization to handle the recovery problem of quantized compressive sensing. The sparsity regularization constraints every patch by using bandwise distribution model in transform domain. In addition, we bring in the quantization cost function to quantify the influence of measurement quantization. Experimental results demonstrate that our CS recovery strategy achieves significant performance improvements over the current state-of-the-art schemes with both unquantized measurements and quantized measurements.