Multiscale block compressed sensing with smoothed projected Landweber reconstruction

A multiscale variant of the block compressed sensing with smoothed projected Landweber reconstruction algorithm is proposed for the compressed sensing of images. In essence, block-based compressed-sensing sampling is deployed independently within each subband of each decomposition level of a wavelet transform of an image. The corresponding multiscale reconstruction interleaves Landweber steps on the individual blocks with a smoothing filter in the spatial domain of the image as well as thresholding within a sparsity transform. Experimental results reveal that the proposed multiscale reconstruction preserves the fast computation associated with block-based compressed sensing while rivaling the reconstruction quality of a popular total-variation algorithm known for both its high-quality reconstruction as well as its exceedingly large computational cost.