2019/07/23 by Amirafshar Moshtaghpour, Moshtaghpour, Amirafshar, José M. Bioucas‐Dias +3
Engineering · Physics and Astronomy · #FOS: Computer and information sciences #Information Theory (cs.IT) #Photoacoustic and Ultrasonic Imaging #Random lasers and scattering media #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1907.09795
openalex publication_date 2019/07/23 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
We investigate the problems of 1-D and 2-D signal recovery from subsampled\nHadamard measurements using Haar wavelet sparsity prior. These problems are of\ninterest in, e.g., computational imaging applications relying on optical\nmultiplexing or single-pixel imaging. However, the realization of such\nmodalities is often hindered by the coherence between the Hadamard and Haar\nbases. The variable and multilevel density sampling strategies solve this issue\nby adjusting the subsampling process to the local and multilevel coherence,\nrespectively, between the two bases; hence enabling successful signal recovery.\nIn this work, we compute an explicit sample-complexity bound for Hadamard-Haar\nsystems as well as uniform and non-uniform recovery guarantees; a seemingly\nmissing result in the related literature. We explore the faithfulness of the\nnumerical simulations to the theoretical results and show in a practically\nrelevant instance, e.g., single-pixel camera, that the target signal can be\nobtained from a few Hadamard measurements.\n