2010/11/05 by Rajiv Soundararajan, Sriram Vishwanath, Soundararajan, Rajiv +1
Computer Science · Engineering · Mathematics · #FOS: Computer and information sciences #Image and Signal Denoising Methods #Information Theory (cs.IT) #Microwave Imaging and Scattering Analysis #Sparse and Compressive Sensing Techniques #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1011.1503
10 pages, 1 figure, submitted to DCC 2011
arxiv created 2010/11/05 · openalex publication_date 2010/11/05 · arxiv updated 2010/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The problem of compressing a real-valued sparse source using compressive sensing techniques is studied. The rate distortion optimality of a coding scheme in which compressively sensed signals are quantized and then reconstructed is established when the reconstruction is also required to be sparse. The result holds in general when the distortion constraint is on the expected p-norm of error between the source and the reconstruction. A new restricted isometry like property is introduced for this purpose and the existence of matrices that satisfy this property is shown.