2007/09/11 by Moshe Mishali, Yonina C. Eldar, Mishali, Moshe +1 · 4 citations
Computer Science · Engineering · Medicine · Physics and Astronomy · #Advanced MRI Techniques and Applications #Cellular Automata and Lattice Gases (nlin.CG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Image and Signal Denoising Methods #Sparse and Compressive Sensing Techniques #nlin.CG #nlin.SI
paper · pdf · doi:10.48550/arxiv.0709.1563
30 pages, figures included
arxiv created 2007/09/11 · openalex publication_date 2007/09/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We address the problem of reconstructing a multi-band signal from its sub-Nyquist point-wise samples. To date, all reconstruction methods proposed for this class of signals assumed knowledge of the band locations. In this paper, we develop a non-linear blind perfect reconstruction scheme for multi-band signals which does not require the band locations. Our approach assumes an existing blind multi-coset sampling method. The sparse structure of multi-band signals in the continuous frequency domain is used to replace the continuous reconstruction with a single finite dimensional problem without the need for discretization. The resulting problem can be formulated within the framework of compressed sensing, and thus can be solved efficiently using known tractable algorithms from this emerging area. We also develop a theoretical lower bound on the average sampling rate required for blind signal reconstruction, which is twice the minimal rate of known-spectrum recovery. Our method ensures perfect reconstruction for a wide class of signals sampled at the minimal rate. Numerical experiments are presented demonstrating blind sampling and reconstruction with minimal sampling rate.