2013/11/20 by Yipeng Liu, Liu, Yipeng
Computer Science · Engineering · Mathematics · Medicine · #Advanced MRI Techniques and Applications #Applications (stat.AP) #Computer Vision and Pattern Recognition (cs.CV) #Electrical and Bioimpedance Tomography #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Machine Learning (stat.ML) #Representation Theory (math.RT) #Sparse and Compressive Sensing Techniques #cs.CV #cs.IT #math.IT #math.RT #stat.AP #stat.ML
paper · pdf · doi:10.48550/arxiv.1311.4924
17 pages, 8 figures
openalex publication_date 2013/11/20 · arxiv created 2015/07/02 · arxiv updated 2015/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be known exactly in advance. However, uncertainties exist due to sampling distortion, finite grids of the parameter space of dictionary, etc. In this paper, we take a generalized sparse signal model, which simultaneously considers the sampling and representation matrix uncertainties. Based on the new signal model, a new optimization model for robust sparse signal reconstruction is proposed. This optimization model can be deduced with stochastic robust approximation analysis. Both convex relaxation and greedy algorithms are used to solve the optimization problem. For the convex relaxation method, a sufficient condition for recovery by convex relaxation is given; For the greedy algorithm, it is realized by the introduction of a pre-processing of the sensing matrix and the measurements. In numerical experiments, both simulated data and real-life ECG data based results show that the proposed method has a better performance than the current methods.