2016/04/27 by Penghang Yin, Jack Xin, Yin, Penghang +1
Engineering · #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Microwave Imaging and Scattering Analysis #Optimization and Control (math.OC) #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1604.07924
openalex publication_date 2016/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An algorithmic framework, based on the difference of convex functions algorithm (DCA), is proposed for minimizing a class of concave sparse metrics for compressed sensing problems. The resulting algorithm iterates a sequence of ℓ1 minimization problems. An exact sparse recovery theory is established to show that the proposed framework always improves on the basis pursuit (ℓ1 minimization) and inherits robustness from it. Numerical examples on success rates of sparse solution recovery illustrate further that, unlike most existing non-convex compressed sensing solvers in the literature, our method always out-performs basis pursuit, no matter how ill-conditioned the measurement matrix is. Moreover, the iterative ℓ1 (IL1) algorithm lead by a wide margin the state-of-the-art algorithms on ℓ1/2 and logarithimic minimizations in the strongly coherent (highly ill-conditioned) regime, despite the same objective functions. Last but not least, in the application of magnetic resonance imaging (MRI), IL1 algorithm easily recovers the phantom image with just 7 line projections.