A Reliable Iteration Algorithm for One-Bit Compressive Sensing on the Unit Sphere

作     者：Yan-cheng LU Ning BI An-hua WAN Yan-cheng LU;Ning BI;An-hua WAN

作者机构：School of MathematicsSun Yat-sen UniversityGuangzhou 510275China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2024年第40卷第3期

页      面：801-822页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China(Nos.12171496,12171490,11971491 and U1811461) Guangdong Basic and Applied Basic Research Foundation(2024A1515012057)。 

主　　题：one-bit compressed sensing difference of convex algorithm iteration algorithm ■1-minimization 

摘      要：The one-bit compressed sensing problem is of fundamental importance in many areas,such as wireless communication,statistics,and so on.However,the optimization of one-bit problem coustrained on the unit sphere lacks an algorithm with rigorous mathematical proof of convergence and validity.In this paper,an iteration algorithm is established based on difference-of-convex algorithm for the one-bit compressed sensing problem constrained on the unit sphere,with iterating formula■,where C is the convex cone generated by the one-bit measurements andη_(1)η_(2)1/2.The new algorithm is proved to converge as long as the initial point is on the unit sphere and accords with the measurements,and the convergence to the global minimum point of the l_(1)norm is discussed.