Analysis of the equivalence relationship between l(0)-minimization and l(p)-minimization

作者：Wang, Changlong; Peng, Jigen^*

来源：JOURNAL OF INEQUALITIES AND APPLICATIONS, 2017, 2017(1): 313.

DOI：10.1186/s13660-017-1590-x

• sparse recovery
• null space constant
• null space property
• l(0)-minimization
• l(p)-minimization

In signal processing theory, l(0)-minimization is an important mathematical model. Unfortunately, l(0)-minimization is actually NP-hard. The most widely studied approach to this NP-hard problem is based on solving l(p)-minimization (0 < p <= 1). In this paper, we present an analytic expression of p*(A, b), which is formulated by the dimension of the matrix A is an element of R-mxn, the eigenvalue of the matrix A(T)A, and the vector b is an element of R-m, such that every k-sparse vector x is an element of R-n can be exactly recovered via l(p)-minimization whenever 0 < p < p*(A, b), that is, l(p)-minimization is equivalent to l(0)-minimization whenever 0 < p < p*(A, b). The superiority of our results is that the analytic expression and each its part can be easily calculated. Finally, we give two examples to confirm the validity of our conclusions.

• 出版日期2017-12-21
• 单位西安交通大学