学术报告-中南大学数学与统计学院

学术报告

发布时间:2018年07月28日 作者:向淑晃   消息来源:    阅读次数:[]

学术报告: Spherical designs and non-convex minimization for recovery of sparse signals on the sphere

报告人:Chair Professor Xiaojun Chen, Dean of Department of Applied Mathematics, The Hong Kong Polytechnic University

摘要:This talk considers the use of spherical designs and non-convex minimization for recovery of sparse signals on the unit sphere S^2. The available information consists of low order, potentially noisy, Fourier coefficients for S^2. As Fourier coefficients are integrals of the product of a function and spherical harmonics, a good cubature rule is essential for the recovery. A spherical t-design is a set of points on S^2, which are nodes of an equal weight cubature rule integrating exactly all spherical polynomials of degree ≤ t. We will show that a spherical t-design provides a sharp error bound for the approximation signals. Moreover, the resulting coefficient matrix has orthonormal rows. In general the L_1 minimization model for recovery of sparse signals on S^2 using spherical harmonics has infinitely many minimizers, which means that most existing sufficient conditions for sparse recovery do not hold. To induce the sparsity, we replace the L_1-norm by the L_q-norm (0<q<1) in the basis pursuit denoise model. Recovery properties and optimality conditions are discussed. Moreover, we show that the penalty method with a starting point obtained from the re-weighted L_1 method is promising to solve the L_q basis pursuit denoise model. Numerical performance on nodes using spherical t-designs and t_ε-designs (extremal fundamental systems) are compared with tensor product nodes. We also compare the basis pursuit denoise problem with q=1 and 0<q<1.

地点:数理楼145报告厅 时间:7月31日15:00-18:00



打印】【收藏】 【关闭