Analysis and algorithms for some compressed sensing models based on the ratio of $\ell_1$ and $\ell_2$ norms

发布时间：2021-09-16 作者：浏览次数：

Speaker:	曾燎原	DateTime:	2021年9月24日(星期五)下午 15:00--16:00
Brief Introduction to Speaker: 曾燎原，香港理工大学。		Place:	腾讯会议（会议号请联系张雄军老师）
Abstract:Recently, the ratio of $\ell_1$ and $\ell_2$ norms has been proposed as a sparsity inducing function for noiseless compressed sensing (CS). In this talk, we further study properties of such model in the noiseless setting, and propose an algorithm for minimizing the ratio of $\ell_1$ and $\ell_2$ when the measurements are subject to noise. Specifically, we first present conditions that guarantee solution existence for these models. We then derive an explicit Kurdyka-{\L}ojasiewicz exponent for the model in the noiseless setting, which enables us to deduce linear convergence of a recently proposed Dinkelbach type algorithm for the noiseless model. Furthermore, we extend this algorithm to deal with noisy scenario by incorporating moving-balls-approximation techniques, and analyze its convergence. Finally, we present numerical tests on CS problems with Cauchy measurement noise and badly scaled CS problems with Gaussian measurement noise.