Matrix Optimization and Convex Programming
Blind Deconvolution Using Convex Programming
Abstract: We study the question of recovering two signals w and x from their convolution y = w ∗ x. Generally, the solution to this blind deconvolution problem is non-unique and non-convex. But with assumptions on sparsity, subspace structure and transformed variable, we can convert the non-convex nuclear norm into a convex problem by ”dual-dual” relaxation. In this project, we also implement the convex algorithm proposed in Blind Deconvolution Using Convex Programming, and compare its performance with non-blind and non-convex algorithms. Moreover, the evaluation shows that the convex algorithm is robust against sparsity violation, but sensitive to low-rank condition. At last, we try to extend the algorithm to 2D deconvolution by recovering a blurred image. But the result on 2D deconvolution still need improvement.
Empirical success rate for the blind deconvolution of 1D and 2D matrices.
ML-based Matrix Optimization in Massive MIMO
Abstract: In the downlink of massive MIMO, the transmitter uses precoding technology to reduce interference and improve spectrum efficiency. A complex-valued gradient neural network (CVGNN) is proposed to solve the Moore-Penrose inverse of the complex matrix in massive MIMO precoding algorithms. Theoretical linear convergence and numerical results are provided to corroborate the application of CVGNN in wireless communication senarios.
Linear convergence of CVGNN when solving complex matrix inverse.