Low tubal rank tensor sensing and robust PCA from quantized measurements

发布时间：2022-03-23 作者：浏览次数：

Speaker:	王建军	DateTime:	2022年3月25日（周五）上午9:30--10:30
Brief Introduction to Speaker: 王建军，教授，西南大学。		Place:	腾讯会议：841657597
Abstract:Low-rank tensor Sensing (LRTS) is a natural extension of low-rank matrix Sensing (LRMS) to high-dimensional arrays, which aims to reconstruct an underlying tensor X from incomplete linear measurements M(X). However, LRTS ignores the error caused by quantization, limiting its application when the quantization is low-level. In this work, we take into account the impact of extreme quantization and suppose the quantizer degrades into a comparator that only acquires the signs of M(X). We still hope to recover X from these binary measurements. Under the tensor Singular Value Decomposition (t-SVD) framework, two recovery methods are proposed---the first is a tensor hard singular tube thresholding method; the second is a constrained tensor nuclear norm minimization method. These methods can recover a real n1n2n3 tensor X with tubal rank r from m random Gaussian binary measurements with errors decaying at a polynomial speed of the oversampling factor lambda:=m/((n_1+n_2)n_3r). To improve t...