1-Bit compressed sensing of positive semi-definite matrices via rank-1 measurement matrices
In this paper, we investigate the problem of recovering positive semi-definite (PSD) matrix from 1-bit sensing. The measurement matrix is rank-1 and constructed by the outer product of a pair of vectors, whose entries are independent and identically distributed (i.i.d.) Gaussian variables. The recovery problem is solved in closed form through a convex programming. Our analysis reveals that the solution is biased in general. However, in case of error-free measurement, we find that for rank-r PSD matrix with bounded condition number, the bias decreases with an order of O(1/r). Therefore, an approximate recovery is still possible. Numerical experiments are conducted to verify our analysis.
Summary form only given, as follows. A study is presented of precision constraints imposed by a hybrid chip architecture with analog neurons and digital backpropagation calculations. Conversions between the analog and digital domains and weight storage restrictions impose precision limits on both analog and digital calculations. It is shown through simulations that a learning system of this nature can be implemented in spite of limited resolution in the analog circuits and using fixed-point arithmetic to implement the backpropagation algorithm. >