Seminar Details
2019-03-12 (14:00) : One-Bit Sensing of Low-Rank and Bisparse Matrices
At Euler building (room A.002)
Organized by Mathematical Engineering
Speaker :
Jacques, Laurent
Abstract :
In this talk, we will consider the worst-case recovery error of
low-rank and bisparse matrices as a function of the number of one-bit
measurements used to acquire them, i.e., when these matrices are
randomly projected into a low-dimensional domain and only the signs of
the resulting coordinates are recorded.
Such matrices are of practical interest for instance in the problems of
sparse phase retrieval, sparse PCA, or in optical applications involving
far-field observations of sparse scenes. First, by way of the concept of
consistency width, we will review precise estimates on how fast the
recovery error can in theory decay. Next, we will analyze an idealized
recovery method reaching the fourth-root of the optimal decay rate for
Gaussian sensing schemes. This idealized method being impractical, an
implementable recovery algorithm will be finally proposed in the context
of factorized Gaussian sensing schemes. In this case, the recovery error
provably decays as the sixth-root of the optimal rate.
Joint work with Simon Foucart (Texas A&M University, USA)