Probabilistic low-rank matrix recovery from quantized measurements: Application to image denoising

We consider the recovery of a low-rank matrix or image M given its noisy quantized (or discrete) measurements. We consider constrained maximum likelihood estimation of M, under a constraint on the entry-wise infinity-norm of M and an exact rank constraint. We provide an upper bound on the Frobenius norm of the matrix estimation error under this model. Past work on theoretical investigations have been restricted to binary quantizers, and based on convex relaxation of the rank. We consider a globally convergent optimization algorithm exploiting existing work on low-rank factorization of M and validate the method on synthetic and real images.