Nonlinear blind compressed sensing under signal dependent noise

Ajit Rajwade

Abstract:

In this paper, we consider the problem of nonlinear blind
compressed sensing, i.e. jointly estimating the sparse codes
and sparsity-promoting basis, under signal-dependent noise.
We focus our efforts on the Poisson noise model, though
other signal-dependent noise models can be considered. By
employing a well-known variance stabilizing transform such
as the Anscombe transform, we formulate our task as a nonlinear least squares problem with the `1 penalty imposed for
promoting sparsity. We solve this objective function under
non-negativity constraints imposed on both the sparse codes
and the basis. To this end, we propose a multiplicative
update rule, similar to that used in non-negative matrix
factorization (NMF), for our alternating minimization algorithm. To the best of our knowledge, this is the first attempt
at a formulation for nonlinear blind compressed sensing,
with and without the Poisson noise model. Further, we also
provide some theoretical bounds on the performance of our
algorithm