PLUGIn-CS: A simple algorithm for compressive sensing with generative prior

Abstract

We consider the problem of recovering an unknown latent code vector under a known generative model from compressive measurements. For a d-layer deep generative network G:R^n_0 R^n_d with ReLU activation functions and compressive measurement matrix R^m n_d, let the observation be G(x)+ where is noise. We introduce a simple novel algorithm, Partially Linearized Update for Generative Inversion in Compressive Sensing (PLUGIn-CS), to estimate x (and thus G(x)). We prove that, when sensing matrix and weights are Gaussian, if layer widths n_i 5^i n_0 and number of measurements m 2^dn_0 (both up to log factors), then the algorithm converges geometrically to a (small) neighbourhood of x with high probability. Note the inequality on layer widths allows n_i>n_i+1 when i 1 and thus allows the network to have some contractive layers. After a sufficient number of iterations, the estimation errors for both x and G(x) are at most in the order of 4^dn_0/m \|\|. Numerical experiments on synthetic data and real data are provided to validate our theoretical results and to illustrate that the algorithm can effectively recover images from compressive measurements.

Tasks

Reproductions