MSR-GaN: Multi-segment reconstruction via adversarial learning

Multi-segment reconstruction (MSR) is the problem of estimating a signal given noisy partial observations. Here each observation corresponds to a randomly located segment of the signal. While previous works address this problem using template or moment-matching, in this paper we address MSR from an unsupervised adversarial learning standpoint, named MSR-GAN. We formulate MSR as a distribution matching problem where the goal is to recover the signal and the probability distribution of the segments such that the distribution of the generated measurements following a known forward model is close to the real observations. This is achieved once a min-max optimization involving a generator-discriminator pair is solved. MSR-GAN is mainly inspired by CryoGAN [1]. However, in MSR-GAN we no longer assume the probability distribution of the latent variables, i.e. segment locations, is given and seek to recover it alongside the unknown signal. For this purpose, we show that the loss at the generator side originally is non-differentiable with respect to the segment distribution. Thus, we propose to approximate it using Gumbel-Softmax reparametrization trick. Our proposed solution is generalizable to a wide range of inverse problems. Our simulation results and comparison with various baselines verify the potential of our approach in different settings.