Modeling Sparse Deviations for Compressed Sensing using Generative Models
This addresses the limitation of existing generative model methods in compressed sensing, which are restricted to a small support set, by allowing sparse deviations for broader applicability.
The paper tackles the problem of compressed sensing by proposing Sparse-Gen, a framework that combines domain-specific generative models with sparse deviations to enable reconstruction over the full signal space, achieving consistent improvements in accuracy, especially in transfer compressed sensing scenarios.
In compressed sensing, a small number of linear measurements can be used to reconstruct an unknown signal. Existing approaches leverage assumptions on the structure of these signals, such as sparsity or the availability of a generative model. A domain-specific generative model can provide a stronger prior and thus allow for recovery with far fewer measurements. However, unlike sparsity-based approaches, existing methods based on generative models guarantee exact recovery only over their support, which is typically only a small subset of the space on which the signals are defined. We propose Sparse-Gen, a framework that allows for sparse deviations from the support set, thereby achieving the best of both worlds by using a domain specific prior and allowing reconstruction over the full space of signals. Theoretically, our framework provides a new class of signals that can be acquired using compressed sensing, reducing classic sparse vector recovery to a special case and avoiding the restrictive support due to a generative model prior. Empirically, we observe consistent improvements in reconstruction accuracy over competing approaches, especially in the more practical setting of transfer compressed sensing where a generative model for a data-rich, source domain aids sensing on a data-scarce, target domain.