Deep generative demixing: Recovering Lipschitz signals from noisy subgaussian mixtures
Generative neural networks (GNNs) have gained renown for efficaciously capturing intrinsic low-dimensional structure in natural images. Here, we investigate the subgaussian demixing problem for two Lipschitz signals, with GNN demixing as a special case. In demixing, one seeks identification of two signals given their sum and prior structural information. Here, we assume each signal lies in the range of a Lipschitz function, which includes many popular GNNs as a special case. We prove a sample complexity bound for nearly optimal recovery error that extends a recent result of Bora, et al. (2017) from the compressed sensing setting with gaussian matrices to demixing with subgaussian ones. Under a linear signal model in which the signals lie in convex sets, McCoy & Tropp (2014) have characterized the sample complexity for identification under subgaussian mixing. In the present setting, the signal structure need not be convex. For example, our result applies to a domain that is a non-convex union of convex cones. We support the efficacy of this demixing model with numerical simulations using trained GNNs, suggesting an algorithm that would be an interesting object of further theoretical study.
Code (0)
등록된 구현이 없습니다.
Tasks
compressed sensingSimilar Papers 제목 키워드 기반
Fast Algorithms for Demixing Sparse Signals from Nonlinear Observations
We study the problem of demixing a pair of sparse signals from noisy, nonlinear observations of their superposition. Mathematically, we consider a nonlinear signal observation model, $y_i = g(a_i^Tx) + e_i, \ i=1,\ldots,…
AstronomyNonconvex Demixing From Bilinear Measurements
We consider the problem of demixing a sequence of source signals from the sum of noisy bilinear measurements. It is a generalized mathematical model for blind demixing with blind deconvolution, which is prevalent across …
Dictionary LearningLEARNING GENERATIVE MODELS FOR DEMIXING OF STRUCTURED SIGNALS FROM THEIR SUPERPOSITION USING GANS
Recently, Generative Adversarial Networks (GANs) have emerged as a popular alternative for modeling complex high dimensional distributions. Most of the existing works implicitly assume that the clean samples from the tar…
Compressive SensingDenoisingLearning Generative Models of Structured Signals from Their Superposition Using GANs with Application to Denoising and Demixing
Recently, Generative Adversarial Networks (GANs) have emerged as a popular alternative for modeling complex high dimensional distributions. Most of the existing works implicitly assume that the clean samples from the tar…
Compressive SensingDenoisingUnsupervised Demixing of Structured Signals from Their Superposition Using GANs
Recently, Generative Adversarial Networks (GANs) have emerged as a popular alternative for modeling complex high dimensional distributions. Most of the existing works implicitly assume that the clean samples from the tar…