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The goal of compressed sensing is to estimate a high dimensional vector from an underdetermined system of noisy linear equations. In analogy to classical compressed sensing, here we assume a generative model as a prior, that is, we assume the vector is represented by a deep generative model $G: mathbb{R}^k rightarrow mathbb{R}^n$. Classical recovery approaches such as empirical risk minimization (ERM) are guaranteed to succeed when the measurement matrix is sub-Gaussian. However, when the measurement matrix and measurements are heavy-tailed or have outliers, recovery may fail dramatically. In this paper we propose an algorithm inspired by the Median-of-Means (MOM). Our algorithm guarantees recovery for heavy-tailed data, even in the presence of outliers. Theoretically, our results show our novel MOM-based algorithm enjoys the same sample complexity guarantees as ERM under sub-Gaussian assumptions. Our experiments validate both aspects of our claims: other algorithms are indeed fragile and fail under heavy-tailed and/or corrupted data, while our approach exhibits the predicted robustness.
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 domai
We introduce a recursive algorithm for performing compressed sensing on streaming data. The approach consists of a) recursive encoding, where we sample the input stream via overlapping windowing and make use of the previous measurement in obtaining t
This letter proposes a sparse diffusion steepest-descent algorithm for one bit compressed sensing in wireless sensor networks. The approach exploits the diffusion strategy from distributed learning in the one bit compressed sensing framework. To esti
The CSGM framework (Bora-Jalal-Price-Dimakis17) has shown that deep generative priors can be powerful tools for solving inverse problems. However, to date this framework has been empirically successful only on certain datasets (for example, human fac
A pre-trained generator has been frequently adopted in compressed sensing (CS) due to its ability to effectively estimate signals with the prior of NNs. In order to further refine the NN-based prior, we propose a framework that allows the generator t