Related papers: Constant-Expansion Suffices for Compressed Sensing…
Compressive sensing is a signal acquisition framework based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable recovery. In this paper we introduce a new theory for…
The ability to discriminate similar visual stimuli is an important index of memory function. This ability is widely thought to be supported by expanding the dimensionality of relevant neural codes, such that neural representations for…
Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can…
The rapid expansion of computational capabilities and the ever-growing scale of modern HPC systems present formidable challenges in managing exascale scientific data. Faced with such vast datasets, traditional lossless compression…
Deep neural networks have achieved state-of-the-art performance across numerous applications, but their high memory and computational demands present significant challenges, particularly in resource-constrained environments. Model…
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…
In this paper we consider the problem of recovering a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model that can efficiently restrict the degrees of freedom of the problem and is…
One of the challenges in the study of Generative Adversarial Networks (GANs) is the difficulty of its performance control. Lipschitz constraint is essential in guaranteeing training stability for GANs. Although heuristic methods such as…
We present a smooth probabilistic reformulation of $\ell_0$ regularized regression that does not require Monte Carlo sampling and allows for the computation of exact gradients, facilitating rapid convergence to local optima of the best…
Deep generative models are rapidly gaining traction in medical imaging. Nonetheless, most generative architectures struggle to capture the underlying probability distributions of volumetric data, exhibit convergence problems, and offer no…
What learning algorithms can be run directly on compressively-sensed data? In this work, we consider the question of accurately and efficiently computing low-rank matrix or tensor factorizations given data compressed via random projections.…
This paper presents a novel compressed sensing (CS) approach to high dimensional wireless channel estimation by optimizing the input to a deep generative network. Channel estimation using generative networks relies on the assumption that…
We characterize the measurement complexity of compressed sensing of signals drawn from a known prior distribution, even when the support of the prior is the entire space (rather than, say, sparse vectors). We show for Gaussian measurements…
Recent advances in quantized compressed sensing and high-dimensional estimation have shown that signal recovery is even feasible under strong non-linear distortions in the observation process. An important characteristic of associated…
Deep Neural Networks (DNNs) have aroused great attention in Compressed Sensing (CS) restoration. However, the working mechanism of DNNs is not explainable, thereby it is unclear that how to design an optimal DNNs for CS restoration. In this…
Brenier proved that under certain conditions on a source and a target probability measure there exists a strictly convex function such that its gradient is a transport map from the source to the target distribution. This function is called…
This paper shows how sparse, high-dimensional probability distributions could be represented by neurons with exponential compression. The representation is a novel application of compressive sensing to sparse probability distributions…
In order to handle large data sets omnipresent in modern science, efficient compression algorithms are necessary. Here, a Bayesian data compression (BDC) algorithm that adapts to the specific measurement situation is derived in the context…
The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an…
We introduce Parseval networks, a form of deep neural networks in which the Lipschitz constant of linear, convolutional and aggregation layers is constrained to be smaller than 1. Parseval networks are empirically and theoretically…