Related papers: Robust Recovery via Implicit Bias of Discrepant Le…

Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can…

While overparameterization in machine learning models offers great benefits in terms of optimization and generalization, it also leads to increased computational requirements as model sizes grow. In this work, we show that by leveraging the…

Neural networks trained to minimize the logistic (a.k.a. cross-entropy) loss with gradient-based methods are observed to perform well in many supervised classification tasks. Towards understanding this phenomenon, we analyze the training…

This paper considers a large class of problems where we seek to recover a low rank matrix and/or sparse vector from some set of measurements. While methods based on convex relaxations suffer from a (possibly large) estimator bias, and other…

The data consistency for the physical forward model is crucial in inverse problems, especially in MR imaging reconstruction. The standard way is to unroll an iterative algorithm into a neural network with a forward model embedded. The…

Deep convolutional neural networks trained on large datsets have emerged as an intriguing alternative for compressing images and solving inverse problems such as denoising and compressive sensing. However, it has only recently been realized…

Recent research in neural networks and machine learning suggests that using many more parameters than strictly required by the initial complexity of a regression problem can result in more accurate or faster-converging models -- contrary to…

Discriminative self-supervised learning allows training models on any random group of internet images, and possibly recover salient information that helps differentiate between the images. Applied to ImageNet, this leads to object centric…

We study a new family of inverse problems for recovering representations of corrupted data. We assume access to a pre-trained representation learning network R(x) that operates on clean images, like CLIP. The problem is to recover the…

Significant challenges exist in efficient data analysis of most advanced experimental and observational techniques because the collected signals often include unwanted contributions--such as background and signal distortions--that can…

We consider the case of inpainting single depth images. Without corresponding color images, previous or next frames, depth image inpainting is quite challenging. One natural solution is to regard the image as a matrix and adopt the low rank…

Traditional algorithms for compressive sensing recovery are computationally expensive and are ineffective at low measurement rates. In this work, we propose a data driven non-iterative algorithm to overcome the shortcomings of earlier…

We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…

Over parameterization is a common technique in deep learning to help models learn and generalize sufficiently to the given task; nonetheless, this often leads to enormous network structures and consumes considerable computing resources…

In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…

Deep learning is emerging as a new paradigm for solving inverse imaging problems. However, the deep learning methods often lack the assurance of traditional physics-based methods due to the lack of physical information considerations in…

Although statistical learning theory provides a robust framework to understand supervised learning, many theoretical aspects of deep learning remain unclear, in particular how different architectures may lead to inductive bias when trained…

We introduce a structured low rank matrix completion algorithm to recover a series of images from their under-sampled measurements, where the signal along the parameter dimension at every pixel is described by a linear combination of…

We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often…

In practical instances of nonconvex matrix factorization, the rank of the true solution $r^{\star}$ is often unknown, so the rank $r$ of the model can be overspecified as $r>r^{\star}$. This over-parameterized regime of matrix factorization…