Related papers: Simple Alternating Minimization Provably Solves Co…
We propose and analyze a new family of algorithms for training neural networks with ReLU activations. Our algorithms are based on the technique of alternating minimization: estimating the activation patterns of each ReLU for all given…
Learning optimal dictionaries for sparse coding has exposed characteristic sparse features of many natural signals. However, universal guarantees of the stability of such features in the presence of noise are lacking. Here, we provide very…
Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries…
In this paper, we propose an algorithm based on the Alternating Minimization technique to solve the uplink massive MIMO detection problem. The proposed algorithm provides a lower complexity compared to the conventional MMSE detection…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
The dictionary learning problem concerns the task of representing data as sparse linear sums drawn from a smaller collection of basic building blocks. In application domains where such techniques are deployed, we frequently encounter…
We consider the task of aligning two sets of points in high dimension, which has many applications in natural language processing and computer vision. As an example, it was recently shown that it is possible to infer a bilingual lexicon,…
Owing to the edge preserving ability and low computational cost of the total variation (TV), variational models with the TV regularization have been widely investigated in the field of multiplicative noise removal. The key points of the…
In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…
A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…
Sparse coding and dictionary learning are popular techniques for linear inverse problems such as denoising or inpainting. However in many cases, the measurement process is nonlinear, for example for clipped, quantized or 1-bit measurements.…
This article presents novel results concerning the recovery of signals from undersampled data in the common situation where such signals are not sparse in an orthonormal basis or incoherent dictionary, but in a truly redundant dictionary.…
We analyze the performance of alternating minimization for loss functions optimized over two variables, where each variable may be restricted to lie in some potentially nonconvex constraint set. This type of setting arises naturally in…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex…
We describe and examine an algorithm for tomographic image reconstruction where prior knowledge about the solution is available in the form of training images. We first construct a nonnegative dictionary based on prototype elements from the…
Modeling data with linear combinations of a few elements from a learned dictionary has been the focus of much recent research in machine learning, neuroscience and signal processing. For signals such as natural images that admit such sparse…
In this paper, we propose and study the use of alternating direction algorithms for several $\ell_1$-norm minimization problems arising from sparse solution recovery in compressive sensing, including the basis pursuit problem, the…
Automatic segmentation of text into minimal content-bearing units is an unsolved problem even for languages like English. Spaces between words offer an easy first approximation, but this approximation is not good enough for machine…
A judicious combination of dictionary learning methods, block sparsity and source recovery algorithm are used in a hierarchical manner to identify the noises and the speakers from a noisy conversation between two people. Conversations are…