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Lensless cameras provide a framework to build thin imaging systems by replacing the lens in a conventional camera with an amplitude or phase mask near the sensor. Existing methods for lensless imaging can recover the depth and intensity of…
Highly multiplexed microscopy enables rich spatial characterization of tissues at single-cell resolution, yet most analyses rely on two-dimensional sections despite inherently three-dimensional tissue organization. Acquiring dense…
We consider the problem of recovering a compactly-supported function from a finite collection of pointwise samples of its Fourier transform taking nonuniformly. First, we show that under suitable conditions on the sampling frequencies -…
Let $K$ be a field of characteristic $0$. We present an explicit algorithm that, given the invariants of a generic homogeneous polynomial $f$ under the linear action of $\mathrm{GL}_n$ or $\mathrm{SL}_n$, returns a polynomial differing from…
Low rank matrix recovery problems, including matrix completion and matrix sensing, appear in a broad range of applications. In this work we present GNMR -- an extremely simple iterative algorithm for low rank matrix recovery, based on a…
This paper proposes a polynomial-time algorithm to construct the monotone stepwise curve that minimizes the sum of squared errors with respect to a given cloud of data points. The fitted curve is also constrained on the maximum number of…
Sparse dictionary coding represents signals as linear combinations of a few dictionary atoms. It has been applied to images, time series, graph signals and multi-way spatio-temporal data by jointly employing temporal and spatial…
The task of reconstructing a low rank matrix from incomplete linear measurements arises in areas such as machine learning, quantum state tomography and in the phase retrieval problem. In this note, we study the particular setup that the…
In this paper, we consider the problem of reconstructing piecewise smooth functions to high accuracy from nonuniform samples of their Fourier transform. We use the framework of nonuniform generalized sampling (NUGS) to do this, and to…
We propose a compressive sensing algorithm that exploits geometric properties of images to recover images of high quality from few measurements. The image reconstruction is done by iterating the two following steps: 1) estimation of normal…
In this paper, we consider the problem of recovering a compactly supported multivariate function from a collection of pointwise samples of its Fourier transform taken nonuniformly. We do this by using the concept of weighted Fourier frames.…
Phase retrieval arises in various fields of science and engineering and it is well studied in a finite-dimensional setting. In this paper, we consider an infinite-dimensional phase retrieval problem to reconstruct real-valued signals living…
This paper investigates graph clustering in the planted cluster model in the presence of {\em small clusters}. Traditional results dictate that for an algorithm to provably correctly recover the clusters, {\em all} clusters must be…
We analyze a practical algorithm for sparse PCA on incomplete and noisy data under a general non-random sampling scheme. The algorithm is based on a semidefinite relaxation of the $\ell_1$-regularized PCA problem. We provide theoretical…
We consider network topology identification subject to a signal smoothness prior on the nodal observations. A fast dual-based proximal gradient algorithm is developed to efficiently tackle a strongly convex, smoothness-regularized network…
Exploring deep convolutional neural networks of high efficiency and low memory usage is very essential for a wide variety of machine learning tasks. Most of existing approaches used to accelerate deep models by manipulating parameters or…
Recent work on background subtraction has shown developments on two major fronts. In one, there has been increasing sophistication of probabilistic models, from mixtures of Gaussians at each pixel [7], to kernel density estimates at each…
Many problems in data science can be treated as estimating a low-rank matrix from highly incomplete, sometimes even corrupted, observations. One popular approach is to resort to matrix factorization, where the low-rank matrix factors are…
We propose a simple mechanism by which scaling laws emerge from feature learning in multi-layer networks. We study a high-dimensional hierarchical target that is a globally high-degree function, but that can be represented by a combination…
Multi-index models - functions which only depend on the covariates through a non-linear transformation of their projection on a subspace - are a useful benchmark for investigating feature learning with neural nets. This paper examines the…