Low-rank plus sparse trajectory decomposition for direct exoplanet imaging

Abstract: We propose a direct imaging method for the detection of exoplanets based on a combined low-rank plus structured sparse model. For this task, we develop a dictionary of possible effective circular trajectories a planet can take during the observation time, elements of which can be efficiently computed using rotation and convolution operation.

Signal Processing with Optical Quadratic Random Sketches

Abstract: Random data sketching (or projection) is now a classical technique enabling, for instance, approximate numerical linear algebra and machine learning algorithms with reduced computational complexity and memory. In this context, the possibility of performing data processing (such as pattern detection or classification) directly in the sketched domain without accessing the original data was previously achieved for linear random sketching methods and compressive sensing.

ROP inception: signal estimation with quadratic random sketching

Abstract: Rank-one projections (ROP) of matrices and quadratic random sketching of signals support several data processing and machine learning methods, as well as recent imaging applications, such as phase retrieval or optical processing units.

An Interferometric view of Speckle Imaging

Abstract: Lensless endoscopy (LE) with multicore fibers (MCF) enables fluorescent imaging of biological samples at cellular scale. In this work, we show that the corresponding imaging process is tantamount to collecting multiple rank-one projections (ROP) of an Hermitian interferometric matrix—a matrix encoding a subsampling of the Fourier transform of the sample image.

The Separation Capacity of Random Neural Networks

Abstract: Neural networks (NNs) with random weights appear in a variety of machine learning applications, perhaps most prominently as initialization of many deep learning algorithms. We take one step closer to their theoretical foundation by addressing the following data separation problem: Under what conditions can a random NN make two classes \(\mathcal X^{-}, \mathcal X^{\plus} \subset \mathbb R^{d}\) (with positive distance) linearly separable?

Going Below and Beyond, Off-the-Grid Velocity Estimation from 1-bit Radar Measurements

Abstract: In this paper we propose to bridge the gap between using extremely low resolution 1-bit measurements and estimating targets’ parameters, such as their velocities, that exist in a continuum, i.

Sparse Factorization-based Detection of Off-the-Grid Moving targets using FMCW radars

Abstract: In this paper, we investigate the application of continuous sparse signal reconstruction algorithms for the estimation of the ranges and speeds of multiple moving targets using an FMCW radar. Conventionally, to be reconstructed, continuous sparse signals are approximated by a discrete representation.

Compressive Learning of Generative Networks

Abstract: Generative networks implicitly approximate complex densities from their sampling with impressive accuracy. However, because of the enormous scale of modern datasets, this training process is often computationally expensive. We cast generative network training into the recent framework of compressive learning: we reduce the computational burden of large-scale datasets by first harshly compressing them in a single pass as a single sketch vector.

Factorization over interpolation: A fast continuous orthogonal matching pursuit

Abstract: We propose a fast greedy algorithm to compute sparse representations of signals from continuous dictionaries that are factorizable, i.e., with atoms that can be separated as a product of sub-atoms.

Keep the phase! Signal recovery in phase-only compressive sensing

Abstract: We demonstrate that a sparse signal can be estimated from the phase of complex random measurements, in a “phase-only compressive sensing” (PO-CS) scenario. With high probability and up to a global unknown amplitude, we can perfectly recover such a signal if the sensing matrix is a complex Gaussian random matrix and the number of measurements is large compared to the signal sparsity.