Related papers: Simultaneous Phase Retrieval and Blind Deconvoluti…
In this paper we analyze the blind deconvolution of an image and an unknown blur in a coded imaging system. The measurements consist of subsampled convolution of an unknown blurring kernel with multiple random binary modulations (coded…
Alternating minimization, or Fienup methods, have a long history in phase retrieval. We provide new insights related to the empirical and theoretical analysis of these algorithms when used with Fourier measurements and combined with convex…
We study phase retrieval from magnitude measurements of an unknown signal as an algebraic estimation problem. Indeed, phase retrieval from rank-one and more general linear measurements can be treated in an algebraic way. It is verified that…
Low-rank matrix recovery from structured measurements has been a topic of intense study in the last decade and many important problems like matrix completion and blind deconvolution have been formulated in this framework. An important…
Many applications have benefited remarkably from low-dimensional models in the recent decade. The fact that many signals, though high dimensional, are intrinsically low dimensional has given the possibility to recover them stably from a…
Recent progress in robust statistical learning has mainly tackled convex problems, like mean estimation or linear regression, with non-convex challenges receiving less attention. Phase retrieval exemplifies such a non-convex problem,…
In this paper, we introduce two symmetric directed graphs depending on supports of signals and windows, and we show that the connectivity of those graphs provides either necessary and sufficient conditions to phase retrieval of a signal…
Blind deconvolution and demixing is the problem of reconstructing convolved signals and kernels from the sum of their convolutions. This problem arises in many applications, such as blind MIMO. This work presents a separable approach to…
Magnetic Particle Imaging (MPI) is an emerging imaging modality that maps the spatial distribution of magnetic nanoparticles. The x-space reconstruction in MPI results in highly blurry images, where the resolution depends on both system…
In this paper, we consider recovery of jointly sparse multichannel signals from incomplete measurements. Several approaches have been developed to recover the unknown sparse vectors from the given observations, including thresholding,…
The recovery of a signal from the magnitude of its Fourier transform, also known as phase retrieval, is of fundamental importance in many scientific fields. It is well known that due to the loss of Fourier phase the problem in 1D is…
We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover…
This paper discusses the noisy phase retrieval problem: recovering a complex image signal with independent noise from quadratic measurements. Inspired by the dark fringes shown in the measured images of the array detector, a novel phase…
We develop a fast phase retrieval method which can utilize a large class of local phaseless correlation-based measurements in order to recover a given signal ${\bf x} \in \mathbb{C}^d$ (up to an unknown global phase) in near-linear…
Mean field theory has provided theoretical insights into various algorithms by letting the problem size tend to infinity. We argue that the applications of mean-field theory go beyond theoretical insights as it can inspire the design of…
We consider the problem of recovering an unknown signal $\pmb{x}_0\in \mathbb{R}^{n}$ from phaseless measurements. In this paper, we study the convex phase retrieval problem via PhaseLift from linear Gaussian measurements perturbed by…
We solve the compressive sensing problem via convolutional factor analysis, where the convolutional dictionaries are learned {\em in situ} from the compressed measurements. An alternating direction method of multipliers (ADMM) paradigm for…
Multi-channel sparse blind deconvolution, or convolutional sparse coding, refers to the problem of learning an unknown filter by observing its circulant convolutions with multiple input signals that are sparse. This problem finds numerous…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
In many applications and physical phenomena, bivariate signals are polarized, i.e. they trace an elliptical trajectory over time when viewed in the 2D planes of their two components. The smooth evolution of this elliptical trajectory,…