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Speckle noise is an inherent disturbance in coherent imaging systems such as digital holography, synthetic aperture radar, optical coherence tomography, or ultrasound systems. These systems usually produce only single observation per view…
Most existing bounds for signal reconstruction from compressive measurements make the assumption of additive signal-independent noise. However in many compressive imaging systems, the noise statistics are more accurately represented by…
Conventional sparse phase retrieval schemes can recover sparse signals from the magnitude of linear measurements only up to a global phase ambiguity. This work proposes a novel approach that instead utilizes the magnitude of affine…
We propose two novel approaches to the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as simplex…
Phase recovery from the bispectrum is a central problem in speckle interferometry which can be posed as an optimization problem minimizing a weighted nonlinear least-squares objective function. We look at two different formulations of the…
Coherent X-ray diffraction imaging (CXDI) experiments are intrinsically limited by shot noise, a lack of prior knowledge about the sample's support, and missing measurements due to the experimental geometry. We propose a flexible, iterative…
Rapid development of sparse sampling methodology offers dramatic increase in power and efficiency of magnetic resonance techniques in medicine, chemistry, molecular structural biology, and other fields. We suggest to use available yet…
In this work we develop an algorithm for signal reconstruction from the magnitude of its Fourier transform in a situation where some (non-zero) parts of the sought signal are known. Although our method does not assume that the known part…
We demonstrate through numerical simulations with real data the feasibility of using compressive sensing techniques for the acquisition of spectro-polarimetric data. This allows us to combine the measurement and the compression process into…
We propose a general framework to recover underlying images from noisy phaseless diffraction measurements based on the alternating directional method of multipliers and the plug-and-play technique. The algorithm consists of three-step…
Phase retrieval with pre-defined optical masks can provide extra constraint and thus achieve improved performance. The recent progress in optimization theory demonstrates the superiority of random masks in phase retrieval algorithms.…
We consider the problem of finding a low rank symmetric matrix satisfying a system of linear equations, as appears in phase retrieval. In particular, we solve the gauge dual formulation, but use a fast approximation of the spectral…
Phase retrieval refers to the problem of reconstructing an unknown vector $x_0 \in \mathbb{C}^n$ or $x_0 \in \mathbb{R}^n $ from $m$ measurements of the form $y_i = \big\vert \langle \xi^{\left(i\right)}, x_0 \rangle \big\vert^2 $, where $…
The null vector method, based on a simple linear algebraic concept, is proposed as a solution to the phase retrieval problem. In the case with complex Gaussian random measurement matrices, a non-asymptotic error bound is derived, yielding…
Medical image segmentation is a challenging task with inherent ambiguity and high uncertainty, attributed to factors such as unclear tumor boundaries and multiple plausible annotations. The accuracy and diversity of segmentation masks are…
This article describes a fast iterative algorithm for image denoising and deconvolution with signal-dependent observation noise. We use an optimization strategy based on variable splitting that adapts traditional Gaussian noise-based…
The support recovery problem consists of determining a sparse subset of variables that is relevant in generating a set of observations. In this paper, we study the support recovery problem in the phase retrieval model consisting of noisy…
The paper analyses the possibility to recover different biomedical signals if limited number of samples is available. Having in mind that monitoring of health condition is done by measuring and observing key parameters such as heart…
In this paper, we study the phase retrieval problem in the situation where the vector to be recovered has an a priori structure that can encoded into a regularization term. This regularizer is intended to promote solutions conforming to…
In this paper, we study the problem of sparse vector recovery at the fusion center of a sensor network from linear sensor measurements when there is missing data. In the presence of missing data, the random sampling approach employed in…