Related papers: Undersampled Phase Retrieval with Outliers
Phase diversity is a widefield aberration correction method that uses multiple images to estimate the phase aberration at the pupil plane of an imaging system by solving an optimization problem. This estimated aberration can then be used to…
Fourier phase retrieval is the problem of reconstructing a signal given only the magnitude of its Fourier transformation. Optimization-based approaches, like the well-established Gerchberg-Saxton or the hybrid input output algorithm,…
We report on progress in algorithms for iterative phase retrieval. The theory of convex optimization is used to develop and to gain insight into counterparts for the nonconvex problem of phase retrieval. We propose a relaxation of averaged…
This paper studies inference in the high-dimensional linear regression model with outliers. Sparsity constraints are imposed on the vector of coefficients of the covariates. The number of outliers can grow with the sample size while their…
The total variation (TV) regularization method is an effective method for image deblurring in preserving edges. However, the TV based solutions usually have some staircase effects. In this paper, in order to alleviate the staircase effect,…
The phase retrieval problem is a fundamental problem in many fields, which is appealing for investigation. It is to recover the signal vector $\tilde{x}\in\mathbb{C}^d$ from a set of $N$ measurements $b_n=|f^*_n\tilde{x}|^2,\ n=1,\cdots,…
Phase noise correction is crucial to exploit full advantage of orthogonal frequency division multiplexing (OFDM) in modern high-data-rate communications. OFDM channel estimation with simultaneous phase noise compensation has therefore drawn…
We consider the problem of robust compressed sensing whose objective is to recover a high-dimensional sparse signal from compressed measurements corrupted by outliers. A new sparse Bayesian learning method is developed for robust compressed…
Recovering images corrupted by multiplicative noise is a well known challenging task. Motivated by the success of multiscale hierarchical decomposition methods (MHDM) in image processing, we adapt a variety of both classical and new…
Implicit samplers are algorithms for producing independent, weighted samples from multi-variate probability distributions. These are often applied in Bayesian data assimilation algorithms. We use Laplace asymptotic expansions to analyze two…
Bayesian hierarchical models can provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models typically comprise a conditionally Gaussian prior model for the unknown which is augmented by a generalized…
In this work we analyze the problem of phase retrieval from Fourier measurements with random diffraction patterns. To this end, we consider the recently introduced PhaseLift algorithm, which expresses the problem in the language of convex…
Recent work has demonstrated the effectiveness of gradient descent for directly recovering the factors of low-rank matrices from random linear measurements in a globally convergent manner when initialized properly. However, the performance…
This paper presents an adaptive and intelligent sparse model for digital image sampling and recovery. In the proposed sampler, we adaptively determine the number of required samples for retrieving image based on space-frequency-gradient…
Recent research has explored using neural networks to reconstruct undersampled magnetic resonance imaging (MRI) data. Because of the complexity of the artifacts in the reconstructed images, there is a need to develop task-based approaches…
Image structure-texture decomposition is a long-standing and fundamental problem in both image processing and computer vision fields. In this paper, we propose a generalized semi-sparse regularization framework for image structural analysis…
Given a real-valued function $f$ defined over a manifold $M$ embedded in $\mathbb{R}^d$, we are interested in recovering structural information about $f$ from the sole information of its values on a finite sample $P$. Existing methods…
Sparsity promoting norms are frequently used in high dimensional regression. A limitation of such Lasso-type estimators is that the optimal regularization parameter depends on the unknown noise level. Estimators such as the concomitant…
We consider the problem of learning an unknown $f$ with a sparse Fourier spectrum in the presence of outlier noise. In particular, the algorithm has access to a noisy oracle for (an unknown) $f$ such that (i) the Fourier spectrum of $f$ is…
A simple, yet general, formalism for the optimized linear combination of astrophysical images is constructed and demonstrated. The formalism allows the user to combine multiple undersampled images to provide oversampled output at high…