Related papers: DOLPHIn - Dictionary Learning for Phase Retrieval

In dictionary learning, also known as sparse coding, the algorithm is given samples of the form $y = Ax$ where $x\in \mathbb{R}^m$ is an unknown random sparse vector and $A$ is an unknown dictionary matrix in $\mathbb{R}^{n\times m}$…

A host of problems involve the recovery of structured signals from a dimensionality reduced representation such as a random projection; examples include sparse signals (compressive sensing) and low-rank matrices (matrix completion). Given…

In this paper we study the reconstruction of binary sparse signals from partial random circulant measurements. We show that the reconstruction via the least-squares algorithm is as good as the reconstruction via the usually used program…

Sparse phase retrieval with redundant dictionary is to reconstruct the signals of interest that are (nearly) sparse in a redundant dictionary or frame from the phaseless measurements via the optimization models. Gao [7] presented conditions…

We propose a new algorithm for recovery of sparse signals from their compressively sensed samples. The proposed algorithm benefits from the strategy of gradual movement to estimate the positions of non-zero samples of sparse signal. We…

A new algorithm is proposed for a) unsupervised learning of sparse representations from subsampled measurements and b) estimating the parameters required for linearly reconstructing signals from the sparse codes. We verify that the new…

We study an approach to solving the phase retrieval problem as it arises in a phase-less imaging modality known as ptychography. In ptychography, small overlapping sections of an unknown sample (or signal, say $x_0\in \mathbb{C}^d$) are…

The phase retrieval problem asks to recover a natural signal $y_0 \in \mathbb{R}^n$ from $m$ quadratic observations, where $m$ is to be minimized. As is common in many imaging problems, natural signals are considered sparse with respect to…

This work examines the multi-view compressive phase retrieval problem in a distributed sensor network, where each sensor device, limited by storage and sensing capabilities, can access only intensity measurements from an unknown part of the…

This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal $x \in \mathbb{R}^p$ from noisy quadratic measurements $y_j = (a_j' x )^2 + \epsilon_j$, $j=1, \ldots, m$, with independent sub-exponential noise…

We present a computational imaging mode for large scale electron microscopy data, which retrieves a complex wave from noisy/sparse intensity recordings using a deep learning approach and subsequently reconstructs an image of the specimen…

In the undersampled phase retrieval problem, the goal is to recover an $N$-dimensional complex signal $\mathbf{x}$ from only $M<N$ noisy intensity measurements without phase information. This problem has drawn a lot of attention to reduce…

Imaging systems' performance at low light intensity is affected by shot noise, which becomes increasingly strong as the power of the light source decreases. In this paper we experimentally demonstrate the use of deep neural networks to…

This paper considers the problem of recovering a $k$-sparse, $N$-dimensional complex signal from Fourier magnitude measurements. It proposes a Fourier optics setup such that signal recovery up to a global phase factor is possible with very…

We consider the problem of recovering a signal $\mathbf{x}^* \in \mathbf{R}^n$, from magnitude-only measurements $y_i = |\left\langle\mathbf{a}_i,\mathbf{x}^*\right\rangle|$ for $i=[m]$. Also called the phase retrieval, this is a…

We propose a robust and efficient approach to the problem of compressive phase retrieval in which the goal is to reconstruct a sparse vector from the magnitude of a number of its linear measurements. The proposed framework relies on…

We apply basic statistical reasoning to signal reconstruction by machine learning -- learning to map corrupted observations to clean signals -- with a simple and powerful conclusion: it is possible to learn to restore images by only looking…

We address the problem of signal reconstruction from intensity measurements with respect to a measurement frame. This non-convex inverse problem is known as phase retrieval. The case considered in this paper concerns phaseless measurements…

Dictionary learning and sparse coding have been widely studied as mechanisms for unsupervised feature learning. Unsupervised learning could bring enormous benefit to the processing of hyperspectral images and to other remote sensing data…

In the compressive phase retrieval problem, or phaseless compressed sensing, or compressed sensing from intensity only measurements, the goal is to reconstruct a sparse or approximately $k$-sparse vector $x \in \mathbb{R}^n$ given access to…