Related papers: PRIME: Phase Retrieval via Majorization-Minimizati…
Proximal algorithms have gained popularity in recent years in large-scale and distributed optimization problems. One such problem is the phase retrieval problem, for which proximal operators have been proposed recently. The phase retrieval…
The problem of recovering a one-dimensional signal from its Fourier transform magnitude, called Fourier phase retrieval, is ill-posed in most cases. We consider the closely-related problem of recovering a signal from its phaseless…
Recovering an unknown complex signal from the magnitude of linear combinations of the signal is referred to as phase retrieval. We present an exact performance analysis of a recently proposed convex-optimization-formulation for this…
This monograph presents a theoretical background and a broad introduction to the Min-Max Framework for Majorization-Minimization (MM4MM), an algorithmic methodology for solving minimization problems by formulating them as min-max problems…
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…
Stochastic majorization-minimization (SMM) is a class of stochastic optimization algorithms that proceed by sampling new data points and minimizing a recursive average of surrogate functions of an objective function. The surrogates are…
This paper considers phase retrieval from the magnitude of 1D over-sampled Fourier measurements, a classical problem that has challenged researchers in various fields of science and engineering. We show that an optimal vector in a…
Phase retrieval (PR) concerns the recovery of complex phases from complex magnitudes. We identify the connection between the difficulty level and the number and variety of symmetries in PR problems. We focus on the most difficult far-field…
We propose a new majorization-minimization (MM) method for non-smooth and non-convex programs, which is general enough to include the existing MM methods. Besides the local majorization condition, we only require that the difference between…
Block majorization-minimization (BMM) is a simple iterative algorithm for constrained nonconvex optimization that sequentially minimizes majorizing surrogates of the objective function in each block while the others are held fixed. BMM…
The problem of recovering a signal $\mathbf{x}\in \mathbb{R}^n$ from a set of magnitude measurements $y_i=|\langle \mathbf{a}_i, \mathbf{x} \rangle |, \; i=1,\ldots,m$ is referred as phase retrieval, which has many applications in fields of…
Phase retrieval problems in antenna measurements arise when a reference phase cannot be provided to all measurement locations. Phase retrieval algorithms require sufficiently many independent measurement samples of the radiated fields to be…
In this short note we propose a simple two-stage sparse phase retrieval strategy that uses a near-optimal number of measurements, and is both computationally efficient and robust to measurement noise. In addition, the proposed strategy is…
Missing data is a common problem in clinical data collection, which causes difficulty in the statistical analysis of such data. To overcome problems caused by incomplete data, we propose a new imputation method called projective resampling…
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.…
In this work we propose a nonconvex two-stage \underline{s}tochastic \underline{a}lternating \underline{m}inimizing (SAM) method for sparse phase retrieval. The proposed algorithm is guaranteed to have an exact recovery from $O(s\log n)$…
We propose a general framework for reconstructing transform-sparse images from undersampled (squared)-magnitude data corrupted with outliers. This framework is implemented using a multi-layered approach, combining multiple initializations…
Phase retrieval deals with the estimation of complex-valued signals solely from the magnitudes of linear measurements. While there has been a recent explosion in the development of phase retrieval algorithms, the lack of a common interface…
In diffraction imaging, one is tasked with reconstructing a signal from its power spectrum. To resolve the ambiguity in this inverse problem, one might invoke prior knowledge about the signal, but phase retrieval algorithms in this vein…
Phase retrieval refers to the problem of recovering real- or complex-valued vectors from magnitude measurements. The best-known algorithms for this problem are iterative in nature and rely on so-called spectral initializers that provide…