Related papers: Scalable Incremental Nonconvex Optimization Approa…
We analyze stochastic gradient algorithms for optimizing nonconvex, nonsmooth finite-sum problems. In particular, the objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a possibly…
Phase retrieval (PR) is an ill-conditioned inverse problem which can be found in various science and engineering applications. Assuming sparse priority over the signal of interest, recent algorithms have been developed to solve the phase…
We propose a new randomized algorithm for solving convex optimization problems that have a large number of constraints (with high probability). Existing methods like interior-point or Newton-type algorithms are hard to apply to such…
Compressive phase retrieval refers to the problem of recovering a structured $n$-dimensional complex-valued vector from its phase-less under-determined linear measurements. The non-linearity of measurements makes designing…
We consider the problem of signal reconstruction from quadratic measurements that are encoded as +1 or -1 depending on whether they exceed a predetermined positive threshold or not. Binary measurements are fast to acquire and inexpensive in…
In this paper, we propose a new decomposition approach named the proximal primal dual algorithm (Prox-PDA) for smooth nonconvex linearly constrained optimization problems. The proposed approach is primal-dual based, where the primal step…
Phase retrieval has important applications in optical imaging, communications and sensing. Lifting the dimensionality of the problem allows phase retrieval to be approximated as a convex optimization problem in a higher-dimensional space.…
In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…
This paper considers the problem of solving systems of quadratic equations, namely, recovering an object of interest $\mathbf{x}^{\natural}\in\mathbb{R}^{n}$ from $m$ quadratic equations/samples…
Phase retrieval aims at recovering a complex-valued signal from magnitude-only measurements, which attracts much attention since it has numerous applications in many disciplines. However, phase recovery involves solving a system of…
We improve a phase retrieval approach that uses correlation-based measurements with compactly supported measurement masks [27]. The improved algorithm admits deterministic measurement constructions together with a robust, fast recovery…
We present a novel, practical, and provable approach for solving diagonally constrained semi-definite programming (SDP) problems at scale using accelerated non-convex programming. Our algorithm non-trivially combines acceleration motions…
We propose a novel approach and algorithm based on two preliminary tests of the optical system elements to enhance the super-resolved complex-valued imaging. The approach is developed for inverse phase imaging in a single-shot lensless…
We propose a new method for robust PCA -- the task of recovering a low-rank matrix from sparse corruptions that are of unknown value and support. Our method involves alternating between projecting appropriate residuals onto the set of…
In this work, we consider the low rank decomposition (SDPR) of general convex semidefinite programming problems (SDP) that contain both a positive semidefinite matrix and a nonnegative vector as variables. We develop a rank-support-adaptive…
Nonlinear convex problems arise in various areas of applied mathematics and engineering. Classical techniques such as the relaxed proximal point algorithm (PPA) and the prediction correction (PC) method were proposed for linearly…
Phase retrieval refers to algorithmic methods for recovering a signal from its phaseless measurements. Local search algorithms that work directly on the non-convex formulation of the problem have been very popular recently. Due to the…
We propose and study a class of novel algorithms that aim at solving bilinear and quadratic inverse problems. Using a convex relaxation based on tensorial lifting, and applying first-order proximal algorithms, these problems could be solved…
Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…
The cone of positive-semidefinite (PSD) matrices is fundamental in convex optimization, and we extend this notion to tensors, defining PSD tensors, which correspond to separable quantum states. We study the convex optimization problem over…