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This work considers stochastic optimization problems in which the objective function values can only be computed by a blackbox corrupted by some random noise following an unknown distribution. The proposed method is based on sequential…
$L_1$ regularization is used for finding sparse solutions to an underdetermined linear system. As sparse signals are widely expected in remote sensing, this type of regularization scheme and its extensions have been widely employed in many…
Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…
Purpose: To develop a fast, general-purpose framework for voxelwise noise characterization in linear and nonlinear iterative MRI reconstructions, recovering the image-domain noise variance from which SNR, $g$-factor, and related…
In this work, we study the performance of sub-gradient method (SubGM) on a natural nonconvex and nonsmooth formulation of low-rank matrix recovery with $\ell_1$-loss, where the goal is to recover a low-rank matrix from a limited number of…
The ability for an agent to localize itself within an environment is crucial for many real-world applications. For unknown environments, Simultaneous Localization and Mapping (SLAM) enables incremental and concurrent building of and…
In this paper, we focus on solving an important class of nonconvex optimization problems which includes many problems for example signal processing over a networked multi-agent system and distributed learning over networks. Motivated by…
We propose a method that achieves near-optimal rates for smooth stochastic convex optimization and requires essentially no prior knowledge of problem parameters. This improves on prior work which requires knowing at least the initial…
Optical computing holds promise for high-speed, energy-efficient information processing, with diffractive optical networks emerging as a flexible platform for implementing task-specific transformations. A challenge, however, is the…
In this article, we study several reconstruction methods for the inverse source problem of photoacoustic tomography (PAT) with spatially variable sound speed and damping. The backbone of these methods is the adjoint operators, which we…
Real-time dense scene reconstruction during unstable camera motions is crucial for robotics, yet current RGB-D SLAM systems fail when cameras experience large viewpoint changes, fast motions, or sudden shaking. Classical optimization-based…
Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional…
Bayesian Optimization (BO) methods are useful for optimizing functions that are expen- sive to evaluate, lack an analytical expression and whose evaluations can be contaminated by noise. These methods rely on a probabilistic model of the…
We study spectral learning for orthogonally decomposable (odeco) tensors, emphasizing the interplay between statistical limits, optimization geometry, and initialization. Unlike matrices, recovery for odeco tensors does not hinge on…
Stochastic Gradient (SG) is the defacto iterative technique to solve stochastic optimization (SO) problems with a smooth (non-convex) objective $f$ and a stochastic first-order oracle. SG's attractiveness is due in part to its simplicity of…
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…
The back-end module of Distributed Collaborative Simultaneous Localization and Mapping (DCSLAM) requires solving a nonlinear Pose Graph Optimization (PGO) under a distributed setting, also known as SE(d)-synchronization. Most existing…
Object-oriented SLAM is a popular technology in autonomous driving and robotics. In this paper, we propose a stereo visual SLAM with a robust quadric landmark representation method. The system consists of four components, including deep…
Quantum image processing is a growing field attracting attention from both the quantum computing and image processing communities. We propose a novel method in combining a graph-theoretic approach for optimal surface segmentation and hybrid…
This paper develops a robust angles-only IROD method based on polynomial optimization for arbitrary nonlinear dynamics. First, the relative motion is approximated by high-order Taylor polynomials within the differential algebra framework,…