SIAM Journal on Imaging Sciences

A rank-$r$ matrix $X \in \mathbb{R}^{m \times n}$ can be written as a product $U V^\top$, where $U \in \mathbb{R}^{m \times r}$ and $V \in \mathbb{R}^{n \times r}$. One could exploit this observation in optimization: e.g., consider the minimization of a ...

We propose BinaryRelax, a simple two-phase algorithm, for training deep neural networks with quantized weights. The set constraint that characterizes the quantization of weights is not imposed until the late stage of training, and a sequence of pseudo ...

A crucial limitation of current high-resolution 3D photoacoustic tomography (PAT) devices that employ sequential scanning is their long acquisition time. In previous work, we demonstrated how to use compressed sensing techniques to improve upon this: ...

In recent years, improvements in various image acquisition techniques gave rise to the need for adaptive processing methods, aimed particularly for large datasets corrupted by noise and deformations. In this work, we consider datasets of images sampled ...

Extraction of local features constitutes a first step of many algorithms used in computer vision. The choice of keypoints and local features is often driven by the optimization of a performance criterion on a given computer vision task, which sometimes ...

The goal of this paper is to develop a globally convergent numerical method for the inverse problem which would work with the optical experimental data collected by this research group. Only the intensity (modulus square) of the total complex valued wave ...

This paper is concerned with applications of the theory of approximation and interpolation based on compensated convex transforms developed in [K. Zhang, E. Crooks, and A. Orlando, SIAM J. Math. Anal., 48 (2016), pp. 4126--4154]. We apply our methods to (i) ...

In recent years, the mathematical and algorithmic aspects of the phase retrieval problem have received considerable attention. Many papers in this area mention crystallography as a principal application. In crystallography, the signal to be recovered is ...

Exemplar-based texture synthesis consists in producing new synthetic images which have the same perceptual characteristics as a given texture sample while exhibiting sufficient innovation (to avoid verbatim copy). In this paper, we propose to address this ...

The minimization of a nonconvex composite function can model a variety of imaging tasks. A popular class of algorithms for solving such problems are majorization-minimization techniques which iteratively approximate the composite nonconvex function by a ...

Deformable image registration (DIR) represent a powerful computational method for image analysis, with promising applications in the diagnosis of human disease. Despite being widely used in the medical imaging community, the mathematical and numerical ...

Patch priors have become an important component of image restoration. A powerful approach in this category of restoration algorithms is the popular expected patch log-likelihood (EPLL) algorithm. EPLL uses a Gaussian mixture model (GMM) prior learned on ...

Semantic segmentation and other pixel-level labeling tasks have made significant progress recently due to the deep learning paradigm. Many state-of-the-art structured prediction methods also include a random field model with a hand-crafted Gaussian ...

This paper concerns an optimization algorithm for unconstrained nonconvex problems where the objective function has sparse connections between the unknowns. The algorithm is based on applying a dissipation preserving numerical integrator, the Itoh--Abe ...

We establish exact recovery for the Least Unsquared Deviations (LUD) algorithm of Özyeşil and Singer. More precisely, we show that for sufficiently many cameras with given corrupted pairwise directions, where both camera locations and pairwise directions ...

The premise of our work is deceptively familiar: A black box $f(\cdot)$ has altered an image $\mathbf{x} \rightarrow f(\mathbf{x})$, but only mildly. Recover the image $\mathbf{x}$. This black box might be any number of simple or complicated things: a ...

In this paper, we propose a Riemannian steepest descent method for solving a blind deconvolution problem, which is to recover two unknown signals from their circular convolution. We assume that the two signals are in two known subspaces, one of which is ...

This article provides a mathematical analysis of singular (nonsmooth) artifacts added to reconstructions by filtered backprojection (FBP) type algorithms for X-ray computed tomography (CT) with arbitrary incomplete data. We prove that these singular ...

This work addresses the problem of patch-based image denoising through the unsupervised learning of a probabilistic high-dimensional mixture model on the noisy patches. The model, called HDMI, proposes a full modeling of the process that is supposed to ...

Photoacoustic tomography (PAT) is a hybrid imaging modality that intends to construct high-resolution images of optical properties of heterogeneous media from measured acoustic data generated by the photoacoustic effect. To date, most of the model-based ...