SIAM Journal on Imaging Sciences

In this work we introduce a formulation for a nonlocal Hessian that combines the ideas of higher-order and nonlocal regularization for image restoration, extending the idea of nonlocal gradients to higher-order derivatives. By intelligently choosing the ...

In this paper we analyze the blind deconvolution of an image and an unknown blur in a coded imaging system. The measurements consist of subsampled convolution of an unknown blurring kernel with multiple random binary modulations (coded masks) of the image. ...

The alternating direction method of multipliers (ADMM) is a popular and efficient first-order method that has recently found numerous applications, and the proximal ADMM is an important variant of it. The main contributions of this paper are the ...

We consider standard finite-dimensional variational models used in signal/image processing that consist of minimizing an energy involving a data fidelity term and a regularization term. We propose new contributions from a theoretical perspective which give a ...

Nonsmooth nonconvex optimization models have been widely used in the restoration and reconstruction of real images. In this paper, we consider a linearly constrained optimization problem with a non-Lipschitz regularization term in the objective function ...

This article details a novel numerical scheme to approximate gradient flows for optimal transport (i.e., Wasserstein) metrics. These flows have proved useful to tackle theoretically and numerically nonlinear diffusion equations that model, for instance, ...

The Cahn--Hilliard equation provides a simple and fast tool for binary image inpainting. By now, two generalizations to gray value images exist: bitwise binary inpainting and TV-H$^{-1}$ inpainting. This paper outlines a model based on the vector-valued ...

We develop a representation of reverse-time migration (RTM) in terms of Fourier integral operators, the canonical relations of which are graphs. Through the dyadic parabolic decomposition of phase space, we obtain the solution of the wave equation with a ...

In this paper we introduce a new family of partial difference operators on graphs and study equations involving these operators. This family covers local variational $p$-Laplacian, $\infty$-Laplacian, nonlocal $p$-Laplacian and $\infty$-Laplacian, $p$-...

To address the classic interior tomography problem where projections at each view extend only to the shadow of a circular region completely interior to the subject being scanned, previously we showed that the exact recovery of two- and three-dimensional ...

Natural signals and images are well known to be approximately sparse in transform domains such as wavelets and discrete cosine transform. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed ...

Most computer vision applications rely on algorithms finding local correspondences between different images. These algorithms detect and compare stable local invariant descriptors centered at scale-invariant keypoints. Because of the importance of the problem,...

Recently, nonconvex regularization models have been introduced in order to provide a better prior for gradient distributions in real images. They are based on using concave energies $\phi$ in the total variation--type functional ${TV}^\phi(u) := \int \phi(|\...

We propose a two-step algorithm that automatically estimates the noise level function of stationary noise from a single image, i.e., the noise variance as a function of the image intensity. First, the image is divided into small square regions and a ...

The Poisson--Gaussian model can accurately describe the noise present in a number of imaging systems. However most existing restoration methods rely on approximations of the Poisson--Gaussian noise statistics. We propose a convex optimization strategy for ...

We consider passive synthetic aperture imaging where a single moving receiver antenna records signals that are generated by distant unknown noise sources and backscattered by one or several reflectors. The reflectors can be imaged by migrating the ...

We present a preconditioning of a generalized forward-backward splitting algorithm for finding a zero of a sum of maximally monotone operators $\sum_{i=1}^{n} A_i + B$ with $B$ cocoercive, involving only the computation of $B$ and of the resolvent of each ...

We present a new flexible wavefront propagation algorithm for the boundary value problem for sub-Riemannian (SR) geodesics in the roto-translation group $SE(2) = \mathbb{R}^2 \rtimes S^1$ with a metric tensor depending on a smooth external cost $\mathcal{C}:...

We present a novel method for affine transformation estimation of image regions. We illustrate the benefits of using the proposed method in three realms: (1) locating large amounts of point matches with highly accurate localization; (2) producing very ...

A variational model for image reconstruction is introduced and analyzed in function space. Specific to the model is the data fidelity, which is realized via a basis transformation with respect to a Riesz basis followed by interval constraints. This setting ...

The present work is the second of two papers on a variational model for image reconstruction whose specific features are twofold: First, data fidelity is realized by interval constraints on the coefficients of a Riesz basis representation, and second, ...

We propose a new shape-based modeling technique for applications in imaging problems. Given a collection of shape priors (a shape dictionary), we define our problem as choosing the right dictionary elements and geometrically composing them through basic set ...

It is well documented that natural images are compressible in wavelet bases and tend to exhibit fractal properties. In this paper, we investigate statistical models that mimic these behaviors. We then use our models to make predictions on the statistics of ...

Restoring images degraded by spatially varying blur is a problem encountered in many disciplines such as astrophysics, computer vision, and biomedical imaging. One of the main challenges in performing this task is to design efficient numerical algorithms to ...

We study array imaging of a sparse scene of point-like sources or scatterers in a homogeneous medium. For source imaging, the sensors in the array are receivers that collect measurements of the wave field. For imaging scatterers, the array probes the medium ...