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Purpose: To develop a general phase regularized image reconstruction method, with applications to partial Fourier imaging, water-fat imaging and flow imaging. Theory and Methods: The problem of enforcing phase constraints in reconstruction…
A Bayesian hierarchical model for total variation regularisation is presented in this paper. All the parameters of an inverse problem, including the "regularisation parameter", are estimated simultaneously from the data in the model. The…
We consider regularized cutting-plane methods to minimize a convex function that is the sum of a large number of component functions. One important example is the dual problem obtained from Lagrangian relaxation on a decomposable problem.…
In this paper we study the problem of computing wavelet coefficients of compactly supported functions from their Fourier samples. For this, we use the recently introduced framework of generalized sampling. Our first result demonstrates that…
We consider a separation problem where the observation consists of the sum of a high amplitude smooth signal and a low amplitude transient signal. We propose a method for decomposition that relies on solving instances of a `constrained…
Convexity prior is one of the main cue for human vision and shape completion with important applications in image processing, computer vision. This paper focuses on characterization methods for convex objects and applications in image…
Segmentation of overlapping convex objects has various applications, for example, in nanoparticles and cell imaging. Often the segmentation method has to rely purely on edges between the background and foreground making the analyzed images…
Pan-sharpening algorithms utilize a panchromatic image and a multispectral image to generate a high spatial and high spectral image. However, the optimizations of the algorithms are designed with different standards. We employ a simple…
In this paper, we will present a generalization for a minimization problem from I. Daubechies, M. Defrise, and C. Demol [3]. This generalization is useful for solving many practical problems in which more than one constraint are involved.…
We introduce a simple, general, and convergent scheme to compute generalized eigenfunctions of self-adjoint operators with continuous spectra on rigged Hilbert spaces. Our approach does not require prior knowledge about the eigenfunctions,…
This paper deals with a method for the approximation of a spectral density function among the solutions of a generalized moment problem a` la Byrnes/Georgiou/Lindquist. The approximation is pursued with respect to the Kullback-Leibler…
We address the problem of image reconstruction from incomplete measurements, encompassing both upsampling and inpainting, within a learning-based framework. Conventional supervised approaches require fully sampled ground truth data, while…
In this paper, we propose a novel approach to hyperspectral image super-resolution by modeling the global spatial-and-spectral correlation and local smoothness properties over hyperspectral images. Specifically, we utilize the tensor…
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…
A new decomposition optimization algorithm, called \textit{path-following gradient-based decomposition}, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this…
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…
We present a method that takes as input a single dual-pixel image, and simultaneously estimates the image's defocus map -- the amount of defocus blur at each pixel -- and recovers an all-in-focus image. Our method is inspired from recent…
Although much research has been devoted to the problem of restoring Poissonian images, namely in the fields of medical and astronomical imaging, applying the state of the art regularizers (such as those based on wavelets or total variation)…
In this paper, we consider the algorithms and convergence for a general optimization problem, which has a wide range of applications in image segmentation, topology optimization, flow network formulation, and surface reconstruction. In…
Distributed optimization often requires finding the minimum of a global objective function written as a sum of local functions. A group of agents work collectively to minimize the global function. We study a continuous-time decentralized…