where Sn (also known as the symmetric group on n elements) is the set of all permutations of {1, 2, . . . , n}, i.e., all the ways of pairing up the n rows of the matrix with the n columns, and I(π) is the inversion number of π, the minimal number of transpositions of adjacent columns needed to turn π into the identity permutation. This formula [1] is practical for some simple matrices such as ...

We propose a theoretical analysis of the super-resolution performance of the BLASSO “off-the-grid” recovery method from Laplace transform measurements. This transform is not translation invariant, thus requiring the use of theoretical and algorithmic tools that go beyond traditional deconvolution-based methods. We show that the BLASSO offers a stable and computationally tractable super-resoluti...

The inversion of the one-dimensional Radon transform on the rotation group SO(3) is an ill-posed inverse problem that can be applied to X-ray tomography with polycrystalline materials. This paper is concerned with the development of a method to stably approximate the inverse of the noisy Radon transform on SO(3). The proposed approach is composed by basic building blocks of the coorbit theory o...

We apply a nonlocal adaptive spectral transform for sparse modeling of phase and amplitude of a coherent wave eld. The reconstruction of this complex-valued wave eld from Gaussian noisy observations is considered. The problem is formulated as a multi-objective alternating constrained optimization. The developed iterative algorithm decouples the inversion of the forward propagation operator and ...

Diffusion nuclear magnetic resonance (NMR) is a powerful technique for studying porous media, but yields ambiguous results when the sample comprises multiple regions with different pore sizes, shapes, and orientations. Inspired by solid-state NMR techniques for correlating isotropic and anisotropic chemical shifts, we propose a diffusion NMR method to resolve said ambiguity. Numerical data inve...

We study a relative optimization framework for the quasimaximum likelihood blind source separation and relative Newton method as its particular instance. Convergence of the Newton method is stabilized by the line search and by the modification of the Hessian, which forces its positive definiteness. The structure of the Hessian allows fast approximate inversion. We demonstrate the efficiency of ...

We present a contrast source inversion (CSI) algorithm using a finite-difference (FD) approach as its backbone for reconstructing the unknown material properties of inhomogeneous objects embedded in a known inhomogeneous background medium. Unlike the CSI method using the integral equation (IE) approach, the FD-CSI method can readily employ an arbitrary inhomogeneous medium as its background. Th...

Background Accumulation of diffuse myocardial fibrosis / extracellular volume (ECV) in the myocardium is common to various cardiac diseases and is associated with an unfavorable prognosis. Various cardiac magnetic resonance (CMR) T1 mapping techniques have recently been proposed for the quantification of ECV, including: 1. Modified Look-Locker Inversion recovery (MOLLI) T1 mapping including cal...

We propose two new methods to estimate secular trends in the incidence of a chronic disease from a series of prevalence studies and mortality data. One method is a direct inversion formula, the second method is a least squares estimation. Both methods are validated in a simulation study based on data from a diabetes register. The results of the validation show that the proposed methods may be u...

Hyperspectral (HS) super-resolution reconstruction is an ill-posed inversion problem, for which the solution from reconstruction constraint is not unique. To address this, an HS image super-resolution method is proposed to first utilize the joint regulation of spatial and spectral nonlocal similarities. We then fused the HS and panchromatic images with sparse regulation. With these two regulati...