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  • Optimal control and inverse problems
    Inverse Probl. (IF 1.858) Pub Date : 2020-05-27
    Christian Clason and Barbara Kaltenbacher

    Description unavailable

    更新日期:2020-05-27
  • Local solvability of an inverse problem to the Navier–Stokes equation with memory term
    Inverse Probl. (IF 1.858) Pub Date : 2020-05-14
    Yu Jiang, Jishan Fan, Sei Nagayasu and Gen Nakamura

    In this paper, we consider the Navier–Stokes equation with memory term in a three-dimensional bounded domain. The equation is the so-called Oldroyd fluid model equation, which can describe the stress relaxation as well as the retardation of deformation due to the memory term. For this equation we considered the inverse problem for recovering the kernel of memory term in this model equation from the

    更新日期:2020-05-14
  • Non-unique games over compact groups and orientation estimation in cryo-EM
    Inverse Probl. (IF 1.858) Pub Date : 2020-05-14
    Afonso S Bandeira, Yutong Chen, Roy R Lederman and Amit Singer

    Let ##IMG## [http://ej.iop.org/images/0266-5611/36/6/064002/ipab7d2cieqn1.gif] {$\mathcal{G}$} be a compact group and let ##IMG## [http://ej.iop.org/images/0266-5611/36/6/064002/ipab7d2cieqn2.gif] {${f}_{ij}\in C\left(\mathcal{G}\right)$} . We define the non-unique games (NUG) problem as finding ##IMG## [http://ej.iop.org/images/0266-5611/36/6/064002/ipab7d2cieqn3.gif] {${g}_{1},\dots ,\;{g}_{n}\in

    更新日期:2020-05-14
  • Bilevel optimization, deep learning and fractional Laplacian regularizatin with applications in tomography
    Inverse Probl. (IF 1.858) Pub Date : 2020-05-14
    Harbir Antil, Zichao Wendy Di and Ratna Khatri

    In this work we consider a generalized bilevel optimization framework for solving inverse problems. We introduce fractional Laplacian as a regularizer to improve the reconstruction quality, and compare it with the total variation regularization. We emphasize that the key advantage of using fractional Laplacian as a regularizer is that it leads to a linear operator, as opposed to the total variation

    更新日期:2020-05-14
  • Inverse problems for one dimensional conformable fractional Dirac type integro differential system
    Inverse Probl. (IF 1.858) Pub Date : 2020-05-14
    Baki Keskin

    In this paper, one dimensional conformable fractional Dirac-type integro differential system is considered. The asymptotic formulae for the solutions, eigenvalues and nodal points are obtained. We investigate the inverse nodal problem and give an effective procedure for solving the inverse nodal problem with respect to given a dense subset of nodal points.

    更新日期:2020-05-14
  • A dual approach to Kohn–Vogelius regularization applied to data completion problem
    Inverse Probl. (IF 1.858) Pub Date : 2020-05-14
    Fabien Caubet and Jérémi Dardé

    This paper focuses on the data completion problem, which is well known to be an ill-posed inverse problem. We propose a dual regularization strategy without regularization parameter, based on the minimization of a functional which, instead of acting on the space of solutions, acts on the space of data. We prove the well-posedness of the minimization problem and the convergence of our regularized solution

    更新日期:2020-05-14
  • Uniqueness criteria in multi-energy CT
    Inverse Probl. (IF 1.858) Pub Date : 2020-05-14
    Guillaume Bal and Fatma Terzioglu

    Multi-energy computed tomography (ME-CT) is a medical imaging modality aiming to reconstruct the spatial density of materials from the attenuation properties of probing x-rays. For each line in two- or three-dimensional space, ME-CT measurements may be written as a nonlinear mapping from the integrals of the unknown densities of a finite number of materials along said line to an equal or larger number

    更新日期:2020-05-14
  • Numerical results for Saito’s uniqueness theorem in inverse scattering theory
    Inverse Probl. (IF 1.858) Pub Date : 2020-05-14
    Teemu Tyni

    We consider an inverse scattering problem for the Schrödinger operator in two dimensions. The aim of this work is to discuss some first numerical results on Saito’s formula. Saito’s formula is an explicit integral formula, which at the high-frequency limit gives a uniqueness result for the inverse scattering problem. The numeric approach is quite straight-forward: we take a large enough fixed wave

    更新日期:2020-05-14
  • Discrete total variation of the normal vector field as shape prior with applications in geometric inverse problems
    Inverse Probl. (IF 1.858) Pub Date : 2020-05-04
    Ronny Bergmann, Marc Herrmann, Roland Herzog, Stephan Schmidt and José Vidal-Núñez

    An analogue of the total variation prior for the normal vector field along the boundary of piecewise flat shapes in 3D is introduced. A major class of examples are triangulated surfaces as they occur for instance in finite element computations. The analysis of the functional is based on a differential geometric setting in which the unit normal vector is viewed as an element of the two-dimensional sphere

    更新日期:2020-05-04
  • On existence and regularity of a terminal value problem for the time fractional diffusion equation
    Inverse Probl. (IF 1.858) Pub Date : 2020-05-03
    Nguyen Huy Tuan, Tran Bao Ngoc, Yong Zhou and Donal O’Regan

    In this paper we consider a final value problem for a diffusion equation with time-space fractional differentiation on a bounded domain D of ##IMG## [http://ej.iop.org/images/0266-5611/36/5/055011/ipab730dieqn1.gif] {${\mathbb{R}}^{k}$} , k ≥ 1, which includes the fractional power ##IMG## [http://ej.iop.org/images/0266-5611/36/5/055011/ipab730dieqn2.gif] {${\mathcal{L}}^{\beta }$} , 0 < β ≤ 1, of a

    更新日期:2020-05-03
  • Tomographic reconstruction with spatially varying parameter selection
    Inverse Probl. (IF 1.858) Pub Date : 2020-05-03
    Yiqiu Dong and Carola-Bibiane Schönlieb

    In this paper we propose a new approach for tomographic reconstruction with spatially varying regularization parameter. Our work is based on the SA-TV image restoration model proposed by Dong et al (2011 J. Math. Imag. Vis. 40 82–104) where an automated parameter selection rule for spatially varying parameters has been proposed. Their parameter selection rule, however, only applies if measured imaging

    更新日期:2020-05-03
  • ℓ 1 − αℓ 2 minimization methods for signal and image reconstruction with impulsive noise removal
    Inverse Probl. (IF 1.858) Pub Date : 2020-05-03
    Peng Li, Wengu Chen, Huanmin Ge and Michael K Ng

    In this paper, we study ℓ 1 − αℓ 2 (0 < α ⩽ 1) minimization methods for signal and image reconstruction with impulsive noise removal. The data fitting term is based on ℓ 1 fidelity between the reconstruction output and the observational data, and the regularization term is based on ℓ 1 − αℓ 2 nonconvex minimization of the reconstruction output or its total variation. Theoretically, we show that under

    更新日期:2020-05-03
  • Semivariogram methods for modeling Whittle–Matérn priors in Bayesian inverse problems
    Inverse Probl. (IF 1.858) Pub Date : 2020-05-03
    Richard D Brown, Johnathan M Bardsley and Tiangang Cui

    We present a new technique, based on semivariogram methodology, for obtaining point estimates for use in prior modeling for solving Bayesian inverse problems. This method requires a connection between Gaussian processes with covariance operators defined by the Matérn covariance function and Gaussian processes with precision (inverse-covariance) operators defined by the Green’s functions of a class

    更新日期:2020-05-03
  • Total variation of the normal vector field as shape prior
    Inverse Probl. (IF 1.858) Pub Date : 2020-05-03
    Ronny Bergmann, Marc Herrmann, Roland Herzog, Stephan Schmidt and José Vidal-Núñez

    An analogue of the total variation prior for the normal vector field along the boundary of smooth shapes in 3D is introduced. The analysis of the total variation of the normal vector field is based on a differential geometric setting in which the unit normal vector is viewed as an element of the two-dimensional sphere manifold. It is shown that spheres are stationary points when the total variation

    更新日期:2020-05-03
  • An inverse source problem for distributed order time-fractional diffusion equation
    Inverse Probl. (IF 1.858) Pub Date : 2020-05-03
    Chunlong Sun and Jijun Liu

    We consider an inverse time-dependent source problem governed by a distributed time-fractional diffusion equation using interior measurement data. Such a problem arises in some ultra-slow diffusion phenomena in many applied areas. Based on the regularity result of the solution to the direct problem, we establish the solvability of this inverse problem as well as the conditional stability in suitable

    更新日期:2020-05-03
  • The quadratic Wasserstein metric for inverse data matching
    Inverse Probl. (IF 1.858) Pub Date : 2020-04-30
    Björn Engquist, Kui Ren and Yunan Yang

    This work characterizes, analytically and numerically, two major effects of the quadratic Wasserstein ( W 2 ) distance as the measure of data discrepancy in computational solutions of inverse problems. First, we show, in the infinite-dimensional setup, that the W 2 distance has a smoothing effect on the inversion process, making it robust against high-frequency noise in the data but leading to a reduced

    更新日期:2020-04-30
  • A partial data problem in linear elasticity
    Inverse Probl. (IF 1.858) Pub Date : 2020-04-30
    Moritz Doll, André Froehly and René Schulz

    We discuss the determination of the Lamé parameters of an elastic material by the means of boundary measurements. We will combine previous results of Eskin–Ralston and Isakov to prove inverse results in the case of bounded domains with partial data. Moreover, we generalise these results to domains with cylindrical ends.

    更新日期:2020-04-30
  • On the local Lipschitz stability of Bayesian inverse problems
    Inverse Probl. (IF 1.858) Pub Date : 2020-04-30
    Björn Sprungk

    In this note we consider the stability of posterior measures occurring in Bayesian inference w.r.t. perturbations of the prior measure and the log-likelihood function. This extends the well-posedness analysis of Bayesian inverse problems. In particular, we prove a general local Lipschitz continuous dependence of the posterior on the prior and the log-likelihood w.r.t. various common distances of probability

    更新日期:2020-04-30
  • A new class of accelerated regularization methods, with application to bioluminescence tomography
    Inverse Probl. (IF 1.858) Pub Date : 2020-04-30
    Rongfang Gong, Bernd Hofmann and Ye Zhang

    In this paper we propose a new class of iterative regularization methods for solving ill-posed linear operator equations. The prototype of these iterative regularization methods is in the form of second order evolution equation with a linear vanishing damping term, which can be viewed not only as an extension of the asymptotical regularization, but also as a continuous analog of the Nesterov’s acceleration

    更新日期:2020-04-30
  • Solving phase retrieval via graph projection splitting
    Inverse Probl. (IF 1.858) Pub Date : 2020-04-30
    Ji Li and Hongkai Zhao

    Phase retrieval with prior information can be cast as a nonsmooth and nonconvex optimization problem. To decouple the signal and measurement variables, we introduce an auxiliary variable and reformulate it as an optimization with an equality constraint. We then solve the reformulated problem by graph projection splitting (GPS), where the two proximity subproblems and the graph projection step can be

    更新日期:2020-04-30
  • One-bit compressed sensing via ℓ p ( 0 < p < 1 )-minimization method
    Inverse Probl. (IF 1.858) Pub Date : 2020-04-29
    Jingyao Hou, Jianjun Wang, Feng Zhang and Jianwen Huang

    One-bit compressed sensing aims to recover unknown sparse signals from extremely quantized linear measurements which just capture their signs. In this paper, we propose a nonconvex ℓ p (0 < p < 1) minimization model for one-bit compressed sensing problem and define the set of ℓ p effectively s -sparse signals which contains genuinely s -sparse signals. Utilizing properties of covering number, we show

    更新日期:2020-04-29
  • A Bayesian filtering approach to layer stripping for electrical impedance tomography
    Inverse Probl. (IF 1.858) Pub Date : 2020-04-29
    D Calvetti, S Nakkireddy and E Somersalo

    Layer stripping is a method for solving inverse boundary value problems for elliptic PDEs, originally proposed in the literature for solving the Calderón problem of electrical impedance tomography (EIT), where the data consist of the Neumann-to-Dirichlet operator on the boundary. Defining a tangent–normal coordinate system near the boundary, the data are extended to a family of boundary operators on

    更新日期:2020-04-29
  • Reduced order models for spectral domain inversion: embedding into the continuous problem and generation of internal data
    Inverse Probl. (IF 1.858) Pub Date : 2020-04-29
    L Borcea, V Druskin, A Mamonov, S Moskow and M Zaslavsky

    We generate data-driven reduced order models (ROMs) for inversion of the one and two dimensional Schrödinger equation in the spectral domain given boundary data at a few frequencies. The ROM is the Galerkin projection of the Schrödinger operator onto the space spanned by solutions at these sample frequencies. The ROM matrix is in general full, and not good for extracting the potential. However, using

    更新日期:2020-04-29
  • Sampled limited memory methods for massive linear inverse problems
    Inverse Probl. (IF 1.858) Pub Date : 2020-04-29
    Julianne Chung, Matthias Chung, J Tanner Slagel and Luis Tenorio

    In many modern imaging applications the desire to reconstruct high resolution images, coupled with the abundance of data from acquisition using ultra-fast detectors, have led to new challenges in image reconstruction. A main challenge is that the resulting linear inverse problems are massive. The size of the forward model matrix exceeds the storage capabilities of computer memory, or the observational

    更新日期:2020-04-29
  • Projected Newton method for noise constrained Tikhonov regularization
    Inverse Probl. (IF 1.858) Pub Date : 2020-04-29
    J Cornelis, N Schenkels and W Vanroose

    Tikhonov regularization is a popular approach to obtain a meaningful solution for ill-conditioned linear least squares problems. A relatively simple way of choosing a good regularization parameter is given by Morozov’s discrepancy principle. However, most approaches require the solution of the Tikhonov problem for many different values of the regularization parameter, which is computationally demanding

    更新日期:2020-04-29
  • Global uniqueness in a passive inverse problem of helioseismology
    Inverse Probl. (IF 1.858) Pub Date : 2020-04-28
    A D Agaltsov, T Hohage and R G Novikov

    We consider the inverse problem of recovering the spherically symmetric sound speed, density and attenuation in the Sun from the observations of the acoustic field randomly excited by turbulent convection. We show that observations at two heights above the photosphere and at two frequencies above the acoustic cutoff frequency uniquely determine the solar parameters. We also present numerical simulations

    更新日期:2020-04-28
  • Data completion method for the Helmholtz equation via surface potentials for partial Cauchy data
    Inverse Probl. (IF 1.858) Pub Date : 2020-04-28
    Matthieu Aussal, Yosra Boukari and Houssem Haddar

    We propose and study a data completion algorithm for recovering missing data from the knowledge of Cauchy data on parts of the same boundary. The algorithm is based on surface representation of the solution and is presented for the Helmholtz equation. This work is an extension of the data completion algorithm proposed by the two last authors where the case of data available of a closed boundary was

    更新日期:2020-04-28
  • Stability of the inverse source problem for the Helmholtz equation in R 3
    Inverse Probl. (IF 1.858) Pub Date : 2020-04-28
    Adrian Kirkeby, Mads T R Henriksen and Mirza Karamehmedović

    We consider the reconstruction of a compactly supported source term in the constant-coefficient Helmholtz equation in R 3 , from the measurement of the outgoing solution at a source-enclosing sphere. The measurement is taken at a finite number of frequencies. We explicitly characterize certain finite-dimensional spaces of sources that can be stably reconstructed from such measurements. The characterization

    更新日期:2020-04-28
  • Spatial-Spectral Cube Matching Frame for Spectral CT Reconstruction.
    Inverse Probl. Pub Date : 2019-03-25
    Weiwen Wu,Yanbo Zhang,Qian Wang,Fenglin Liu,Fulin Luo,Hengyong Yu

    Spectral computed tomography (CT) reconstructs the same scanned object from projections of multiple narrow energy windows, and it can be used for material identification and decomposition. However, the multi-energy projection dataset has a lower signal-noise-ratio (SNR), resulting in poor reconstructed image quality. To address this thorny problem, we develop a spectral CT reconstruction method, namely

    更新日期:2019-11-01
  • Multicompartment Magnetic Resonance Fingerprinting.
    Inverse Probl. Pub Date : 2019-03-19
    Sunli Tang,Carlos Fernandez-Granda,Sylvain Lannuzel,Brett Bernstein,Riccardo Lattanzi,Martijn Cloos,Florian Knoll,Jakob Assländer

    Magnetic resonance fingerprinting (MRF) is a technique for quantitative estimation of spin- relaxation parameters from magnetic-resonance data. Most current MRF approaches assume that only one tissue is present in each voxel, which neglects intravoxel structure, and may lead to artifacts in the recovered parameter maps at boundaries between tissues. In this work, we propose a multicompartment MRF model

    更新日期:2019-11-01
  • Nonreciprocal broken ray transforms with applications to fluorescence imaging.
    Inverse Probl. Pub Date : 2019-02-26
    Lucia Florescu,Vadim A Markel,John C Schotland

    Broken ray transforms (BRTs) are typically considered to be reciprocal, meaning that the transform is independent of the direction in which a photon travels along a given broken ray. However, if the photon can change its energy (or be absorbed and re-radiated at a different frequency) at the vertex of the ray, then reciprocity is lost. In optics, non-reciprocal BRTs are applicable to imaging problems

    更新日期:2019-11-01
  • Coupled regularization with multiple data discrepancies.
    Inverse Probl. Pub Date : 2019-01-29
    Martin Holler,Richard Huber,Florian Knoll

    We consider a class of regularization methods for inverse problems where a coupled regularization is employed for the simultaneous reconstruction of data from multiple sources. Applications for such a setting can be found in multi-spectral or multimodality inverse problems, but also in inverse problems with dynamic data. We consider this setting in a rather general framework and derive stability and

    更新日期:2019-11-01
  • Nonlocal low-rank and sparse matrix decomposition for spectral CT reconstruction.
    Inverse Probl. Pub Date : 2018-10-09
    Shanzhou Niu,Gaohang Yu,Jianhua Ma,Jing Wang

    Spectral computed tomography (CT) has been a promising technique in research and clinic because of its ability to produce improved energy resolution images with narrow energy bins. However, the narrow energy bin image is often affected by serious quantum noise because of the limited number of photons used in the corresponding energy bin. To address this problem, we present an iterative reconstruction

    更新日期:2019-11-01
  • Nonsmooth Convex Optimization for Structured Illumination Microscopy Image Reconstruction.
    Inverse Probl. Pub Date : 2018-08-08
    Jérôme Boulanger,Nelly Pustelnik,Laurent Condat,Lucie Sengmanivong,Tristan Piolot

    In this paper, we propose a new approach for structured illumination microscopy image reconstruction. We first introduce the principles of this imaging modality and describe the forward model. We then propose the minimization of nonsmooth convex objective functions for the recovery of the unknown image. In this context, we investigate two data-fitting terms for Poisson-Gaussian noise and introduce

    更新日期:2019-11-01
  • Joint reconstruction of the initial pressure and speed of sound distributions from combined photoacoustic and ultrasound tomography measurements.
    Inverse Probl. Pub Date : 2018-05-02
    Thomas P Matthews,Mark A Anastasio

    The initial pressure and speed of sound (SOS) distributions cannot both be stably recovered from photoacoustic computed tomography (PACT) measurements alone. Adjunct ultrasound computed tomography (USCT) measurements can be employed to estimate the SOS distribution. Under the conventional image reconstruction approach for combined PACT/USCT systems, the SOS is estimated from the USCT measurements alone

    更新日期:2019-11-01
  • Can Linear Superiorization Be Useful for Linear Optimization Problems?
    Inverse Probl. Pub Date : 2018-01-18
    Yair Censor

    Linear superiorization considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not necessarily minimal) target function values. The two questions that we set out to explore experimentally are (i) Does linear superiorization provide a feasible point

    更新日期:2019-11-01
  • A framelet-based iterative maximum-likelihood reconstruction algorithm for spectral CT.
    Inverse Probl. Pub Date : 2017-10-21
    Yingmei Wang,Ge Wang,Shuwei Mao,Wenxiang Cong,Zhilong Ji,Jian-Feng Cai,Yangbo Ye

    Standard computed tomography (CT) cannot reproduce spectral information of an object. Hardware solutions include dual-energy CT which scans the object twice in different x-ray energy levels, and energy-discriminative detectors which can separate lower and higher energy levels from a single x-ray scan. In this paper, we propose a software solution and give an iterative algorithm that reconstructs an

    更新日期:2019-11-01
  • Superiorization-based multi-energy CT image reconstruction.
    Inverse Probl. Pub Date : 2017-10-07
    Q Yang,W Cong,G Wang

    The recently-developed superiorization approach is efficient and robust for solving various constrained optimization problems. This methodology can be applied to multi-energy CT image reconstruction with the regularization in terms of the prior rank, intensity and sparsity model (PRISM). In this paper, we propose a superiorized version of the simultaneous algebraic reconstruction technique (SART) based

    更新日期:2019-11-01
  • SHAPE BASED IMAGE RECONSTRUCTION USING LINEARIZED DEFORMATIONS.
    Inverse Probl. Pub Date : 2017-09-01
    Ozan Öktem,Chong Chen,Nevzat Onur Domaniç,Pradeep Ravikumar,Chandrajit Bajaj

    We introduce a reconstruction framework that can account for shape related a priori information in ill-posed linear inverse problems in imaging. It is a variational scheme that uses a shape functional defined using deformable templates machinery from shape theory. As proof of concept, we apply the proposed shape based reconstruction to 2D tomography with very sparse measurements, and demonstrate strong

    更新日期:2019-11-01
  • Fourier rebinning and consistency equations for time-of-flight PET planograms.
    Inverse Probl. Pub Date : 2016-01-01
    Yusheng Li,Michel Defrise,Samuel Matej,Scott D Metzler

    Due to the unique geometry, dual-panel PET scanners have many advantages in dedicated breast imaging and on-board imaging applications since the compact scanners can be combined with other imaging and treatment modalities. The major challenges of dual-panel PET imaging are the limited-angle problem and data truncation, which can cause artifacts due to incomplete data sampling. The time-of-flight (TOF)

    更新日期:2019-11-01
  • An Inverse Problem for a Class of Conditional Probability Measure-Dependent Evolution Equations.
    Inverse Probl. Pub Date : 2016-01-01
    Inom Mirzaev,Erin C Byrne,David M Bortz

    We investigate the inverse problem of identifying a conditional probability measure in measure-dependent evolution equations arising in size-structured population modeling. We formulate the inverse problem as a least squares problem for the probability measure estimation. Using the Prohorov metric framework, we prove existence and consistency of the least squares estimates and outline a discretization

    更新日期:2019-11-01
  • A discrete convolution kernel for No-DC MRI.
    Inverse Probl. Pub Date : 2015-08-01
    Gengsheng L Zeng,Ya Li

    An analytical inversion formula for the exponential Radon transform with an imaginary attenuation coefficient was developed in 2007 (2007 Inverse Problems 23 1963-71). The inversion formula in that paper suggested that it is possible to obtain an exact MRI (magnetic resonance imaging) image without acquiring low-frequency data. However, this un-measured low-frequency region (ULFR) in the k-space (which

    更新日期:2019-11-01
  • Parallel Magnetic Resonance Imaging as Approximation in a Reproducing Kernel Hilbert Space.
    Inverse Probl. Pub Date : 2015-05-20
    Vivek Athalye,Michael Lustig,Martin Uecker

    In Magnetic Resonance Imaging (MRI) data samples are collected in the spatial frequency domain (k-space), typically by time-consuming line-by-line scanning on a Cartesian grid. Scans can be accelerated by simultaneous acquisition of data using multiple receivers (parallel imaging), and by using more efficient non-Cartesian sampling schemes. To understand and design k-space sampling patterns, a theoretical

    更新日期:2019-11-01
  • A projection-based approach to diffraction tomography on curved boundaries.
    Inverse Probl. Pub Date : 2015-01-20
    Gregory T Clement

    An approach to diffraction tomography is investigated for two-dimensional image reconstruction of objects surrounded by an arbitrarily-shaped curve of sources and receivers. Based on the integral theorem of Helmholtz and Kirchhoff, the approach relies upon a valid choice of the Green's functions for selected conditions along the (possibly-irregular) boundary. This allows field projections from the

    更新日期:2019-11-01
  • A direct D-bar reconstruction algorithm for recovering a complex conductivity in 2-D.
    Inverse Probl. Pub Date : 2013-05-04
    S J Hamilton,C N L Herrera,J L Mueller,A Von Herrmann

    A direct reconstruction algorithm for complex conductivities in W2,∞ (Ω), where Ω is a bounded, simply connected Lipschitz domain in ℝ2, is presented. The framework is based on the uniqueness proof by Francini [Inverse Problems 20 2000], but equations relating the Dirichlet-to-Neumann to the scattering transform and the exponentially growing solutions are not present in that work, and are derived here

    更新日期:2019-11-01
  • Accelerated perturbation-resilient block-iterative projection methods with application to image reconstruction.
    Inverse Probl. Pub Date : 2013-02-27
    T Nikazad,R Davidi,G T Herman

    We study the convergence of a class of accelerated perturbation-resilient block-iterative projection methods for solving systems of linear equations. We prove convergence to a fixed point of an operator even in the presence of summable perturbations of the iterates, irrespective of the consistency of the linear system. For a consistent system, the limit point is a solution of the system. In the inconsistent

    更新日期:2019-11-01
  • Preconditioned Alternating Projection Algorithms for Maximum a Posteriori ECT Reconstruction.
    Inverse Probl. Pub Date : 2012-12-29
    Andrzej Krol,Si Li,Lixin Shen,Yuesheng Xu

    We propose a preconditioned alternating projection algorithm (PAPA) for solving the maximum a posteriori (MAP) emission computed tomography (ECT) reconstruction problem. Specifically, we formulate the reconstruction problem as a constrained convex optimization problem with the total variation (TV) regularization. We then characterize the solution of the constrained convex optimization problem and show

    更新日期:2019-11-01
  • A Bayesian approach to the detection of small low emission sources.
    Inverse Probl. Pub Date : 2012-02-22
    Xiaolei Xun,Bani Mallick,Raymond J Carroll,Peter Kuchment

    This paper addresses the problem of detecting the presence and location of a small low emission source inside an object, when the background noise dominates. This problem arises, for instance, in some homeland security applications. The goal is to reach the signal-to-noise ratio levels in the order of 10(-3). A Bayesian approach to this problem is implemented in 2D. The method allows inference not

    更新日期:2019-11-01
  • Multi-energy CT based on a prior rank, intensity and sparsity model (PRISM).
    Inverse Probl. Pub Date : 2012-01-10
    Hao Gao,Hengyong Yu,Stanley Osher,Ge Wang

    We propose a compressive sensing approach for multi-energy computed tomography (CT), namely the prior rank, intensity and sparsity model (PRISM). To further compress the multi-energy image for allowing the reconstruction with fewer CT data and less radiation dose, the PRISM models a multi-energy image as the superposition of a low-rank matrix and a sparse matrix (with row dimension in space and column

    更新日期:2019-11-01
  • High-order total variation minimization for interior SPECT.
    Inverse Probl. Pub Date : 2012-01-05
    Jiansheng Yang,Hengyong Yu,Ming Jiang,Ge Wang

    Recently, we developed an approach for solving the computed tomography (CT) interior problem based on the high-order TV (HOT) minimization, assuming that a region-of-interest (ROI) is piecewise polynomial. In this paper, we generalize this finding from the CT field to the single-photon emission computed tomography (SPECT) field, and prove that if an ROI is piecewise polynomial, then the ROI can be

    更新日期:2019-11-01
  • STABILITY OF THE INTERIOR PROBLEM FOR POLYNOMIAL REGION OF INTEREST.
    Inverse Probl. Pub Date : 2012-01-01
    E Katsevich,A Katsevich,G Wang

    In many practical applications, it is desirable to solve the interior problem of tomography without requiring knowledge of the attenuation function fa on an open set within the region of interest (ROI). It was proved recently that the interior problem has a unique solution if fa is assumed to be piecewise polynomial on the ROI. In this paper, we tackle the related question of stability. It is well-known

    更新日期:2019-11-01
  • Reconstruction from a Few Projections by ℓ(1)-Minimization of the Haar Transform.
    Inverse Probl. Pub Date : 2011-09-13
    E Garduño,G T Herman,R Davidi

    Much recent activity is aimed at reconstructing images from a few projections. Images in any application area are not random samples of all possible images, but have some common attributes. If these attributes are reflected in the smallness of an objective function, then the aim of satisfying the projections can be complemented with the aim of having a small objective value. One widely investigated

    更新日期:2019-11-01
  • Comparison of Optimal Design Methods in Inverse Problems.
    Inverse Probl. Pub Date : 2011-08-23
    H T Banks,Kathleen Holm,Franz Kappel

    Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here

    更新日期:2019-11-01
  • Contrast-enhanced microwave imaging of breast tumors: a computational study using 3-D realistic numerical phantoms.
    Inverse Probl. Pub Date : 2010-10-12
    J D Shea,P Kosmas,B D Van Veen,S C Hagness

    The detection of early-stage tumors in the breast by microwave imaging is challenged by both the moderate endogenous dielectric contrast between healthy and malignant glandular tissues and the spatial resolution available from illumination at microwave frequencies. The high endogenous dielectric contrast between adipose and fibroglandular tissue structures increases the difficulty of tumor detection

    更新日期:2019-11-01
  • Perturbation Resilience and Superiorization of Iterative Algorithms.
    Inverse Probl. Pub Date : 2010-07-09
    Y Censor,R Davidi,G T Herman

    Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little demand on computer resources. For other problems, such as finding that point in the intersection at which the value of a given function is optimal, algorithms tend

    更新日期:2019-11-01
  • Advancements to the planogram frequency-distance rebinning algorithm.
    Inverse Probl. Pub Date : 2010-05-04
    Kyle M Champley,Raymond R Raylman,Paul E Kinahan

    In this paper we consider the task of image reconstruction in positron emission tomography (PET) with the planogram frequency-distance rebinning (PFDR) algorithm. The PFDR algorithm is a rebinning algorithm for PET systems with panel detectors. The algorithm is derived in the planogram coordinate system which is a native data format for PET systems with panel detectors. A rebinning algorithm averages

    更新日期:2019-11-01
  • High Order Total Variation Minimization for Interior Tomography.
    Inverse Probl. Pub Date : 2010-04-23
    Jiansheng Yang,Hengyong Yu,Ming Jiang,Ge Wang

    Recently, an accurate solution to the interior problem was proposed based on the total variation (TV) minimization, assuming that a region of interest (ROI) is piecewise constant. In this paper, we generalize that assumption to allow a piecewise polynomial ROI, introduce the high order TV (HOT), and prove that an ROI can be accurately reconstructed from projection data associated with x-rays through

    更新日期:2019-11-01
  • Deblurring of Class-Averaged Images in Single-Particle Electron Microscopy.
    Inverse Probl. Pub Date : 2010-03-12
    Wooram Park,Dean R Madden,Daniel N Rockmore,Gregory S Chirikjian

    This paper proposes a method for deblurring of class-averaged images in single-particle electron microscopy (EM). Since EM images of biological samples are very noisy, the images which are nominally identical projection images are often grouped, aligned and averaged in order to cancel or reduce the background noise. However, the noise in the individual EM images generates errors in the alignment process

    更新日期:2019-11-01
  • Calculating tissue shear modulus and pressure by 2D Log-Elastographic methods.
    Inverse Probl. Pub Date : 2010-01-01
    Joyce R McLaughlin,Ning Zhang,Armando Manduca

    Shear modulus imaging, often called elastography, enables detection and characterization of tissue abnormalities. In this paper the data is two displacement components obtained from successive MR or ultrasound data sets acquired while the tissue is excited mechanically. A 2D plane strain elastic model is assumed to govern the 2D displacement, u. The shear modulus, μ, is unknown and whether or not the

    更新日期:2019-11-01
  • Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction?
    Inverse Probl. Pub Date : 2009-01-01
    Xiaochuan Pan,Emil Y Sidky,Michael Vannier

    Despite major advances in x-ray sources, detector arrays, gantry mechanical design and especially computer performance, one component of computed tomography (CT) scanners has remained virtually constant for the past 25 years-the reconstruction algorithm. Fundamental advances have been made in the solution of inverse problems, especially tomographic reconstruction, but these works have not been translated

    更新日期:2019-11-01
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