Estimates of the convergence rate for a dynamical reconstruction algorithm

Super-resolution reconstruction for image breaks through the resolution limit of imaging systems without hardware change. The algorithm of projection onto convex set (POCS) is a typical super-resolution reconstruction algorithm in spatial domain. The classical algorithm of POCS lacks the overall constraint for the image, and the convergence rate for iteration is incontrollable. A new super-resolution restoration algorithm for image based on entropy constraint and POCS is proposed in this paper, and experiments with optical and millimeter wave images demonstrate that the new algorithm is effective in improving the precision of super-resolution restoration.

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A Doubly Constrained TV Algorithm for Image Reconstruction

Mathematical Problems in Engineering ◽

10.1155/2020/5382106 ◽

2020 ◽

Vol 2020 ◽

pp. 1-15

Author(s):

Zhiwei Qiao ◽

Gage Redler ◽

Boris Epel ◽

Howard Halpern

Keyword(s):

Image Reconstruction ◽

Convergence Rate ◽

Simulated Data ◽

Reconstruction Algorithm ◽

Model Parameters ◽

Resonance Imaging ◽

Reconstruction Accuracy ◽

Paramagnetic Resonance ◽

Positron Emission ◽

Tv Model

Purpose. The total variation (TV) minimization algorithm is an effective image reconstruction algorithm capable of accurately reconstructing images from sparse and/or noisy data. The TV model consists of two terms: a data fidelity term and a TV regularization term. Two constrained TV models, data divergence-constrained TV minimization (DDcTV) and TV-constrained data divergence minimization (TVcDM), have been successfully applied to computed tomography (CT) and electron paramagnetic resonance imaging (EPRI). In this work, we propose a new constrained TV model, a doubly constrained TV (dcTV) model, which has the potential to further improve the reconstruction accuracy for the two terms which are both of constraint forms. Methods. We perform an inverse crime study to validate the model and its Chambolle-Pock (CP) solver and characterize the performance of the dcTV-CP algorithm in the context of CT. To demonstrate the superiority of the dcTV model, we compare the convergence rate and the reconstruction accuracy with the DDcTV and TVcDM models via simulated data. Results and Conclusions. The performance-characterizing study shows that the dcTV-CP algorithm is an accurate and convergent algorithm, with the model parameters impacting the reconstruction accuracy and the algorithm parameters impacting the convergence path and rate. The comparison studies show that the dcTV-CP algorithm has a relatively fast convergence rate and can achieve higher reconstruction accuracy from sparse projections or noisy projections relative to the other two single-constrained TV models. The knowledge and insights gained in the work may be utilized in the application of the new model in other imaging modalities including divergence-beam CT, magnetic resonance imaging (MRI), positron emission tomography (PET), and EPRI.

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On dynamical reconstruction of boundary and distributed inputs in a Schlögl equation

Journal of Inverse and Ill-Posed Problems ◽

10.1515/jiip-2019-0048 ◽

2019 ◽

Vol 27 (6) ◽

pp. 877-889

Author(s):

Vyacheslav I. Maksimov

Keyword(s):

Convergence Rate ◽

Unknown Input ◽

Phase Coordinates ◽

Guaranteed Control ◽

Dynamical Reconstruction

Abstract The problem of reconstructing an unknown input under measuring a phase coordinates of a Schlögl equation is considered. We propose a solving algorithm that is stable to perturbations and is based on the combination of ideas from the theory of dynamical inversion and the theory of guaranteed control. The convergence rate of the algorithm is obtained.

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An improved convergence rate of A-P reconstruction algorithm and application in signal processing

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2015.02.009 ◽

2015 ◽

Vol 287 ◽

pp. 12-19

Author(s):

Chen Zhao ◽

Bencheng Chai ◽

Xuelin Chen

Keyword(s):

Signal Processing ◽

Convergence Rate ◽

Reconstruction Algorithm

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The methods of dynamical reconstruction of an input in a system of ordinary differential equations

Journal of Inverse and Ill-Posed Problems ◽

10.1515/jiip-2020-0040 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Vyacheslav I. Maksimov

Keyword(s):

Feedback Control ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Reconstruction Algorithm ◽

System A ◽

Ill Posed ◽

Computational Errors ◽

Combination Of Methods ◽

Input Reconstruction ◽

Dynamical Reconstruction

AbstractIn the paper, for systems described by ordinary differential equations a review of algorithms of dynamical input reconstruction by results of inaccurate observations of its solutions is given. The problem under discussion is referred to the class of dynamical inverse problems. The proposed algorithms are stable with respect to informational noises and computational errors. They are based on the combination of methods of the theory of ill-posed problems and the theory of feedback control. The essence of the methodology underlying the algorithms suggested in the paper consists in the representation of a reconstruction algorithm in the form of a feedback control algorithm for a certain artificial dynamical system, a model; such an algorithm, whose output is the realization of the control in the model, is dynamical by its definition.

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Nondestructive Inspection of Thin, Low-Z Samples using Multiplexed Compton Scatter Tomography

MRS Proceedings ◽

10.1557/proc-503-297 ◽

1997 ◽

Vol 503 ◽

Cited By ~ 1

Author(s):

B. L. Evans ◽

J. B. Martin ◽

L. W. Burggraf

Keyword(s):

Signal To Noise Ratio ◽

Reconstruction Algorithm ◽

Filtered Backprojection ◽

Line Broadening ◽

Compton Scatter ◽

X Ray ◽

Tomography System ◽

Transmission Computed Tomography ◽

High Purity Germanium ◽

Scattered Energy

ABSTRACTThe viability of a Compton scattering tomography system for nondestructively inspecting thin, low Z samples for corrosion is examined. This technique differs from conventional x-ray backscatter NDI because it does not rely on narrow collimation of source and detectors to examine small volumes in the sample. Instead, photons of a single energy are backscattered from the sample and their scattered energy spectra are measured at multiple detector locations, and these spectra are then used to reconstruct an image of the object. This multiplexed Compton scatter tomography technique interrogates multiple volume elements simultaneously. Thin samples less than 1 cm thick and made of low Z materials are best imaged with gamma rays at or below 100 keV energy. At this energy, Compton line broadening becomes an important resolution limitation. An analytical model has been developed to simulate the signals collected in a demonstration system consisting of an array of planar high-purity germanium detectors. A technique for deconvolving the effects of Compton broadening and detector energy resolution from signals with additive noise is also presented. A filtered backprojection image reconstruction algorithm with similarities to that used in conventional transmission computed tomography is developed. A simulation of a 360–degree inspection gives distortion-free results. In a simulation of a single-sided inspection, a 5 mm × 5 mm corrosion flaw with 50% density is readily identified in 1-cm thick aluminum phantom when the signal to noise ratio in the data exceeds 28.

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