Introduction Toimage Reconstruction and Inverse Problems

Thiébaut, Éric

doi:10.1007/1-4020-3437-7_25

Cited by 35 publications

(33 citation statements)

References 15 publications

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“…When we analyse the results of calculations presented in Figure 4, we can notice a regularity which becomes the basis for employing the discrete Fourier transform to solving the ill-conditioned algebraic system of linear Equations (11). This figure presents a comparison between the coefficients of the analytical solution expansion (32) by the formula (12) and coefficients obtained from solving the inverse problem by the system of Equations (19).…”

Section: Introductionmentioning

confidence: 94%

“…Distributions of temperature and the normal derivative of the temperature sought after on the inner Inverse Problems in Science and Engineering boundary of the ring were shown in Figure 3(right). Such posed inverse problem is the Cauchy problem in the double-connected domain and is reduced to solving the system of Equations (11). Therefore, one may solve this system of equations using the discrete Fourier transform with reduced number of components of the solution vector or using the Tikhonov regularization.…”

Section: Introductionmentioning

confidence: 99%

“…The Fourier transform is universally used for solving image reconstruction inverse problems in astronomy [11] and medicine (computed tomography), [12,13] among others. In inverse heat conduction problems, an integral Fourier transform is applied to identify boundary conditions [14,15] and to identify the source function.…”

Section: Introductionmentioning

confidence: 99%

“…The vector b in the Equation (11) may represent measurement data containing error. This error has a significant influence on solving the system of Equations (11). Inverse problems belong to the class of ill-posed problems in the Hadamard's sense [3].…”

Section: Introductionmentioning

confidence: 99%

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Regularization of the inverse heat conduction problem by the discrete Fourier transform

Wróblewska

Frąckowiak

Ciałkowski

2015

Inverse Problems in Science and Engineering

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Two methods of solving the inverse heat conduction problem with employment of the discrete Fournier transform are presented in this article. The first one operates similarly to the SVD algorithm and consists in reducing the number of components of the discrete Fournier transform which are taken into account to determine the solution to the inverse problem. The second method is related to the regularization of the solution to the inverse problem in the discrete Fournier transform domain. Those methods were illustrated by numerical examples. In the first example, an influence of the boundary conditions disturbance by a random error on the solution to the inverse problem (its stability) was examined. In the second example, the temperature distribution on the inner boundary of the multiply connected domain was determined. Results of calculations made in both ways brought very good outcomes and confirm the usefulness of applying the discrete Fournier transform to solving inverse problems.

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Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Regularization of the inverse heat conduction problem by the discrete Fourier transform

Wróblewska

Frąckowiak

Ciałkowski

2015

Inverse Problems in Science and Engineering

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“…The variance of the closure phase and differential phases, if not provided by the instrument pipeline, are estimated assuming independence of phase measurements. Image reconstruction can be seen as an inverse problem [39][40][41]. The model which connects object to the measured data involves a NuDFT, as described in Eq.…”

Section: Inverse Problem Approach a Image Reconstruction Problemmentioning

confidence: 99%

PAINTER: a spatiospectral image reconstruction algorithm for optical interferometry

et al. 2014

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Astronomical optical interferometers sample the Fourier transform of the intensity distribution of a source at the observation wavelength. Because of rapid perturbations caused by atmospheric turbulence, the phases of the complex Fourier samples (visibilities) cannot be directly exploited. Consequently, specific image reconstruction methods have been devised in the last few decades. Modern polychromatic optical interferometric instruments are now paving the way to multiwavelength imaging. This paper is devoted to the derivation of a spatio-spectral ("3D") image reconstruction algorithm, coined PAINTER (Polychromatic opticAl INTErferometric Reconstruction software). The algorithm relies on an iterative process, which alternates estimation of polychromatic images and of complex visibilities. The complex visibilities are not only estimated from squared moduli and closure phases, but also differential phases, which helps to better constrain the polychromatic reconstruction. Simulations on synthetic data illustrate the efficiency of the algorithm and in particular the relevance of injecting a differential phases model in the reconstruction.

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Spectro-astrometry: The Method, its Limitations, and Applications

Whelan

Garcia

Jets From Young Stars II

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Introduction Toimage Reconstruction and Inverse Problems

Cited by 35 publications

References 15 publications

Regularization of the inverse heat conduction problem by the discrete Fourier transform

Regularization of the inverse heat conduction problem by the discrete Fourier transform

PAINTER: a spatiospectral image reconstruction algorithm for optical interferometry

Spectro-astrometry: The Method, its Limitations, and Applications

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