Linear inverse problems in imaging

Ribés, Alejandro; Schmitt, Francis

doi:10.1109/msp.2008.923099

Cited by 128 publications

(101 citation statements)

References 21 publications

Supporting

Mentioning

100

Contrasting

Order By: Relevance

“…Ribé s and Schmitt [61] applied idea of inverse problem in image processing for reconstructing images. As we know, the inverse problem is a classical problem in Physics.…”

Section: E Linear Inverse Problemmentioning

confidence: 99%

A Review on Image Reconstruction through MRI k-Space Data

Jhamb¹,

Rejathalal²,

Govindan³

2015

IJIGSP

View full text Add to dashboard Cite

Abstract-Image reconstruction is the process of generating an image of an object from the signals captured by the scanning machine. Medical imaging is an interdisciplinary field combining physics, biology, mathematics and computational sciences. This paper provides a complete overview of image reconstruction process in MRI (Magnetic Resonance Imaging). It reviews the computational aspect of medical image reconstruction.

show abstract

“…Ribé s and Schmitt [61] applied idea of inverse problem in image processing for reconstructing images. As we know, the inverse problem is a classical problem in Physics.…”

Section: E Linear Inverse Problemmentioning

confidence: 99%

A Review on Image Reconstruction through MRI k-Space Data

Jhamb¹,

Rejathalal²,

Govindan³

2015

IJIGSP

View full text Add to dashboard Cite

show abstract

“…Inverse problems arise from the necessity of knowing the source (or sources) that generates some physical phenomena [72], [79][80]. Normally, in a classical direct problem we know some sources and a mathematical model that describes the behaviour of the physical phenomena in terms of the sources.…”

Section: An Inverse Problem Descriptionmentioning

confidence: 99%

“…In the model of (6.7) the objective is to find the source (source), given a mathematical model describing the system (system) and a set of data (inevitably noisy) containing the answer (answer). For solving (6.7) by a numerical method, which is the most common practice, it is necessary to convert the continuous model in (6.7) into a discrete one [79][80], resulting in the following:…”

Section: An Inverse Problem Descriptionmentioning

confidence: 99%

“…where is a matrix describing the behaviour of the system (or physical phenomena); it is often called coefficient matrix [79][80], is a column vector representing the unknown source and is a column vector containing the answer (e.g., measurements by means of some instrument).…”

Section: An Inverse Problem Descriptionmentioning

confidence: 99%

“…If the three above conditions are satisfied, the problem is defined as wellconditioned but, if at least one of them is not satisfied, the problem is defined as ill-conditioned [73], [76], [79][80]. This ill-conditioning may occurs due to the use of an incorrect mathematical model, in which case it should be modified, or because this ill-conditioning is an intrinsic part of the formulation.…”

Section: Ill-conditioned Problemsmentioning

confidence: 99%

See 2 more Smart Citations

New Strategies to Improve Multilateration Systems in the Air Traffic Control

Gaviria¹,

Antonio²

View full text Add to dashboard Cite

This thesis is focused on the Mode S Multilateration (MLAT) systems for the Air Traffic Control (ATC) operations, specifically on their layout design and on the process of cooperative targets localization performed by them. It addresses the development of new design and localization strategies. The design strategies are based on the application of metaheuristic optimization techniques, whilst the localization ones are based on the application and combination of regularization methods along with some current localization algorithms.The design strategies are composed of an effective, general procedure to emplace both the standard and enhanced MLAT receiving stations on a surveillance volume, and a set of design strategies to be used with such a proposed procedure. This procedure uses the metaheuristic of Genetic Algorithms (GA), and is intended to obtain useful design parameters that allow optimal system configurations that provide suitable performance levels. Furthermore, the procedure developed in this thesis is able to evaluate and improve previous system designs, as well as possible system enhancements. For this context, we overcome several issues like the lack of a general model that relates the system performance parameters with those ones that can be simulated on a computer, the setting of the design problem as a computer optimization one, the development and application of the numerical tools to analyze and evaluate the MLAT systems performance, the complexity evaluation of the resulting computer optimization problem, and the application and modification of the GA components for solving such a optimization problem. To validate the contributions in this context, some simulations are performed on a real airport scenario.The localization strategies are composed of a set of developed regularized location estimators, a set of developed additional improvements, and the use of some current localization algorithms. These strategies can be used for both surface and wide areas surveillance, and solve some practical problems like the loss of position accuracy when using a small number of stations, or viii Abstract for small areas where the stations are close to each other (e.g., airport surface surveillance), and the mitigation of some errors due to multipath effect. Moreover, the proposed localization strategies are found to be highly statistically and numerically efficient, in contrast to current ones that are efficient in only one sense (i.e., statistically or numerically). For this context, we overcome several issues like the identification and evaluation of the numerical causes of the above mentioned problems, the analysis of the current localization algorithms, the adaptation of the regularization methods theory for solving the localization problem, the development of some numerical additional tools that allows the real time implementation of such proposed algorithms, and the combination of the current algorithms with the proposed ones. To validate the contributions in this context, some simulations wit...

show abstract

From the Sensor to Color Images

Losson¹,

Dinet²

2012

Digital Color

View full text Add to dashboard Cite

Linear inverse problems in imaging

Cited by 128 publications

References 21 publications

A Review on Image Reconstruction through MRI k-Space Data

A Review on Image Reconstruction through MRI k-Space Data

New Strategies to Improve Multilateration Systems in the Air Traffic Control

From the Sensor to Color Images

Contact Info

Product

Resources

About