Two iterative image restoration algorithms with applications to nuclear medicine

Two methods for recovering an image that has been degraded while being processed are presented. The restoration problem is formulated as a constrained optimization problem in which a measure of smoothness based on the second derivatives of the restored image is maximized subject to the constraint th...

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Bibliographic Details
Published in:IEEE transactions on medical imaging 1992-03, Vol.11 (1), p.2-8
Main Authors: Charalambous, C., Ghaddar, F.K., Kouris, K.
Format: Article
Language:English
Subjects:
Biological and medical sciences
Constraint optimization
Degradation
Discrete Fourier transforms
Distortion measurement
Energy measurement
Humans
Image restoration
Iterative algorithms
Lagrangian functions
Medical sciences
Miscellaneous
Noise measurement
Radiotherapy. Instrumental treatment. Physiotherapy. Reeducation. Rehabilitation, orthophony, crenotherapy. Diet therapy and various other treatments (general aspects)
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Summary:Two methods for recovering an image that has been degraded while being processed are presented. The restoration problem is formulated as a constrained optimization problem in which a measure of smoothness based on the second derivatives of the restored image is maximized subject to the constraint that noise energy is equal to the energy in the difference between the distorted and blurred images. The approach is based on the Lagrange multiplier method. The first algorithm reduces the problem to the computation of few discrete Fourier transforms and allows control of the degree of sharpness and smoothness of the restored image. The second algorithm with weight matrices included allows the handling of edges and flat regions in the image in a pleasing manner for the human visual system. In this case the iterative conjugate gradient method is used in conjunction with the discrete Fourier transform to minimize the Lagrangian function. The application of these algorithms to nuclear medicine images is presented.< >
ISSN:0278-0062
1558-254X
DOI:10.1109/42.126904