Image restoration and diffusion processes

Alfred S. Carasso

doi:10.1117/12.146607

23 June 1993 Image restoration and diffusion processes

Alfred S. Carasso

Proceedings Volume 2035, Mathematical Methods in Medical Imaging II; (1993) https://doi.org/10.1117/12.146607
Event: SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, 1993, San Diego, CA, United States

Abstract

A new supplementary a-priori constraint, the slow evolution from the boundary constraint, (SEB), sharply reduces noise contamination in a large class of space-invariant image deblurring problems that occur in medical, industrial, surveillance, environmental, and astronomical application. The noise suppressing properties of SEB restoration can be proved mathematically, on the basis of rigorous error bounds for the reconstruction, as a function of the noise level in the blurred image data. This analysis proceeds by reformulating the image deblurring problem into an equivalent ill-posed problem for a time-reversed diffusion equation. The SEB constraint does not require smoothness of the image. An effective, fast, non-iterative procedure, based on FFT algorithms, may be used to compute SEB restorations. For a 512 X 512 image, the procedure requires about 45 seconds of cpu time on a Sun/sparc2. A documented deblurring experiment, on an image with significant high frequency content, illustrates the computational significance of the SEB constraint by comparing SEB and Tikhonov-Miller reconstructions using optimal values of the regularization parameters.

Citation Download Citation

Alfred S. Carasso "Image restoration and diffusion processes", Proc. SPIE 2035, Mathematical Methods in Medical Imaging II, (23 June 1993); https://doi.org/10.1117/12.146607

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