Thursday, September 18, 1997
We present a new class of algorithms for edge-preserving restoration of piecewise-smooth images measured in non-Gaussian noise under shift-variant blur. The algorithms are based on maximizing a penalized-likelihood objective function, and are guaranteed to monotonically increase the objective function. The algorithms are derived by using a combination of two previously unconnected concepts: A. De Pierro's convexity technique for optimization transfer, and P. Huber's modified 1-D Newton method. Convergence to the unique global maximum is guaranteed for concave objective functions. The convergence rate is shown to be very fast relative to conventional gradient-based iterations. The proposed algorithms are flexibly parallelizable, and easily accommodate nonnegativity constraints and arbitrary neighborhood structures. Implementation in Matlab is remarkably simple, requiring no cumbersome line searches or tolerance parameters. Examples of both medical and non-medical images will be shown.
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