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Two new filters for image enhancement are developed, extending the early work of the authors. Une filter uses a new nonlinear time dependent partial differential equation and its discretization, the second uses a discretization which contrains the backwards heat equation and keeps it variation bounded. The evolution of the initial image as t increases through U(x, y, t) is the filtering process. The processed image is piecewise smooth, nonoscillatory and apparently an accurate reconstruction. The algorithms are fast and easy to program. INTRODUCTIONThe accurate and sharp restoration of images and their singularities when corrupted by noise and or blur remains a central problem in numerical image processing.Classical techniques applied to this problem invariably involve a global smoothing (usually via the Fourier transform and/or statistical or probabilistic techniques), a global deconvolution, and an edge detector. The difficulties these approaches introduce are: (i) smearing of edges during noise removal; (ii) ringing, i.e. nonphysical oscillations resembling Gibbs' phenomena near edges and features; (iii) inferior edge detection due to these phenomena.We shall report here on a new approach which is highly nonlinear, nonsmearing, and nonoscillatory. The techniques emphasize the processing and reconstruction of singularities, e.g. edges, in the signals. The goal is the removal of noise, the deblurring of smoothed out images, and the accurate and sharp reconstruction of edges in the signal.In fact the image processing tasks that we (and collaborators) have handled using these techniques include: deblurring, denoising, simultaneously deblurring and denoising, recovery of shapes from shading, edge detection, segmentation and compression. In this paper we shall concentrate on our deblurring algorithms.In our first paper, we proposed a new class of techniques for enhancementi.e.Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/25/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx SPIE Vol. 1567 Applications of Digital Image Processing XIV (1991) / 415 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/25/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx