Recovery of Blocky Images from Noisy and Blurred Data

David C. Dobson; Fadil Santosa

doi:10.1137/s003613999427560x

Abstract

The purpose of this investigation is to understand situations under which an enhancement method succeeds in recovering an image from data which are noisy and blurred. The method in question is due to Rudin and Osher. The method selects, from a class of feasible images, one that has the least total variation. Our investigation is limited to images which have small total variation. We call such images "blocky" as they are commonly piecewise constant (or nearly so) in grey-level values. The image enhancement is applied to three types of problems, each one leading to an optimization problem. The optimization problems are analyzed in order to understand the conditions under which they can be expected to succeed in reconstructing the desired blocky images. We illustrate the main findings of our work in numerical examples.

Keywords

PiecewiseImage (mathematics)Computer scienceConstant (computer programming)Optimization problemArtificial intelligenceImage restorationVariation (astronomy)Class (philosophy)Computer visionMathematicsMathematical optimizationImage processingAlgorithmMathematical analysis

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Publication Info

Year: 1996
Type: article
Volume: 56
Issue: 4
Pages: 1181-1198
Citations: 262
Access: Closed

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APA Style

                            
                                    David C. Dobson, 
                                
                                    Fadil Santosa
                                
                            (1996). 
                            Recovery of Blocky Images from Noisy and Blurred Data. 
                            SIAM Journal on Applied Mathematics
                            , 56
                            (4)
                            , 1181-1198.
                            https://doi.org/10.1137/s003613999427560x

Identifiers

DOI: 10.1137/s003613999427560x