Some General Study on Image Restoration.

Date of Submission

December 1992

Date of Award

Winter 12-12-1993

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Master's Dissertation

Degree Name

Master of Technology

Subject Name

Computer Science


Electronics and Communication Sciences Unit (ECSU-Kolkata)


Ray, Kumar Sankar (ECSU-Kolkata; ISI)

Abstract (Summary of the Work)

Image restoration is a well known problem of image processing. Several works have been developed in this direction by several researchers [1] [2] [3] [4]. But one drawback of all these works is that they have not considered the nonnegativity constraint of the restored gray level value. The negative values in the gray level value implies an absurdity of negative intensities of radiant energy in the original object distribution.Another drawback some of the said works, where of certain optimal conditions are tested, is that there is no explicit test for sufficiency of optimality of the restoration. In addition to this sometimes the necessary extreme point of restoration, is shifted heuristically to achieve nonnegative value of the gray levels of the restored image.Considering all these drawbacks of the existing image restoration methods , in this dissertation, we represent an pproach for unconstrained and constrained image restoration sethods using Quadratic Programming Technique. Along with the suitable constraint equations, needed for improving the quality of the restored image, we consider the non-negativity constraints of the restored gray level image. We also consider the necessary and sufficient conditions of optimality of the objective function.The image represented by a vector of order (n x 1) is degraded due to defocusing and additive noise. The obtained image , represented by a vector of order (m x 1) is formed by the relation g = Hf + 1, where H is the degraded matrix of order (m x n). H is formed by the concept of point spread function [2] [4] and 7 of order (m x 1) is uncorrelated random noise. In the absence of any knowledge about our object isto minimize Z(f) (g Hf) (g - hf) (1) subject to the condition ft≤ 0.To further improve the quality of image add the we following constraint equations,Vf ≤ p where is the vector formed by the second derivative of the given image ‘g’ and V’ is the smoothing matrix [1].We also propose a method to estimate the degradation matrix H on the basis of sample values of original image 'f and degraded image ‘g’.


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Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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