Digital Image Processing Via Singular Value Decomposition

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In this thesis, well studied linear algebra theory \singular value decomposition" (SVD) and its applications is presented. Singular Value Decomposition is extraor- dinarily useful and has many applications such as data analysis, signal processing, pattern recognition, objects detection and weather prediction. SVD method can transform matrix A into product USV T . Some of these application areas dis- cussed include the Moore-Penrose psuedoinverse, the low rank approximation of matrices, the least square solution to linear systems and image face recognition. To perform face recognition with SVD, the set of known faces were treated as vec- tors in a subspace, called \face space", spanned by a small group of \basefaces". The projection of a new image onto the baseface was then compared to the set of known faces to identify the face. The study also investigated the characteristics of singular values and singular vectors in image processing. SVD was found to be a stable and e ective method to decompose a system into a set of linearly independent components. The approach is robust, simple, easy and fast to im- plement and provides a practical solution to image recognition problem. It was also found that, though the singular values are unique, the singular vectors are more important in image processing. MATLAB R2012a with image processing toolbox was used as the development tool for implementing the algorithm.
A Thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfillment of the requirements for the degree of Master of Philosophy, May-2013