Tridiagonal matrix enhanced multivariance products representation for image processing applications

In this study, an examined problem is situated in digital image processing area. The above definition of the problem consists when the noise occuring in obtaining the images, transferring or any other reason and the solution is constituted in Tridiagonal Matrix Enhanced Multivariance Products Representation (TMEMPR) method. In the first part of the study, to a better understanding of approaching methods, Singular Value Decomposition (SVD), High Dimensional Model Representation (HDMR) and Enhanced Multivariance Product Representation (EMPR) methods' definitions are given. In the next part, the scope of digital images matrix structure are mentioned, touched on the image type and the definition of measurement error is made. Additionally, image compression is introduced, applications are performed with both TMEMPR and SVD methods. In the last part of the study, image restoration subject is examined. Noise causes in images are presented, a few of the noise types are defined and the noises are added on images similar to a real life conditions. To eliminate noises in images for the purpose of forming the main objective of the study, TMEMPR and SVD methods are used. TDA method's purpose is to highlight the strengths and weaknesses in comparison to the TMEMPR. Noise in images obtained in this part could not be corrected in terms after applications, and also some special filtering methods are used in addition to this two methods, TMEMPR and SVD. In terms of efficiency and expandability, the effects of the TMEMPR method's initial conditions are studied that can lead to further researches.