טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentRan Kaftory
SubjectColor Image Reconstruction Using the Beltrami
Framework
DepartmentDepartment of Electrical Engineering
Supervisors Dr. Sochen Nir
Professor Emeritus Zeevi Yehoshua


Abstract

A new method for the recovery of noisy and blurred color images is presented. The color image is reconstructed and the blurring kernel is approximated under the assumption of linearity and spatial invariance of the latter, without having a-priori information about the noise and the blur properties. The problem of inverting the blurring kernel and computing the true image from the observed one (the inverse problem) is an ill-posed problem. A general principle for dealing with the instability of the inverse problem is that of regularization, which mainly consists of restricting the set of admissible solutions. The proposed method implements the Beltrami operator as a regularization operator. Consequently image and kernel edges are preserved due to the adaptive smoothing feature of this operator. The color channels are coupled by a Riemannian structure, which is defined on the color image. The restoration scheme is conducted by solving Euler-Lagrange equations using the alternating minimization scheme, linearizing the nonlinear system using the fixed point lagged diffusive method and solving the system using the conjugate gradient scheme. The restoration process was found to be robust and effective with superior properties over other techniques. Results in this representation are demonstrated and compared with other methods, using images blurred by Gaussian, motion and defocus blur.