Estimation theoretical image restoration

Abstract

In this thesis, we have developed an extensive study to evaluate image restoration from a single image, colored or monochromatic. Using a mixture of Gaussian and Poisson noise process, we derived an objective function to estimate the unknown object and point spread function (psf) parameters. We have found that, without constraint enforcement, this blind deconvolution algorithm tended to converge to the trivial solution: delta function as the estimated psf and the detected image as the estimated object. We were able to avoid this solution set by enforcing a priori knowledge about the characteristics of the solution, which included the constraints on object sharpness, energy conservation, impulse response point spread function solution, and object gradient statistics. Applying theses constraints resulted in significantly improved solutions, as evaluated visually and quantitatively using the distance of the estimated to the true function. We have found that the distance of the estimated psf was correlated better with visual observation than the distance metric using the estimated object. Further research needs to be done in this area. To better pose the problem, we expressed the point spread function as a series of Gaussian basis functions, instead of the pixel basis function formalism used above. This procedure has reduced the dimensionality of the parameter space and has resulted in improved results, as expected. We determined a set of weights that yielded optimum algorithm performance.

(cont.) Additional research needs to be done to include the weight set as optimization parameters. This will free the user from having to adjust the weights manually. Of course, if certain knowledge of a weight is available, then it may be better to start with that as an initial guess and optimize from there. With the knowledge that the gradient of the object obeys long-tailed distribution, we have incorporated a constraint using the first two moments, mean and variance, of the gradient of the object in the objective function. Additional research should be done to incorporate the entire distribution in the objective and gradient functions and evaluate the performance.