Applied and Computational Mathematics Seminar
Monday, March 28, 2011 - 2:00pm
1 hour (actually 50 minutes)
Image restoration has been an active research topic in imageprocessing and computer vision. There are vast of literature, mostof which rely on the regularization, or prior information of theunderlying image. In this work, we examine three types of methodsranging from local, nonlocal to global with various applications.A classical approach for local regularization term is achieved bymanipulating the derivatives. We adopt the idea in the localpatch-based sparse representation to present a deblurringalgorithm. The key observation is that the sparse coefficientsthat encode a given image with respect to an over-complete basisare the same that encode a blurred version of the image withrespect to a modified basis. Following an``analysis-by-synthesis'' approach, an explicit generative modelis used to compute a sparse representation of the blurred image,and its coefficients are used to combine elements of the originalbasis to yield a restored image.We follows the framework that generates the neighborhood filtersto an variational formulation for general image reconstructionproblems. Specifically, two extensions regarding to the weightcomputation are investigated. One is to exploit the recurrence ofstructures at different locations, orientations and scales in animage. While previous methods based on ``nonlocal filtering'' identify corresponding patches only up to translations, we consider more general similarity transformation.The second algorithm utilizes a preprocessed data as input for theweight computation. The requirements for preprocessing are (1) fastand (2) containing sharp edges. We get superior results in theapplications of image deconvolution and tomographic reconstruction.A Global approach is explored in a particular scenario, that is,taking a burst of photographs under low light conditions with ahand-held camera. Since each image of the burst is sharp but noisy,our goal is to efficiently denoise these multiple images. Theproposed algorithm is a complex chain involving accurateregistration, video equalization, noise estimation and the use ofstate-of-the-art denoising methods. Yet, we show that this complexchain may become risk free thanks to a key feature: the noise modelcan be estimated accurately from the image burst.