Local, Non-local and Global Methods in Image Reconstruction

Image restoration has been an active research topic in image processing and computer vision. There are vast of literature, most of which rely on the regularization, or prior information of the underlying image. In this work, we examine three types of methods ranging from local, nonlocal to global with various applications.;A classical approach for local regularization term is achieved by manipulating the derivatives. We adopt the idea in the local patch-based sparse representation to present a deblurring algorithm. The key observation is that the sparse coefficients that encode a given image with respect to an over-complete basis are the same that encode a blurred version of the image with respect to a modified basis. Following an "analysis-by-synthesis'' approach, an explicit generative model is used to compute a sparse representation of the blurred image, and its coefficients are used to combine elements of the original basis to yield a restored image.;We follows the framework that generates the neighborhood filters to a variational formulation for general image reconstruction problems. Specifically, two extensions regarding to the weight computation arc investigated. One is to exploit the recurrence of structures at different locations, orientations and scales in an image. 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 the weight computation. The requirements for preprocessing are (1) fast and (2) containing sharp edges. We get superior results in the applications 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 a hand-held camera. Since each image of the burst is sharp but noisy, our goal is to efficiently denoise these multiple images. The proposed algorithm is a complex chain involving accurate registration, video equalization, noise estimation and the use of state-of-the-art denoising methods. Yet, we show that this complex chain may become risk free thanks to a key feature: the noise model can be estimated accurately from the image burst.