A Fast Algorithm for Image Super-Resolution from Blurred Observations

Abstract

We study the problem of reconstruction of a high-resolution image from several blurred low-resolution image frames. The image frames consist of blurred, decimated, and noisy versions of a high-resolution image. The high-resolution image is modeled as a Markov random field (MRF), and a maximum a posteriori (MAP) estimation technique is used for the restoration. We show that with the periodic boundary condition, a high-resolution image can be restored efficiently by using fast Fourier transforms. We also apply the preconditioned conjugate gradient method to restore high-resolution images in the aperiodic boundary condition. Computer simulations are given to illustrate the effectiveness of the proposed approach.

Super-resolution: a comprehensive survey

“…If it is nonconvex, the time consuming simulated annealing can be used [5] (1987), [6], [135], [241], [483], or else Graduated Non-Convexity [95], [293], [496] (with normalized convolution for obtaining an initial good approximation), [540], EM [113], [181], [288], [454], Genetic Algorithm [174], Markov Chain Monte Carlo using Gibbs Sampler [209], [214], [234], [241], [254], [612], Energy Minimization using Graph-Cuts [248], [279], [305], [535], Bregman Iteration [353], [590], proximal iteration [357], (Regularized) Orthogonal Matching Pursuit [390], [464], and Particle Swarm Optimization [448] might be used. [109], [118], [133], [172], [181], [184], [197], [199], [204], [216], [218], [221], [223], [226], [229], [251]...…”

“…In addition to the above mentioned methods in the frequency domain, some other SR algorithms of this domain have borrowed the methods that have been usually used in the spatial domain; among them are: [119], [211], [321], [370], [589] which have used a Maximum Likelihood (ML) method (Section 5.1.5), [144], [178], [201] which have used a regularized ML method, [197], [221], [267], [491], [511], [567] which have used a MAP method (Section 5.1.6), and [141], [175] which have implemented a Projection Onto Convex Set (POCS) method (Section 5.1.4). These will all be explained in the next section.…”

“…This is mostly the case for the Direct SR algorithm in which different types of filters are utilized, for example in [290], [533] adaptive Wiener filter has been used (Section 5.1.3). - [131], [221] preconditioning of the system has been used so that one can use a faster optimization method, like CG.…”

Multiframe image restoration in the presence of noisy blur kernel

“…The idea of using several degraded frames in the reconstruction of a single restored image is not new. Usually, low-resolution noisy-blurry frames are available to obtain a super-resolution image, as in [4], [15].…”

Robust and computationally efficient superresolution algorithm

“…[1][2][3][4] It is also possible to perform motion-free superresolution in which the idea is to generate a HR image from a set of defocused and downsampled observations blurred to different extents. [5][6][7][8] Yet another group of superresolution algorithms called learning-based methods use specific information about the class of images to be superresolved. 9,10 In this paper, we focus on motion-based superresolution for which many algorithms exist.…”