Abstract
Super-resolution image reconstruction produces a high-resolution image from a set of shifted, blurred, and decimated versions thereof. Super-resolution image restoration has become an active research issue in the field of image restoration. In general, super-resolution image restoration is an ill-posed problem. Prior knowledge about the image can be combined to make the problem well-posed, which contributes to some regularization methods. In these regularization methods, however, regularization parameter was selected by experience in some cases. Other techniques to compute the parameter had too heavy computation cost. This paper presents a generalization of restoration theory for the problem of Super-Resolution Reconstruction (SRR) of an image. In the SRR problem, a set of low quality images is given, and a single improved quality image which fuses their information is required. We present a model for this problem, and show how the classic restoration theory tools-ML, MAP and POCS-can be applied as a solution. A hybrid algorithm which joins the POCS and the ML benefits is suggested.
Highlights
The Classic theory of restoration of a single image from linear blur and additive noise has drawn a lot of research attention in the last three decades [1]–[4]
In the single image restoration theory, three major and distinct approaches are extensively used in order to get practical restoration algorithms: 1) Maximum likelihood (ML) estimator [1]–[4], 2) Maximum a posteriori (MAP) probability estimator [1]–[4], and 3) Projection onto convex sets (POCS) approach
The presented methodology enables the incorporation of Projection onto Convex Sets (POCS) into the Maximum Likelihood (ML) or Maximum Posteriori (MAP) restoration algorithms, similar to the way it is done for the iterative single image restoration problem [4], yielding hybrid super-resolution restoration algorithm with further improved performance and assured convergence
Summary
The Classic theory of restoration of a single image from linear blur and additive noise has drawn a lot of research attention in the last three decades [1]–[4]. Super-resolution restoration from a still image is a well recognized example of an ill posed inverse problem Such problems may be approached using regularization methods that constrain the feasible solution space by employing a-priori knowledge. The three approaches merge into one family of algorithms, which generalizes the single image restoration theory [1]–[4] on one hand, and the existing super-resolution algorithms proposed in the literature [5]–[14] on the other hand. The presented methodology enables the incorporation of POCS into the ML or MAP restoration algorithms, similar to the way it is done for the iterative single image restoration problem [4], yielding hybrid super-resolution restoration algorithm with further improved performance and assured convergence
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