Image interpolation using Shearlet based iterative refinement

This paper proposes an image interpolation algorithm exploiting sparse representation for natural images. It involves three main steps: (a) obtaining an initial estimate of the high resolution image using linear methods like FIR filtering, (b) promoting sparsity in a selected dictionary through iterative thresholding, and (c) extracting high frequency information from the approximation to refine the initial estimate. For the sparse modeling, a shearlet dictionary is chosen to yield a multiscale directional representation. The proposed algorithm is compared to several state-of-the-art methods to assess its objective as well as subjective performance. Compared to the cubic spline interpolation method, an average PSNR gain of around 0.8 dB is observed over a dataset of 200 images

Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the proposed framework with structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared to traditional sparse inverse problem techniques. This interpretation also suggests an effective dictionary motivated initialization for the MAP-EM algorithm. We demonstrate that in a number of image inverse problems, including inpainting, zooming, and deblurring, the same algorithm produces either equal, often significantly better, or very small margin worse results than the best published ones, at a lower computational cost.Comment: 30 page

FRESH – FRI-based single-image super-resolution algorithm

In this paper, we consider the problem of single image super-resolution and propose a novel algorithm that outperforms state-of-the-art methods without the need of learning patches pairs from external data sets. We achieve this by modeling images and, more precisely, lines of images as piecewise smooth functions and propose a resolution enhancement method for this type of functions. The method makes use of the theory of sampling signals with finite rate of innovation (FRI) and combines it with traditional linear reconstruction methods. We combine the two reconstructions by leveraging from the multi-resolution analysis in wavelet theory and show how an FRI reconstruction and a linear reconstruction can be fused using filter banks. We then apply this method along vertical, horizontal, and diagonal directions in an image to obtain a single-image super-resolution algorithm. We also propose a further improvement of the method based on learning from the errors of our super-resolution result at lower resolution levels. Simulation results show that our method outperforms state-of-the-art algorithms under different blurring kernels

Single frame super-resolution image system

The estimation of some unknown quantity information from known observable information can be viewed as a specific statistical process which needs an extra source of information prediction strategy. In this regard, image super-resolution is an important application In this thesis, we proposed a new image interpolation method based on Redundant Discrete Wavelet Transform (RDWT) and self-adaptive processes in which edge direction details are considered to solve single-frame image super-resolution task. Information about sharp variations, both in horizontal and vertical directions derived from wavelet transform sub-bands are considered, followed by detection and modification of the aliasing part in the preliminary output in order to increase the visual effect. By exploiting fundamental properties of images such as property of edge direction, different parts of the source image are considered separately in order to predict the vertical and horizontal details accurately, helping to consummate the whole framework in reconstructing the high-resolution image. Extensive tests of the proposed method show that both objective quality (PSNR) and subjective quality are obviously improved compared to several other state-of-the-art methods. And this work also leaved capacious space for further research, not only theoretical but also practical. Some of the related research applications based on this algorithm strategy are also briefly introduced