Abstract
Image super-resolution is an image reconstruction technique which attempts to reconstruct a high resolution image from one or more under-sampled low-resolution images of the same scene. High resolution images aid in analysis and inference in a multitude of digital imaging applications. However, due to limited accessibility to high-resolution imaging systems, a need arises for alternative measures to obtain the desired results. We propose a three-dimensional single image model to improve image resolution by estimating the analog image intensity function. In recent literature, it has been shown that image patches can be represented by a linear combination of appropriately chosen basis functions. We assume that the underlying analog image consists of smooth and edge components that can be approximated using a reproducible kernel Hilbert space function and the Heaviside function respectively. We also extend the proposed method to pansharpening, a technology to fuse a high resolution panchromatic image with a low resolution multi-spectral image for a high resolution multi-spectral image. Various numerical results of the proposed formulation indicate competitive performance when compared to some state-of-the-art algorithms.
Highlights
During image acquisition, we often loose resolution due to the limited density of the imaging sensors and the blurring of the acquisition lens
Similar as in Deng et al [40], we model image intensity function defined on a small image patch as a linear combination of reproducing Kernel Hilbert function (RKHS) and approximated Heaviside function (AHF) which models the smooth and edge components, respectively
Results of Algorithm 2 are compared with component substitituion (CS) methods such as principal component analysis (PCA), IHS, Brovey, GS and Indusion, as well as multiresolution analysis (MRA) methods such as high-pass filtering (HPF), smooth filterbased intensity modulation (SFIM), additive “á trous" wavelet transform (ATWT), additive wavelet luminance proportional (AWLP), generalized Laplacian pyramid (GLP) techniques, and the Deng et al pansharpening model [43]
Summary
We often loose resolution due to the limited density of the imaging sensors and the blurring of the acquisition lens. Dictionary learning based methods explore the self-similarities of the image and Single 3D Image Super Resolution are robust, albeit rather slow training time of the dictionary atoms. The proposed method falls in this category Another category is deep neural network based approach that uses a large amount of training data to obtain super results [19,20,21,22]. Similar as in Deng et al [40], we model image intensity function defined on a small image patch as a linear combination of reproducing Kernel Hilbert function (RKHS) and approximated Heaviside function (AHF) which models the smooth and edge components, respectively. Our proposed model is based on this approach using the Taylor series expansion We review these methods in the following subsections
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