We address the problem of image superresolution and present a novel approach to single-frame superresolution using fractal image coding. The proposed approach takes great advantage of the properties of fractals—resolution independence, similarity preservation, and nonlinear operation—which are suited for image superresolution, specifically for image restoration and magnification. The idea of our work is to estimate the fractal code of the original image from its degraded (blurred and noised) observation and decode it at a higher resolution, and all the strategies are performed in the fractal image coding framework. To achieve this, we employ an adaptive fractal coding scheme in the frequency domain, and further, we introduce an overlapping partition scheme to remove the blocky artifacts and improve the reconstruction quality. Experiments on simulated and real images show that the resulting fractal-based superresolution method yields superior performance to conventional single-frame superresolution methods.
KEYWORDS: Point spread functions, Image processing, Super resolution, Image restoration, Lawrencium, Optical engineering, Image analysis, Image registration, Reconstruction algorithms, Signal to noise ratio
Blind superresolution (BSR) is one of the challenges in image superresolution. We propose a new approach using a unified regularization framework, which solves image registration, point spread function (PSF) estimation, and high-resolution (HR) image reconstruction simultaneously. To achieve this, the anisotropic diffusion techniques are employed as one regularization term to preserve edge information in the HR image estimation, and a generalized version of the eigenvector-based (EVAM) constraint is developed to regularize the PSF. An alternating minimization algorithm is devised to find optimal solutions, and an effective numerical implementation scheme, based on local filtering, is proposed to suppress the ringing artifacts in the image reconstruction. Finally, experiments with synthetic and real data are presented to demonstrate the effectiveness and robustness of our approach, which can handle motion blur well and enhance resolution notably for very noisy images.
Blind super-resolution (BSR) is one of the challenges in the super-resolution image reconstruction area. In this paper, we propose a general approach, which is based on a partial differential equation (PDE) framework, to incorporate the image registration into the point spread function (PSF) estimation process and reconstruct an HR image simultaneously. Since the reconstruction problem is ill-posed, anisotropic diffusion techniques are employed as a regularization term to preserve discontinuities in the HR image estimation.
Furthermore, a generalized version of the eigenvector-based alternating minimization (EVAM) constraint, which was proposed for a multichannel framework recently, is developed as another regularization term for the estimations of the PSFs. In this way, a novel blind super-resolution alternating minimization algorithm (BSR-AM) is developed to solve the general model. Experimental results are provided to demonstrate the performance of the proposed algorithm using simulated and real data. The proposed algorithm yields satisfying results, and quantitative error analysis and comparison with the MAP estimation method is illustrated.