Mathematical analysis of super-resolution methodology

The attainment of super resolution (SR) from a sequence of degraded undersampled images could be viewed as reconstruction of the high-resolution (HR) image from a finite set of its projections on a sampling lattice. This can then be formulated as an optimization problem whose solution is obtained by minimizing a cost function. The approaches adopted and their analysis to solve the formulated optimization problem are crucial, The image acquisition scheme is important in the modeling of the degradation process. The need for model accuracy is undeniable in the attainment of SR along with the design of the algorithm whose robust implementation will produce the desired quality in the presence of model parameter uncertainty. To keep the presentation focused and of reasonable size, data acquisition with multisensors instead of, say a video camera is considered.published_or_final_versio

Preconditioned iterative methods for superresolution image reconstruction with multisensors

We study the problem of reconstructing a super-resolution image f from multiple undersampled, sifted, degraded frames with subpixel displacement errors. The corresponding operator H is a spatially- variant operator. In this paper, we apply the preconditioned conjugate gradient method with cosine transform preconditioners to solve the discrete problems. Preliminary results show that our method converges very fast and gives sound recovery of the super- resolution images.published_or_final_versio

Analysis of displacement errors in high-resolution image reconstruction with multisensors

An image-acquisition system composed of an array of sensors, where each sensor has a subarray of sensing elements of suitable size, has recently been popular for increasing the spatial resolution with high signal-to-noise ratio beyond the performance bound of technologies that constrain the manufacture of imaging devices. Small perturbations around the ideal subpixel locations of the sensing elements (responsible for capturing the sequence of undersampled degraded frames), because of imperfections in fabrication, limit the performance of the signal-processing algorithms for processing and integrating the acquired images for the desired enhanced resolution and quality. The contributions of this paper include an analysis of the displacement errors on the convergence rate of the iterative approach for solving the transform based preconditioned system of equations. Subsequently, it is established that the use of the MAP, L2 norm or H1 norm regularization functional leads to a proof of linear convergence of the conjugate gradient method in terms of the displacement errors caused by the imperfect subpixel locations. Results of simulation support the analytical results.published_or_final_versio

Extending the depth of field in a compound-eye imaging system with super-resolution reconstruction

Optical device miniaturization is highly desirable in many applications. Direct down-scaling of traditional imaging system is one approach, but the extent to which it can be minimized is limited by the effect of diffraction. Compound-eye imaging system, which utilizes multiple microlenses in image capture is a promising alternative. In this paper, we explore the possibility of an incorporation of phase masks in such a system to extend the depth of field. Simulation experiments are conducted to verify the feasibility of the system. © 2006 IEEE.published_or_final_versio

Multiscale and Multitopic Sparse Representation for Multisensor Infrared Image Superresolution

Methods based on sparse coding have been successfully used in single-image superresolution (SR) reconstruction. However, the traditional sparse representation-based SR image reconstruction for infrared (IR) images usually suffers from three problems. First, IR images always lack detailed information. Second, a traditional sparse dictionary is learned from patches with a fixed size, which may not capture the exact information of the images and may ignore the fact that images naturally come at different scales in many cases. Finally, traditional sparse dictionary learning methods aim at learning a universal and overcomplete dictionary. However, many different local structural patterns exist. One dictionary is inadequate in capturing all of the different structures. We propose a novel IR image SR method to overcome these problems. First, we combine the information from multisensors to improve the resolution of the IR image. Then, we use multiscale patches to represent the image in a more efficient manner. Finally, we partition the natural images into documents and group such documents to determine the inherent topics and to learn the sparse dictionary of each topic. Extensive experiments validate that using the proposed method yields better results in terms of quantitation and visual perception than many state-of-the-art algorithms

Superresolution imaging: A survey of current techniques

Cristóbal, G., Gil, E., Šroubek, F., Flusser, J., Miravet, C., Rodríguez, F. B., “Superresolution imaging: A survey of current techniques”, Proceedings of SPIE - The International Society for Optical Engineering, 7074, 2008. Copyright 2008. Society of Photo Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibited.Imaging plays a key role in many diverse areas of application, such as astronomy, remote sensing, microscopy, and tomography. Owing to imperfections of measuring devices (e.g., optical degradations, limited size of sensors) and instability of the observed scene (e.g., object motion, media turbulence), acquired images can be indistinct, noisy, and may exhibit insufficient spatial and temporal resolution. In particular, several external effects blur images. Techniques for recovering the original image include blind deconvolution (to remove blur) and superresolution (SR). The stability of these methods depends on having more than one image of the same frame. Differences between images are necessary to provide new information, but they can be almost unperceivable. State-of-the-art SR techniques achieve remarkable results in resolution enhancement by estimating the subpixel shifts between images, but they lack any apparatus for calculating the blurs. In this paper, after introducing a review of current SR techniques we describe two recently developed SR methods by the authors. First, we introduce a variational method that minimizes a regularized energy function with respect to the high resolution image and blurs. In this way we establish a unifying way to simultaneously estimate the blurs and the high resolution image. By estimating blurs we automatically estimate shifts with subpixel accuracy, which is inherent for good SR performance. Second, an innovative learning-based algorithm using a neural architecture for SR is described. Comparative experiments on real data illustrate the robustness and utilization of both methods.This research has been partially supported by the following grants: TEC2007-67025/TCM, TEC2006-28009-E, BFI-2003-07276, TIN-2004-04363-C03-03 by the Spanish Ministry of Science and Innovation, and by PROFIT projects FIT-070000-2003-475 and FIT-330100-2004-91. Also, this work has been partially supported by the Czech Ministry of Education under the project No. 1M0572 (Research Center DAR) and by the Czech Science Foundation under the project No. GACR 102/08/1593 and the CSIC-CAS bilateral project 2006CZ002

Statistical performance analysis of a fast super-resolution technique using noisy translations

15 pagesInternational audienceIt is well known that the registration process is a key step for super-resolution reconstruction. In this work, we propose to use a piezoelectric system that is easily adaptable on all microscopes and telescopes for controlling accurately their motion (down to nanometers) and therefore acquiring multiple images of the same scene at different controlled positions. Then a fast super-resolution algorithm \cite{eh01} can be used for efficient super-resolution reconstruction. In this case, the optimal use of $r^2$ images for a resolution enhancement factor $r$ is generally not enough to obtain satisfying results due to the random inaccuracy of the positioning system. Thus we propose to take several images around each reference position. We study the error produced by the super-resolution algorithm due to spatial uncertainty as a function of the number of images per position. We obtain a lower bound on the number of images that is necessary to ensure a given error upper bound with probability higher than some desired confidence level