In this paper a solution is provided to the problem of obtaining a high resolution image from several low resolution images that have been subsampled and displaced by different amounts of subpixel shifts. In its most general form, this problem can be broken up into three sub-problems: registration, restoration,andinterpolation. Previous work has either solved all three sub-problems independently, or more recently, solved either the first two steps (registration and restoration) or the last two steps together. However, none of the existing methods solve all three sub-problems simultaneously. This paper poses the low resolution to high resolution problem as a Maximum Likelihood (ML) problem which is solved by the Expectation-Maximization (EM) algorithm. By exploiting the structure of the matrices involved, the problem can be solved in the discrete frequency domain. The ML problem is then the estimation of the sub-pixel shifts, the noise variances of each image, the power spectra of the high resolution image, and the high resolution image itself. Experimental results are shown which demonstrate the effectiveness of this approach.

In this paper, we consider the estimation of the unknown parameters for the problem of reconstructing a high-resolution image from multiple undersampled, shifted, degraded frames with subpixel displacement errors. We derive mathematical expressions for the iterative calculation of the maximum likelihood estimate of the unknown parameters given the low resolution observed images. These iterative procedures require the manipulation of block-semi circulant (BSC) matrices, that is block matrices with circulant blocks. We show how these BSC matrices can be easily manipulated in order to calculate the unknown parameters. Finally the proposed method is tested on real and synthetic images. Index Terms---Bayesian methods, high-resolution image reconstruction, parameter estimation.

In this paper, we propose novel algorithms for total variation (TV) based image restoration and parameter estimation utilizing variational distribution approximations. Within the hierarchical Bayesian formulation, the reconstructed image and the unknown hyperparameters for the image prior and the noise are simultaneously estimated. The proposed algorithms provide approximations to the posterior distributions of the latent variables using variational methods. We show that some of the current approaches to TV-based image restoration are special cases of our framework. Experimental results show that the proposed approaches provide competitive performance without any assumptions about unknown hyperparameters and clearly outperform existing methods when additional information is included.

Abstract—Using a stochastic framework, we propose two algorithms for the problem of obtaining a single high-resolution image from multiple noisy, blurred, and undersampled images. The first is based on a Bayesian formulation that is implemented via the expectation maximization algorithm. The second is based on a maximum a posteriori formulation. In both of our formulations, the registration, noise, and image statistics are treated as unknown parameters. These unknown parameters and the high-resolution image are estimated jointly based on the available observations. We present an efficient implementation of these algorithms in the frequency domain that allows their application to large images. Simulations are presented that test and compare the proposed algorithms.

Previous work has demonstrated the effectiveness of the ExpectationMaximization algorithm to restore noisy and blurred single-channel images and simultaneously identify its blur. In addition, a general framework for processing multichannel images using single-channel techniques has also been developed. This paper combines and extends the two approaches to the simultaneous blur identification and restoration of multi-channel images. Explicit equations for simultaneous identification and restoration of noisy and blurred multi-channel images are developed, for the general case when cross-channel degradations are present. An important difference from the single channel problem is that the cross-power spectra are complex quantities, which further complicates the analysis of the algorithm. The proposed algorithm is very effective at restoring multi-channel images, as is demonstrated experimentally. Subject terms: multi-channel restoration, blur identification, EM algorithm 1 Introduction ...

The use of mathematical morphology in low and mid-level image processing and computer vision applications has allowed the development of a class of techniques for analyzing shape information in monochrome images. In this paper these techniques are extended to color images. We investigate two approaches for "color morphology": a vector approach, in which color vectors are ranked using a multivariate ranking concept known as reduced ordering, and a component-wise approach, in which grayscale morphological operations are applied to each of the three color component images independently. New vector morphological filtering operations are defined, and a set-theoretic analysis of these vector operations is presented. We also present experimental results comparing the performance of the vector approach and the component-wise approach for two applications: multiscale color image analysis and noise suppression in color images. EDICS: IP 1.7 This work was partially supported by the National Scien...

Abstract. We study the structured total least squares (STLS) problem of system of linear equations Ax = b, where A has a block circulant structure with N blocks. We show that by applying the discrete Fourier transform (DFT), the STLS problem decomposes into N unstructured total least squares (TLS) problems. The N solutions of these problems are then assembled to generate the optimal global solution of the STLS problem. Similar results are obtained for elementary block circulant matrices. Here the optimal solution is obtained by assembling two solutions: one of an unstructured TLS problem and the second of a multidimensional TLS problem.

Abstracf- Clinical angiography-the procedure of acquiring radiographic (fluoroscopic) image sequences of patients from x-ray based medical system+has unquestionably aided cardiol-ogists in their assessment of coronary disease. During such trials, however, literally hundreds of x-ray images are gathered, thereby putting these patients and particularly the medical staff at risk. It is desirable to lower the clinical dosages in use to abate this potential danger. With the dosage reduction, however, comes an inevitable sacrifice in image quality. In this paper, the latter problem is addressed by first modeling the noise that arises as a result of this dosage reduction. It is well-known that this noise is signal-dependent and Poisson-distributed. A model for this type of noise in image sequences is formulated and the commonly utilized noise model for single images is shown to be obtainable from the new model. We propose stochastic temporal filtering techniques to enhance clinical fluorosocopy sequences corrupted by quantum mottle. The temporal versions of these filters as developed in this paper are more suitable for filtering image sequences, as correlations along the time axis can be utilized. For these dynamic sequences, the problem of displacement field estimation is treated in conjunction with the filtering stage to ensure that the temporal correlations are taken along the direction of motion to prevent object blur.

This paper deals with the problem of reconstructing high-resolution text images from an incomplete set of undersampled, blurred, and noisy images shifted with subpixel displacement. We derive mathematical expressions for the calculation of the maximum a posteriori estimate of the high resolution image and the estimation of the parameters involved in the model. The method is tested on real text images and car plates, examining the impact of blurring and the number of available low resolution images on the final estimate.

In this paper we consider the estimation of the unknown hyperparameters for the problem of reconstructing a high-resolution image from multiple undersampled, shifted, blurred and degraded frames with subpixel displacement errors. We derive mathematical expressions for the iterative calculation of the maximum likelihood estimate (mle) of the unknown hyperparameters given the low resolution observed images. Finally, the proposed method is tested on a synthetic image.