Super-resolution (SR) is the process of combining multiple aliased low-quality images to produce a high-resolution high-quality image. Aside from registration and fusion of low-resolution images, a key process in SR is the restoration and denoising of the fused images. We present a novel extension of the combined Fourier-wavelet deconvolution and denoising algorithm ForWarD to the multiframe SR application. Our method first uses a fast Fourier-base multiframe image restoration to produce a sharp, yet noisy estimate of the high-resolution image. Our method then applies a space-variant nonlinear wavelet thresholding that addresses the nonstationarity inherent in resolution-enhanced fused images. We describe a computationally efficient method for implementing this space-variant processing that leverages the efficiency of the fast Fourier transform (FFT) to minimize complexity. Finally, we demonstrate the effectiveness of this algorithm for regular imagery as well as in digital mammography.

It has been shown that electro-optical imaging systems designed by integrating optics and digital processing provide system-level advantages such as extended depth-of-field and lower optical component costs. In such imaging systems, the strength of the optical aberration or blur can dramatically change with the f-number, and hence different digital filters in the subsequent digital processing are required to correct the captured images at different f-numbers. However, implementing such number of filters in hardware requires expensive computational resources, which in turn increase the overall system cost. In this paper, we propose a simple image filtering approach which uses a weighted sum of a set of component finite impulse response (FIR) filters to effectively apply a different composite FIR filter for each f-number. The simulation results demonstrate that our approach achieves desirable image quality for variable f-numbers, while substantially reducing the complexity in hardware implementation.

Still-image processing algorithms are tailored to and depend crucially upon the properties of the class of images to which they are applied, for instance natural images in consumer digital cameras, medical images in fMRI machines, and binary text images in some photocopiers. We describe a new and possibly very important class of images and tasks for which traditional algorithms seem ill-suited, and for which new algorithms and general methods and concepts are required. This new class of images arises in imaging systems designed through new, joint optimization methods where the optics and the image processing are designed simultaneously in order to yield a high-quality digital image. These new design methods yield intermediate optical images that have unusual spatial, noise and chromatic properties ill-served by traditional image methods. Moreover, these new images present a number of novel challenges in image processing hardware implementations such as constrained space-variance. We describe these briefly new, joint methods for designing digital-optical imaging systems, characterize the intermediate optical images they yield, and some of the digital image processing challenges for producing high-quality still images from these sensed optical images.

Accurate registration of images is the most important and challenging aspect of multiframe image restoration problems such as super-resolution. The accuracy of super-resolution algorithms is quite often limited by the ability to register a set of low-resolution images. The main challenge in registering such images is the presence of aliasing. In this paper, we analyse the problem of jointly registering a set of aliased images and its relationship to super-resolution. We describe a statistically optimal approach to multiframe registration which exploits the concept of variable projections to achieve very efficient algorithms. Finally, we demonstrate how the proposed algorithm offers accurate estimation under various conditions when standard approaches fail to provide sufficient accuracy for super-resolution.

Our previous work demonstrates the ability to reconstruct a single higher resolution image from fusing a collection of multiple extremely low-dosage aliased X-ray images. While this computationally efficient method eliminates aliasing artifacts associated with undersampling, it does not address the problem of deblurring the reconstructed image. In this paper, we present a fast nonlinear deblurring algorithm, specifically designed to address the nonstationary noise associated with multiframe reconstructed images. The algorithm uses a combination of Fourier sharpening and wavelet denoising similar to the ForWarD algorithm. Experimental results on enhancing digital mammogram images attest to the effectiveness of the presented method.

Recently, there has been a great deal of work developing super-resolution algorithms for combining a set of low-quality images to produce a set of higher quality images. Either explicitly or implicitly, such algorithms must perform the joint task of registering and fusing the low-quality image data. While many such algorithms have been proposed, very little work has addressed the performance bounds for such problems. In this paper, we analyze the performance limits from statistical first principles using Cramér-Rao inequalities. Such analysis offers insight into the fundamental super-resolution performance bottlenecks as they relate to the subproblems of image registration, reconstruction, and image restoration.

Super-resolution reconstruction produces one or a set of high-resolution images from a set of low-resolution images. In the last two decades, a variety of super-resolution methods have been proposed. These methods are usually very sensitive to their assumed model of data and noise, which limits their utility. This paper reviews some of these methods and addresses their short-comings. We propose an alternate approach using L1 norm minimization and robust regularization based on a bilateral prior to deal with different data and noise models. This computationally inexpensive method is robust to errors in motion and blur estimation and results in images with sharp edges. Simulation results confirm the effectiveness of our method and demonstrate its superiority to other super-resolution methods.

The task of image registration is fundamental in image processing. It often is a critical preprocessing step to many modern image processing and computer vision tasks, and many algorithms and techniques have been proposed to address the registration problem. Often, the performances of these techniques have been presented using a variety of relative measures comparing different estimators, leaving open the critical question of overall optimality. In this paper, we present the fundamental performance limits for the problem of image registration as derived from the Cramer-Rao inequality. We compare the experimental performance of several popular methods with respect to this performance bound, and explain the fundamental tradeoff between variance and bias inherent to the problem of image registration. In particular, we derive and explore the bias of the popular gradient-based estimator showing how widely used multiscale methods for improving performance can be explained with this bias expression. Finally, we present experimental simulations showing the general rule-of-thumb performance limits for gradient-based image registration techniques.

In the last two decades, many papers have been published, proposing a variety methods of multiframe resolution enhancement. These methods are usually very sensitive to their assumed model of data and noise, which limits their utility. This paper reviews some of these methods and addresses their shortcomings. We propose a different implementation using L/sub 1/ norm minimization and robust regularization to deal with different data and noise models. This computationally inexpensive method is robust to errors in motion and blur estimation, and results in sharp edges. Simulation results confirm the effectiveness of our method and demonstrate its superiority to other robust super-resolution methods.

While many algorithms have been developed to solve the problem of image registration, their performance has typically been evaluated only by comparing one method with another often in an ad-hoc manner. We propose a statistical performance measure based on the mean square error (MSE) and explore the performance bounds using the Cramer-Rao inequality. We show how these performance bounds depend on image content under observation. By analyzing these bounds we provide insight into the inherent tradeoff between bias and variance found in all image registration algorithms. Specifically, we derive a functional expression for the bias inherent in the popular class of gradient-based image registration algorithms.