Optimal focal-plane restoration

Image restoration can be implemented efficiently by calculating the convolution of the digital image and a small kernel during image acquisition. Processing the image in the focal-plane in this way requires less computation than traditional Fourier-transform-based techniques such as the Wiener filter and constrained least-squares filter. Here, the values of the convolution kernel that yield the restoration with minimum expected mean-square error are determined using a frequency analysis of the end-to-end imaging system. This development accounts for constraints on the size and shape of the spatial kernel and all the components of the imaging system. Simulation results indicate the technique is effective and efficient

Small-kernel image restoration

The goal of image restoration is to remove degradations that are introduced during image acquisition and display. Although image restoration is a difficult task that requires considerable computation, in many applications the processing must be performed significantly faster than is possible with traditional algorithms implemented on conventional serial architectures. as demonstrated in this dissertation, digital image restoration can be efficiently implemented by convolving an image with a small kernel. Small-kernel convolution is a local operation that requires relatively little processing and can be easily implemented in parallel. A small-kernel technique must compromise effectiveness for efficiency, but if the kernel values are well-chosen, small-kernel restoration can be very effective.;This dissertation develops a small-kernel image restoration algorithm that minimizes expected mean-square restoration error. The derivation of the mean-square-optimal small kernel parallels that of the Wiener filter, but accounts for explicit spatial constraints on the kernel. This development is thorough and rigorous, but conceptually straightforward: the mean-square-optimal kernel is conditioned only on a comprehensive end-to-end model of the imaging process and spatial constraints on the kernel. The end-to-end digital imaging system model accounts for the scene, acquisition blur, sampling, noise, and display reconstruction. The determination of kernel values is directly conditioned on the specific size and shape of the kernel. Experiments presented in this dissertation demonstrate that small-kernel image restoration requires significantly less computation than a state-of-the-art implementation of the Wiener filter yet the optimal small-kernel yields comparable restored images.;The mean-square-optimal small-kernel algorithm and most other image restoration algorithms require a characterization of the image acquisition device (i.e., an estimate of the device\u27s point spread function or optical transfer function). This dissertation describes an original method for accurately determining this characterization. The method extends the traditional knife-edge technique to explicitly deal with fundamental sampled system considerations of aliasing and sample/scene phase. Results for both simulated and real imaging systems demonstrate the accuracy of the method

Constrained least-squares digital image restoration

The design of a digital image restoration filter must address four concerns: the completeness of the underlying imaging system model, the validity of the restoration metric used to derive the filter, the computational efficiency of the algorithm for computing the filter values and the ability to apply the filter in the spatial domain. Consistent with these four concerns, this dissertation presents a constrained least-squares (CLS) restoration filter for digital image restoration. The CLS restoration filter is based on a comprehensive, continuous-input/discrete- processing/continuous-output (c/d/c) imaging system model that accounts for acquisition blur, spatial sampling, additive noise and imperfect image reconstruction. The c/d/c model-based CLS restoration filter can be applied rigorously and is easier to compute than the corresponding c/d/c model-based Wiener restoration filter. The CLS restoration filter can be efficiently implemented in the spatial domain as a small convolution kernel. Simulated restorations are used to illustrate the CLS filter\u27s performance for a range of imaging conditions. Restoration studies based, in part, on an actual Forward Looking Infrared (FLIR) imaging system, show that the CLS restoration filter can be used for effective range reduction. The CLS restoration filter is also successfully tested on blurred and noisy radiometric images of the earth\u27s outgoing radiation field from a satellite-borne scanning radiometer used by the National Aeronautics and Space Administration (NASA) for atmospheric research

Estimating Signals with Finite Rate of Innovation from Noisy Samples: A Stochastic Algorithm

As an example of the recently-introduced concept of rate of innovation, signals that are linear combinations of a finite number of Diracs per unit time can be acquired by linear filtering followed by uniform sampling. However, in reality, samples are rarely noiseless. In this paper, we introduce a novel stochastic algorithm to reconstruct a signal with finite rate of innovation from its noisy samples. Even though variants of this problem has been approached previously, satisfactory solutions are only available for certain classes of sampling kernels, for example kernels which satisfy the Strang-Fix condition. In this paper, we consider the infinite-support Gaussian kernel, which does not satisfy the Strang-Fix condition. Other classes of kernels can be employed. Our algorithm is based on Gibbs sampling, a Markov chain Monte Carlo (MCMC) method. Extensive numerical simulations demonstrate the accuracy and robustness of our algorithm.Comment: Submitted to IEEE Transactions on Signal Processin

Single Frame Image super Resolution using Learned Directionlets

In this paper, a new directionally adaptive, learning based, single image super resolution method using multiple direction wavelet transform, called Directionlets is presented. This method uses directionlets to effectively capture directional features and to extract edge information along different directions of a set of available high resolution images .This information is used as the training set for super resolving a low resolution input image and the Directionlet coefficients at finer scales of its high-resolution image are learned locally from this training set and the inverse Directionlet transform recovers the super-resolved high resolution image. The simulation results showed that the proposed approach outperforms standard interpolation techniques like Cubic spline interpolation as well as standard Wavelet-based learning, both visually and in terms of the mean squared error (mse) values. This method gives good result with aliased images also.Comment: 14 pages,6 figure

An Improved Observation Model for Super-Resolution under Affine Motion

Super-resolution (SR) techniques make use of subpixel shifts between frames in an image sequence to yield higher-resolution images. We propose an original observation model devoted to the case of non isometric inter-frame motion as required, for instance, in the context of airborne imaging sensors. First, we describe how the main observation models used in the SR literature deal with motion, and we explain why they are not suited for non isometric motion. Then, we propose an extension of the observation model by Elad and Feuer adapted to affine motion. This model is based on a decomposition of affine transforms into successive shear transforms, each one efficiently implemented by row-by-row or column-by-column 1-D affine transforms. We demonstrate on synthetic and real sequences that our observation model incorporated in a SR reconstruction technique leads to better results in the case of variable scale motions and it provides equivalent results in the case of isometric motions

Recent Progress in Image Deblurring

This paper comprehensively reviews the recent development of image deblurring, including non-blind/blind, spatially invariant/variant deblurring techniques. Indeed, these techniques share the same objective of inferring a latent sharp image from one or several corresponding blurry images, while the blind deblurring techniques are also required to derive an accurate blur kernel. Considering the critical role of image restoration in modern imaging systems to provide high-quality images under complex environments such as motion, undesirable lighting conditions, and imperfect system components, image deblurring has attracted growing attention in recent years. From the viewpoint of how to handle the ill-posedness which is a crucial issue in deblurring tasks, existing methods can be grouped into five categories: Bayesian inference framework, variational methods, sparse representation-based methods, homography-based modeling, and region-based methods. In spite of achieving a certain level of development, image deblurring, especially the blind case, is limited in its success by complex application conditions which make the blur kernel hard to obtain and be spatially variant. We provide a holistic understanding and deep insight into image deblurring in this review. An analysis of the empirical evidence for representative methods, practical issues, as well as a discussion of promising future directions are also presented.Comment: 53 pages, 17 figure

Sub-pixel techniques to improve spatial resolution

Image acquisition using a scene sampling device generally results in a loss of fidelity in the acquired image, particularly if the scene contains high frequency features. Acquired images are also degraded by the blurring effects of acquisition filtering, image reconstruction, and additive noise effects. to compensate for these degradations, a digital restoration filter that attempts to partially eliminate the blurring while avoiding amplification of the noise effects is needed. In addition, to compensate for undersampling, a subpixel technique known as microscanning is required. This dissertation provides research into the spatial resolution enhancement of digital images based on subpixel techniques that will help to minimize the impact of these degradations. Subpixel techniques investigated include microscanning and estimation of the function that measures the amount of blurring incurred during acquisition. These techniques will be used in conjunction with a constrained least squares restoration filter to achieve the best possible representation of the original scene