Analysis and interpretation of an image which was acquired by a nonideal imaging system is the key problem in many application areas. The observed image is usually corrupted by blurring, spatial degradations, and random noise. Classical methods like blind deconvolution try to estimate the blur parameters and to restore the image. In this paper, we propose an alternative approach. We derive the features for image representation which are invariant with respect to blur regardless of the degradation PSF provided that it is centrally symmetric. As we prove in the paper, there exist two classes of such features: the first one in the spatial domain and the second one in the frequency domain. We also derive so-called combined invariants, which are invariant to composite geometric and blur degradations. Knowing these features, we can recognize objects in the degraded scene without any restoration. Index Terms---Degraded image, symmetric blur, blur invariants, image moments, combined invariant...

Abstract—In many image restoration/resolution enhancement applications, the blurring process, i.e., point spread function (PSF) of the imaging system, is not known or is known only to within a set of parameters. We estimate these PSF parameters for this ill-posed class of inverse problem from raw data, along with the regularization parameters required to stabilize the solution, using the generalized cross-validation method (GCV). We propose efficient approximation techniques based on the Lanczos algorithm and Gauss quadrature theory, reducing the computational complexity of the GCV. Data-driven PSF and regularization parameter estimation experiments with synthetic and real image sequences are presented to demonstrate the effectiveness and robustness of our method. Index Terms—Blind restoration, blur identification, generalized cross-validation, quadrature rules, superresolution. I.

This thesis presents a novel blind deconvolution technique for the restoration of linearly degraded images without explicit knowledge of either the original image or point spread function. The technique applies to situations in which the scene consists of a finite support object against a uniformly grey background. This occurs in applications such as astronomy, and medical imaging. The only information required are the nonnegativity of the true image and the support size of the original object. A novel support-finding algorithm is proposed for situations in which the exact object support is unknown. The restoration procedure involves equalization of the blurred image using a convex cost function. The performance of the technique for truncated equalizer parameters, and in the presence of noise are examined analytically. The new approachis experimentally shown to be more reliable and to havefasterconvergence than the existing nonparametric finite support blind deconvolution methods. ii ...

nding board both for the general struggles of graduate school as well as for technical ideas. Our families also supplied large doses of encouragement, enthusiasm, and understanding. My mother was a particular inspiration, often providing reminders of the many "words of wisdom" I iii had given her during her graduate school days. Finally, I would like to thank my God, who alone provides the talents, the opportunity, and the strength for such an undertaking. "Unless the Lord builds the house, they labor in vain who build it." Soli Deo Gloria. iv Contents Acknowledgments ii List of Tables viii List of Figures ix Summary xii 1 Introduction 1 1.1 Statement of the Problem : : : : : : : : : : : : : : : : : : : : : : : : 1 1.2 Scope of the Thesis : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 2 Background 8 2.1 Image Formation : : : : : : : : : : : : : : : : : : : : : : : : : : : : :<F

The estimation of the intensity function of an inhomogeneous Poisson process is considered when the observable data consists of sampled shot noise that results from passing the Poisson process through an unknown linear time-invariant system. The proposed method consists of first estimating a histogram of the underlying point process. The estimated histogram is used to construct a kernel estimate of the intensity function. An estimate of the unknown impulse response of the linear time-invariant system is constructed via a regularized back-substitution of a discrete-time convolution with the estimated histogram. Index Terms --- Blind deconvolution, kernel intensity estimate, system identification. I. Introduction I N A VARIETY of physical applications, including directdetection optical communications systems and quantumlimited imaging, the mathematical models involve inhomogeneous Poisson processes at some stage in the system [1], [3], [9], [15], [22]. The main elements of these proces...

In many image restoration/superresolution applications, the blurring process, i.e., point spread function (PSF) of the imaging system, is not known or known only to within a set of parameters. We estimate these PSF parameters for this ill-posed class of inverse problem from raw data, along with the regularization parameters required to stabilize the solution, using the generalized crossvalidation method (GCV). To reduce the computational complexity of GCV, we propose efficient approximation techniques based on the Lanczos algorithm and Gauss quadrature theory. Data-driven blind restoration/superresolution experiments with synthetic and Forward Looking Infrared (FLIR) image sequences are presented to demonstrate the effectiveness and robustness of our method.

In this paper we examine the applicability of the previously proposedGreatest Common Divisor (GCD) method to blind image deconvolution. In this method, the desired image is approximated as the GCD of the two-dimensional polynomials corresponding to the ztransforms of two or more distorted and noisy versions of the same scene, assuming that the distortion filters areFIRandrelatively co-prime. We justify the breakdown of two-dimensional GCD into one-dimensional Sylvester-type GCD algorithms, which lowers the computational complexity while maintaining the noise robustness. A way of determining the supportsizeofthe true image is also described. We also provide a solution to deblurring using the GCD method when only one blurred image is available. Experimental results are shown using both synthetically blurred images and real motion-blurred pictures.

Blind deconvolution is the recovery of a sharp version of a blurred image when the blur kernel is unknown. Recent algorithms have afforded dramatic progress, yet many aspects of the problem remain challenging and hard to understand. The goal of this paper is to analyze and evaluate recent blind deconvolution algorithms both theoretically and experimentally. We explain the previously reported failure of the naive MAP approach by demonstrating that it mostly favors no-blur explanations. On the other hand we show that since the kernel size is often smaller than the image size a MAP estimation of the kernel alone can be well constrained and accurately recover the true blur. The plethora of recent deconvolution techniques makes an experimental evaluation on ground-truth data important. We have collected blur data with ground truth and compared recent algorithms under equal settings. Additionally, our data demonstrates that the shift-invariant blur assumption made by most algorithms is often violated. 1.

Blind deconvolution is the recovery of a sharp version of a blurred image when the blur kernel is unknown. Recent algorithms have afforded dramatic progress, yet many aspects of the problem remain challenging and hard to understand. The goal of this paper is to analyze and evaluate recent blind deconvolution algorithms both theoretically and experimentally. We explain the previously reported failure of the naive MAP approach by demonstrating that it mostly favors no-blur explanations. On the other hand we show that since the kernel size is often smaller than the image size a MAP estimation of the kernel alone can be well constrained and accurately recover the true blur. The plethora of recent deconvolution techniques makes an experimental evaluation on ground-truth data important. We have collected blur data with ground truth and compared recent algorithms under equal settings. Additionally, our data demonstrates that the shift-invariant blur assumption made by most algorithms is often violated. 1.

Blind deconvolution is the recovery of a sharp version of a blurred image when the blur kernel is unknown. Recent algorithms have afforded dramatic progress, yet many aspects of the problem remain challenging and hard to understand. The goal of this paper is to analyze and evaluate recent blind deconvolution algorithms both theoretically and experimentally. We explain the previously reported failure of the naive MAP approach by demonstrating that it mostly favors no-blur explanations. On the other hand we show that since the kernel size is often smaller than the image size a MAP estimation of the kernel alone can be well constrained and accurately recover the true blur. The plethora of recent deconvolution techniques makes an experimental evaluation on ground-truth data important. We have collected blur data with ground truth and compared recent algorithms under equal settings. Additionally, our data demonstrates that the shift-invariant blur assumption made by most algorithms is often violated. 1.