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.

In this paper, we present a novel blind deconvolution technique for the restoration of linearly degraded images without explicit knowledge of either the original image or the point spread function. The technique applies to situations in which the scene consists of a finite support object against a uniformly black, grey, or white background. This occurs in certain types of astronomical imaging, medical imaging, and one-dimensional (1-D) gamma ray spectra processing, among others. The only information required are the nonnegativity of the true image and the support size of the original object. The restoration procedure involves recursive filtering of the blurred image to minimize a convex cost function. We prove convexity of the cost function, establish sufficient conditions to guarantee a unique solution, and examine the performance of the technique in the presence of noise. The new approach is experimentally shown to be more reliable and to have faster convergence than existing nonparametric finite support blind deconvolution methods. For situations in which the exact object support is unknown, we propose a novel support-finding algorithm.

Super-resolution reconstruction proposes a fusion of several low-quality images into one higher quality result with better optical resolution. Classic super-resolution techniques strongly rely on the availability of accurate motion estimation for this fusion task. When the motion is estimated inaccurately, as often happens for nonglobal motion fields, annoying artifacts appear in the super-resolved outcome. Encouraged by recent developments on the video denoising problem, where state-of-the-art algorithms are formed with no explicit motion estimation, we seek a super-resolution algorithm of similar nature that will allow processing sequences with general motion patterns. In this paper, we base our solution on the Nonlocal-Means (NLM) algorithm. We show how this denoising method is generalized to become a relatively simple super-resolution algorithm with no explicit motion estimation. Results on several test movies show that the proposed method is very successful in providing super-resolution on general sequences.

Cryo-electron microscopy provides the means to quantitatively study macromolecules in their native state. However, the original mass distribution of the macromolecule is distorted by the contrast transfer function (CTF) of the electron microscope. In addition, the zeros of the CTF put a practical limit on the resolution that can be achieved. Substantial improvement to the quality of the results can be accomplished by collecting the data using a series of defocus settings. Such data sets can be combined and the resolution can be extended beyond the first zero of the CTF. This procedure can be applied either at the stage of raw data, or more effectively at the stage of reconstructed volumes which have a high signal-to-noise ratio as a result of averaging over many projections. A method of threedimensional (3D) reconstruction that combines an algebraic, iterative 3D reconstruction technique with CTF correction is proposed. The potential to incorporate a priori knowledge into the reconstruction process is discussed. This approach was used to obtain a 3D reconstruction of the E. coli 70S ribosome from energy-filtered cryo-images. Key Words: Cryo-electron microscopy, energy-filtered cryoimages, three-dimensional reconstruction, contrast transfer function correction. *Address for correspondence:

Can the organization of local edge measurements into curves be directly related to natural image structure? By viewing curve organization as a statistical estimation problem, we suggest that it can. In particular, the classical Gestalt perceptual organization cues of proximity and good continuation---the basis of many current curve organization systems---can be statistically measured in images. As a prior for our estimation approach we introduce the curve indicator random field. In contrast to other techniques that require contour closure or are based on a sparse set of detected edges, the curve indicator random field emphasizes the short-distance, dense nature of organizing curve elements into (possibly) open curves. Its explicit formulation allows the calculation of its properties such as its autocorrelation. On the one hand, the curve indicator random field leads us to introduce the oriented Wiener filter, capturing the blur and noise inherent in the edge measurement process. On the other, it suggests we seek such correlations in natural images. We present the results of some initial edge correlation measurements that not only confirm the presence of Gestalt cues, but also suggest that curvature has a role in curve organization.

Kernel regression is an effective tool for a variety of image processing tasks such as denoising and interpolation [1]. In this paper, we extend the use of kernel regression for deblurring applications. In some earlier examples in the literature, such non-parametric deblurring was sub-optimally performed in two sequential steps, namely, denoising followed by deblurring. In contrast, our optimal solution jointly denoises and deblurs images. The proposed algorithm takes advantage of an effective and novel image prior that generalizes some of the most popular regularization techniques in the literature. Experimental results demonstrate the effectiveness of our method. Index Terms non-parametric estimation, kernel regression, local polynomial, spatially adaptive, deblurring, denois-ing, non-linear filter. I.

INTRODUCTION Images are produced to record or display useful information. Due to imperfections in the imaging and capturing process, however, the recorded image invariably represents a degraded version of the original scene. The undoing of these imperfections is crucial to many of the subsequent image processing tasks. There exists a wide range of different degradations that need to be taken into account, covering for instance noise, geometrical degradations (pin cushion distortion), illumination and color imperfections (under/over-exposure, saturation), and blur. This chapter concentrates on basic methods for removing blur from recorded sampled (spatially discrete) images. There are many excellent overview articles, journal papers, and textbooks on the subject of image restoration and identification. Readers interested in more details than given in this chapter are referred to [2, 3, 9, 11, 14]. Blurring is a form of bandwidth reduction of an ideal image owing to the imperfe

As digital cameras become cheaper and more powerful, driven by the consumer digital photography market, we anticipate significant value in extending their utility as a general office peripheral by adding a paper scanning capability. The main technical challenges in realizing this new scanning interface are insu#cient resolution, blur and lighting variations. We have developed an efficient technique for the recovery of text from digital camera images, which simultaneously treats these three problems, unlike other local thresholding algorithms which do not cope with blur and resolution enhancement. The technique

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 ...