(with shutter speed of 1/100 second, and ISO 1600) due to insufficient light. (c) Noisy image enhanced by adjusting level and gamma. (d) Our deblurred image. Abstract Taking satisfactory photos under dim lighting conditions using a hand-held camera is challenging. If the camera is set to a long exposure time, the image is blurred due to camera shake. On the other hand, the image is dark and noisy if it is taken with a short exposure time but with a high camera gain. By combining information extracted from both blurred and noisy images, however, we show in this paper how to produce a high quality image that cannot be obtained by simply denoising the noisy image, or deblurring the blurred image alone. Our approach is image deblurring with the help of the noisy image. First, both images are used to estimate an accurate blur kernel, which otherwise is difficult to obtain from a single blurred image. Second, and again using both images, a residual deconvolution is proposed to significantly reduce ringing artifacts inherent to image deconvolution. Third, the remaining ringing artifacts in smooth image regions are further suppressed by a gain-controlled deconvolution process. We demonstrate the effectiveness of our approach using a number of indoor and outdoor images taken by off-the-shelf hand-held cameras in poor lighting environments. 1

We address the problem of blind motion deblurring from a single image, caused by a few moving objects. In such situations only part of the image may be blurred, and the scene consists of layers blurred in different degrees. Most of of existing blind deconvolution research concentrates at recovering a single blurring kernel for the entire image. However, in the case of different motions, the blur cannot be modeled with a single kernel, and trying to deconvolve the entire image with the same kernel will cause serious artifacts. Thus, the task of deblurring needs to involve segmentation of the image into regions with different blurs. Our approach relies on the observation that the statistics of derivative filters in images are significantly changed by blur. Assuming the blur results from a constant velocity motion, we can limit the search to one dimensional box filter blurs. This enables us to model the expected derivatives distributions as a function of the width of the blur kernel. Those distributions are surprisingly powerful in discriminating regions with different blurs. The approach produces convincing deconvolution results on real world images with rich texture. 1

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.

In this paper the problem of restoring an image distorted by a linear space-invariant (LSI) point-spread function (psf) which is not exactly known is formulated as the solution of a perturbed set of linear equations. The regularized constrained total least-squares (RCTLS) method is used to solve this set of equations. Using the diagonalization properties of the discrete Fourier transform (DFT) for circulant matrices, the RCTLS estimate is computed in the DFT domain. This significantly reduces the computational cost of this approach and makes its implementation possible even for large images. An error analysis of the RCTLS estimate, based on the mean-squared-error (MSE) criterion is performed to verify its superiority over the constrained total least-squares (CTLS) estimate. Numerical experiments for different psf errors are performed to test the RCTLS estimator for this problem. Objective and visual comparisons are presented with the linear minimum mean-squared-error (LMMSE) and the re...

Classical linear image restoration techniques assume that the linear shift invariant blur, also known as the point-spread function (PSF), is known prior to restoration. In many practical situations, however, the PSF is unknown and the problem of image restoration involves the simultaneous identification of the true image and PSF from the degraded observation. Such a process is referred to as blind deconvolution. This paper presents a novel blind deconvolution method for image restoration. The method is flexible for incorporating different constraints on the true image. An example of the method is given for situations in which the imaged scene consists of a finite support object against a uniformly grey background. The only information required are the nonnegativity of the true image and the support size of the original object. For situations in which the exact object support is unknown, a novel support-finding algorithm is proposed. 1. INTRODUCTION Image restoration refers to the task...

The paper is devoted to the feature-based description of images degraded by linear motion blur. The proposed features are invariant with respect to motion velocity, are based on image moments and are calculated directly from the blurred image. In that way, we are able to describe the original image without the PSF identification and image restoration. In many applications (such as in image recognition against a database) our approach is much more effective than the traditional "blind-restoration" one. The derivation of the motion blur invariants is a major theoretical result of the paper. Numerical experiments are presented to illustrate the utilization of the invariants for blurred image description. Stability of the invariants with respect to additive random noise is also discussed and is shown to be sufficiently high. Finally, another set of features which are invariant not only to motion velocity but also to motion direction is introduced. Index Terms: Blurred image, linear imaging...

We propose a total variation based model for simultaneous image inpainting and blind deconvolution.

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