Euclidean metrics on diffusion tensors. Total word count: 6400.

(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

Representing the image to be inpainted in an appropriate sparse representation dictionary, and combining elements from Bayesian statistics and modern harmonic analysis, we introduce an expectation maximization (EM) algorithm for image inpainting and interpolation. From a statistical point of view, the inpainting/interpolation can be viewed as an estimation problem with missing data. Toward this goal, we propose the idea of using the EM mechanism in a Bayesian framework, where a sparsity promoting prior penalty is imposed on the reconstructed coefficients. The EM framework gives a principled way to establish formally the idea that missing samples can be recovered/ interpolated based on sparse representations. We first introduce an easy and efficient sparserepresentation-based iterative algorithm for image inpainting. Additionally, we derive its theoretical convergence properties. Compared to its competitors, this algorithm allows a high degree of flexibility to recover different structural components in the image (piecewise smooth, curvilinear, texture, etc.). We also suggest some guidelines to automatically tune the regularization parameter.

We are interested in PDE’s (Partial Differential Equations) in order to smooth multi-valued images in an anisotropic manner. Starting from a review of existing anisotropic regularization schemes based on diffusion PDE’s, we point out the pros and cons of the different equations proposed in the literature. Then, we introduce a new tensor-driven PDE, regularizing images while taking the curvatures of specific integral curves into account. We show that this constraint is particularly well suited for the preservation of thin structures in an image restoration process. A direct link is made between our proposed equation and a continuous formulation of the LIC’s (Line Integral Convolutions by Cabral and Leedom [11]). It leads to the design of a very fast and stable algorithm that implements our regularization method, by successive integrations of pixel values along curved integral lines. Besides, the scheme numerically performs with a sub-pixel accuracy and preserves then thin image structures better than classical finite-differences discretizations. Finally, we illustrate the efficiency of our generic curvature-preserving approach- in terms of speed and visual quality- with different comparisons and various applications requiring image smoothing: color images denoising, inpainting and image resizing by nonlinear interpolation.

This paper presents a robust algorithm to deblur two consecutively captured blurred photos from camera shaking. Previous dual motion deblurring algorithms succeeded in small and simple motion blur and are very sensitive to noise. We develop a robust feedback algorithm to perform iteratively kernel estimation and image deblurring. In kernel estimation, the stability and capability of the algorithm is greatly improved by incorporating a robust cost function and a set of kernel priors. The robust cost function serves to reject outliers and noise, while kernel priors, including sparseness and continuity, remove ambiguity and maintain kernel shape. In deblurring, we propose a novel and robust approach which takes two blurred images as input to infer the clear image. The deblurred image is then used as feedback to refine kernel estimation. Our method can successfully estimate large and complex motion blurs which cannot be handled by previous dual or single image motion deblurring algorithms. The results are shown to be significantly better than those of previous approaches. 1.

Abstract—In this paper, we propose K-LLD: a patch-based, locally adaptive denoising method based on clustering the given noisy image into regions of similar geometric structure. In order to effectively perform such clustering, we employ as features the local weight functions derived from our earlier work on steering kernel regression [1]. These weights are exceedingly informative and robust in conveying reliable local structural information about the image even in the presence of significant amounts of noise. Next, we model each region (or cluster)—which may not be spatially contiguous—by “learning ” a best basis describing the patches within that cluster using principal components analysis. This learned basis (or “dictionary”) is then employed to optimally estimate the underlying pixel values using a kernel regression framework. An iterated version of the proposed algorithm is also presented which leads to further performance enhancements. We also introduce a novel mechanism for optimally choosing the local patch size for each cluster using Stein’s unbiased risk estimator (SURE). We illustrate the overall algorithm’s capabilities with several examples. These indicate that the proposed method appears to be competitive with some of the most recently published state of the art denoising methods. Index Terms—Clustering, dictionary learning, image denoising, kernel regression, principal component analysis, Stein’s unbiased risk estimator (SURE). I.

We propose a solution to the problem of inferring the depth map, radiance and motion field of a scene from a collection of motion-blurred and defocused images. We model motion-blurred and defocused images as the solution of an anisotropic diffusion equation, whose initial conditions depend on the radiance and whose diffusion tensor encodes the shape of the scene, the motion field and the optics parameters. We show that this model is well-posed and propose an efficient algorithm to infer the unknowns of the model. Inference is performed by minimizing the discrepancy between the measured defocused images and the ones synthesized via diffusion. Since the problem is ill-posed, we also introduce additional Tikhonov regularization terms. The resulting method is fast and robust to noise as shown by experiments with both synthetic and real data.

We propose a new technique for edge-suppressing operations on images. We introduce cross projection tensors to achieve affine transformations of gradient fields. We use these tensors, for example, to remove edges in one image based on the edge-information in a second image. Traditionally, edge suppression is achieved by setting image gradients to zero based on thresholds. A common application is in the Retinex problem, where the illumination map is recovered by suppressing the reflectance edges, assuming it is slowly varying.

In this paper, image compression utilizing visual redundancy is investigated. Inspired by recent advancements in image inpainting techniques, we propose an image compression framework towards visual quality rather than pixel-wise fidelity. In this framework, an original image is analyzed at the encoder side so that portions of the image are intentionally and automatically skipped. Instead, some information is extracted from these skipped regions and delivered to the decoder as assistant information in the compressed fashion. The delivered assistant information plays a key role in the proposed framework because it guides image inpainting to accurately restore these regions at the decoder side. Moreover, to fully take advantage of the assistant information, a compression-oriented edge-based inpainting algorithm is proposed for image restoration, integrating pixel-wise structure propagation and patch-wise texture synthesis. We also construct a practical system to verify the effectiveness of the compression approach in which edge map serves as assistant information and the edge extraction and region removal approaches are developed accordingly. Evaluations have been made in comparison with baseline JPEG and standard MPEG-4 AVC/H.264 intra-picture coding. Experimental results show that our system achieves up to 44 % and 33 % bits-savings, respectively, at similar visual quality levels. Our proposed framework is a promising exploration towards future image and video compression.

Abstract. We present a spatio-temporal filtering method for significantly increasing the signal-to-noise ratio (SNR) in noisy fluorescence microscopic image sequences where small particles have to be tracked from frame to frame. Image sequence restoration is achieved using a statistical approach involving an appropriate on-line window geometry specification. We have applied this method to noisy synthetic and real microscopic image sequences where a large number of small fluorescently labeled vesicles are moving in regions close to the Golgi apparatus. The SNR is shown to be drastically improved and the enhanced vesicles can be segmented. This novel approach can be further exploited for biological studies where the dynamics of small objects of interest have to be analyzed in molecular and sub-cellular bio-imaging. 1