Leah Bar

Image Deblurring in the Presence of Impulsive Noise

Consider the problem of image deblurring in the presence of impulsive noise. Standard image deconvolution methods rely on the Gaussian noise model and do not perform well with impulsive noise. The main challenge is to deblur the image, recover its discontinuities and at the same time remove the impulse noise. Median-based approaches are inadequate, because at high noise levels they induce nonlinear distortion that hampers the deblurring process. Distinguishing outliers from edge elements is difficult in current gradient-based edge-preserving restoration methods. The suggested approach integrates and extends the robust statistics, line process (half quadratic) and anisotropic diffusion points of view. We present a unified variational approach to image deblurring and impulse noise removal. The objective functional consists of a fidelity term and a regularizer. Data fidelity is quantified using the robust modified L1 norm, and elements from the Mumford-Shah functional are used for regularization. We show that the Mumford-Shah regularizer can be viewed as an extended line process. It reflects spatial organization properties of the image edges, that do not appear in the common line process or anisotropic diffusion. This allows to distinguish outliers from edges and leads to superior experimental results.

Deblurring of Color Images Corrupted by Impulsive Noise

We consider the problem of restoring a multichannel image corrupted by blur and impulsive noise (e.g., salt-and-pepper noise). Using the variational framework, we consider the L1 fidelity term and several possible regularizers. In particular, we use generalizations of the Mumford-Shah (MS) functional to color images and Gamma-convergence approximations to unify deblurring and denoising. Experimental comparisons show that the MS stabilizer yields better results with respect to Beltrami and total variation regularizers. Color edge detection is a beneficial by-product of our methods

Image deblurring in the presence of salt-and-pepper noise

The problem of image deblurring in the presence of salt and pepper noise is considered. Standard image deconvolution algorithms, that are designed for Gaussian noise, do not perform well in this case. Median type filtering is a common method for salt and pepper noise removal. Deblurring an image that has been preprocessed by median-type filtering is however difficult, due to the amplification (in the deconvolution stage) of median-induced distortion. A unified variational approach to salt and pepper noise removal and image deblurring is presented. An objective functional that represents the goals of deblurring, noise-robustness and compliance with the piecewise-smooth image model is formulated. A modified L1 data fidelity term integrates deblurring with robustness to outliers. Elements from the Mumford-Shah functional, that favor piecewise smooth images with simple edge-sets, are used for regularization. Promising experimental results are shown for several blur models.

Semi-blind image restoration via Mumford-Shah regularization

Image restoration and segmentation are both classical problems, that are known to be difficult and have attracted major research efforts. This paper shows that the two problems are tightly coupled and can be successfully solved together. Mutual support of image restoration and segmentation processes within a joint variational framework is theoretically motivated, and validated by successful experimental results. The proposed variational method integrates semi-blind image deconvolution (parametric blur-kernel), and Mumford-Shah segmentation. The functional is formulated using the /spl Gamma/-convergence approximation and is iteratively optimized via the alternate minimization method. While the major novelty of this work is in the unified treatment of the semi-blind restoration and segmentation problems, the important special case of known blur is also considered and promising results are obtained.

A Variational Framework for Simultaneous Motion Estimation and Restoration of Motion-Blurred Video

The problem of motion estimation and restoration of objects in a blurred video sequence is addressed in this paper. Fast movement of the objects, together with the aperture time of the camera, result in a motion-blurred image. The direct velocity estimation from this blurred video is inaccurate. On the other hand, an accurate estimation of the velocity of the moving objects is critical for restoration of motion-blurred video. Therefore, restoration needs accurate motion estimation and vice versa, and a joint process is called for. To address this problem we derive a novel model of the blurring process and propose a Mumford-Shah type of variational framework, acting on consecutive frames, for joint object deblurring and velocity estimation. The proposed procedure distinguishes between the moving object and the background and is accurate also close to the boundary of the moving object. Experimental results both on simulated and real data show the importance of this joint estimation and its superior performance when compared to the independent estimation of motion and restoration.

Variational Pairing of Image Segmentation and Blind Restoration

Segmentation and blind restoration are both classical problems, that are known to be difficult and have attracted major research efforts. This paper shows that the two problems are tightly coupled and can be successfully solved together. Mutual support of the segmentation and blind restoration processes within a joint variational framework is theoretically motivated, and validated by successful experimental results. The proposed variational method integrates Mumford-Shah segmentation with parametric blur-kernel recovery and image deconvolution. The functional is formulated using the Γ-convergence approximation and is iteratively optimized via the alternate minimization method. While the major novelty of this work is in the unified solution of the segmentation and blind restoration problems, the important special case of known blur is also considered and promising results are obtained.

A Continuum Mechanical Approach to Geodesics in Shape Space

In this paper concepts from continuum mechanics are used to define geodesic paths in the space of shapes, where shapes are implicitly described as boundary contours of objects. The proposed shape metric is derived from a continuum mechanical notion of viscous dissipation. A geodesic path is defined as the family of shapes such that the total amount of viscous dissipation caused by an optimal material transport along the path is minimized. The approach can easily be generalized to shapes given as segment contours of multi-labeled images and to geodesic paths between partially occluded objects. The proposed computational framework for finding such a minimizer is based on the time discretization of a geodesic path as a sequence of pairwise matching problems, which is strictly invariant with respect to rigid body motions and ensures a 1–1 correspondence along the induced flow in shape space. When decreasing the time step size, the proposed model leads to the minimization of the actual geodesic length, where the Hessian of the pairwise matching energy reflects the chosen Riemannian metric on the underlying shape space. If the constraint of pairwise shape correspondence is replaced by the volume of the shape mismatch as a penalty functional, one obtains for decreasing time step size an optical flow term controlling the transport of the shape by the underlying motion field. The method is implemented via a level set representation of shapes, and a finite element approximation is employed as spatial discretization both for the pairwise matching deformations and for the level set representations. The numerical relaxation of the energy is performed via an efficient multi-scale procedure in space and time. Various examples for 2D and 3D shapes underline the effectiveness and robustness of the proposed approach.

Mapping apparent eccentricity and residual ensemble anisotropy in the gray matter using angular double-pulsed-field-gradient MRI

Conventional diffusion MRI methods are mostly capable of portraying microarchitectural elements such as fiber orientation in white matter from detection of diffusion anisotropy, which arises from the coherent organization of anisotropic compartments. Double‐pulsed‐field‐gradient MR methods provide a means for obtaining microstructural information such as compartment shape and microscopic anisotropies even in scenarios where macroscopic organization is absent. Here, we apply angular double‐pulsed‐gradient‐spin‐echo MRI in the rat brain both ex vivo and in vivo for the first time. Robust angular dependencies are detected in the brain at long mixing time (tm). In many pixels, the oscillations seem to originate from residual directors in randomly oriented media, i.e., from residual ensemble anisotropy, as corroborated by quantitative simulations. We then developed an analysis scheme that enables one to map of structural indices such as apparent eccentricity (aE) and residual phase (φ) that enables characterization of the rat brain in general, and especially the rat gray matter. We conclude that double‐pulsed‐gradient‐spin‐echo MRI may in principle become important in characterizing gray matter morphological features and pathologies in both basic and applied neurosciences. Magn Reson Med, 2012.

Left-right asymmetry of visual evoked potentials in brain-damaged patients : A mathematical model and experimental results

The left-right asymmetry in the potential amplitude on the scalp was studied in poststroke patients by using flash visual evoked potential (VEP) and a numerical two-dimensional model of the head. The left-right asymmetry of the VEP was measured in three patients after thrombosis, in one after hemorrhage, and in one healthy subject. The numerical model used computed tomography images to define the different comparttential distribution created by a dipole source in the occipital region was solved numerically with use of a finite volume method. Left-right asymmetry was calculated with serveral values of conductivity of the damaged region. The experimental results revealed a negative asymmetry in the three patients after thrombosis (i. e., the potential amplitude over the ischemic hemisphere was smaller than that over the intact hemisphere), whereas, in the patient after hemorrhage, a positive asymmetry was found. Nonsignificant left-right asymmetry was found in the healthy subject. The numerical model revealed that the electrical conductivity of the damaged tissue has a major effect on the left-right asymmetry. Negative asymmetry, such as that found for patients after thrombosis, was obtained when the conductivity of the damaged region was greater than that of the brain, whereas positive asymmetry (hemorrhage patient) was obtained when that conductivity was smaller than that of the brain. This finding indicates that the left-right asymmetry in the scalp VEP of patients after brain damage may be a result of changes in the conductivity of the volume conductor (the ischemic region) between the source and the electrodes.

Restoration of images with piecewise space-variant blur

We address the problem of space-variant image deblurring, where different parts of the image are blurred by different blur kernels. Assuming a region-wise space variant point spread function, we first solve the problem for the case of known blur kernels and known boundaries between the different blur regions in the image. We then generalize the method to the challenging case of unknown boundaries between the blur domains. Using variational and level set techniques, the image is processed globally. The space-variant deconvolution process is stabilized by a unified common regularizer, thus preserving discontinuities between the differently restored image regions. In the case where the blurred subregions are unknown, a segmentation procedure is performed using an evolving level set function, guided by edges and image derivatives.