Blind Curvelet based Denoising of Seismic Surveys in Coherent and Incoherent Noise Environments

The localized nature of curvelet functions, together with their frequency and dip characteristics, makes the curvelet transform an excellent choice for processing seismic data. In this work, a denoising method is proposed based on a combination of the curvelet transform and a whitening filter along with procedure for noise variance estimation. The whitening filter is added to get the best performance of the curvelet transform under coherent and incoherent correlated noise cases, and furthermore, it simplifies the noise estimation method and makes it easy to use the standard threshold methodology without digging into the curvelet domain. The proposed method is tested on pseudo-synthetic data by adding noise to real noise-less data set of the Netherlands offshore F3 block and on the field data set from east Texas, USA, containing ground roll noise. Our experimental results show that the proposed algorithm can achieve the best results under all types of noises (incoherent or uncorrelated or random, and coherent noise)

Mapping neuronal fiber crossings in the human brain

International audienceNew magnetic resonance imaging processing tools allow white-matter fiber bundles to be segmented and tracked in regions of high complexity

Adaptive Design of Sampling Directions in Diffusion Tensor MRI and Validation on Human Brain Images

International audienceDiffusion tensor reconstruction is made possible through the acquisition of several diffusion weighted images, each corresponding to a given sampling direction in the Q-space. In this study, we address the question of sampling efficiency, and show that in case we have some prior knowledge on the diffusion characteristics, we may be able to adapt the sampling directions for better reconstruction of the diffusion tensor. The prior is a tensor distribution function, estimated over a given region of interest, possibly on several subjects. We formulate an energy related to error on tensor reconstruction, and calculate analytical gradient expression for efficient minimization. We validate our approach on a set of 5199 tensors taken within the corpus callosum of the human brain, and show improvement by an order of 10% on the MSE of the reconstructed tensor

Anisotropic Diffusion Partial Differential Equations in Multi-Channel Image Processing : Framework and Applications

We review recent methods based on diffusion PDE's (Partial Differential Equations) for the purpose of multi-channel image regularization. Such methods have the ability to smooth multi-channel images anisotropically and can preserve then image contours while removing noise or other undesired local artifacts. We point out the pros and cons of the existing equations, providing at each time a local geometric interpretation of the corresponding processes. We focus then on an alternate and generic tensor-driven formulation, able to regularize images while specifically taking the curvatures of local image structures into account. This particular diffusion PDE variant is actually well suited for the preservation of thin structures and gives regularization results where important image features can be particularly well preserved compared to its competitors. A direct link between this curvature-preserving equation and a continuous formulation of the Line Integral Convolution technique (Cabral and Leedom, 1993) is demonstrated. It allows the design of a very fast and stable numerical scheme which implements the multi-valued regularization method by successive integrations of the pixel values along curved integral lines. Besides, the proposed implementation, based on a fourth-order Runge Kutta numerical integration, can be applied with a subpixel accuracy and preserves then thin image structures much better than classical finite-differences discretizations, usually chosen to implement PDE-based diffusions. We finally illustrate the efficiency of this diffusion PDE's for multi-channel image regularization - in terms of speed and visual quality - with various applications and results on color images, including image denoising, inpainting and edge-preserving interpolation

An Approach for ECG Feature Extraction using Daubechies 4 (DB4) Wavelet

An Electrocardiogram (ECG) signal describes the electrical activity of the heart recorded by electrodes placed on the surface of human body. It summarizes an important electrical activity used for the primary diagnosis of heart abnormalities such as Tachycardia, Bradycardia, Normalcy, Regularity and Heart Rate Variation. The most clinically useful information of the ECG signal is found in the time intervals between its consecutive waves and amplitudes defined by its features. In this paper, an ECG feature extraction algorithm based on Daubechies Wavelet Transform is presented. DB4 Wavelet is selected due to the similarity of its scaling function to the shape of the ECG signal. R peaks detection is the core of this algorithm’s feature extraction. All other primary peaks are extracted with respect to the location of R peaks through creating windows proportional to their normal intervals. The proposed extraction algorithm is evaluated on MIT-BIH Arrhythmia Database. Experimental results indicate that the algorithm can successfully detect and extract all the primary features with a deviation error of less than 10%

Diffusion Tensor Magnetic Resonance Imaging : Brain Connectivity Mapping

Diffusion tensor MRI probes and quantifies the anisotropic diffusion of water molecules in biological tissues, making it possible to non-invasively infer the architecture of the underlying structures. We introduce a novel approach to the cerebral white matter connectivity mapping from diffusion tensor MRI. We address the problem of consistent neural fibers reconstruction in areas of complex diffusion profiles with potentially multiple fibers orientations. Our method relies on a global modelization of the acquired MRI volume as a Riemannian manifold M and proceeds in 4 majors steps:1. We establish the link between Brownian motion and diffusion MRI by using the Laplace-Beltrami operator on M.2. We then expose how the sole knowledge of the diffusion properties of water molecules on M is sufficient to infer its geometry. There exists a direct mapping between the diffusion tensor and the metric of M.3. Having access to that metric, we propose a novel level set formulation to approximate the distance function related to a radial Brownian motion on M.4. On that basis, a rigorous numerical scheme using the exponential map is derived to estimate the geodesics of M, seen as the diffusion paths of water molecules.Numerical experimentations conducted on synthetic and real diffusion MRI datasets illustrate the potentialities of this global approach

Optimal Real-Time QBI using Regularized Kalman Filtering with Incremental Orientation Sets

Diffusion MRI has become an established research tool for the investigation of tissue structure and orientation from which has stemmed a number of variations, such as Diffusion Tensor Imaging (DTI), Diffusion Spectrum Imaging (DSI) and Q-Ball Imaging (QBI). The acquisition and analysis of such data is very challenging due to its complexity. Recently, an exciting new Kalman filtering framework has been proposed for DTI and QBI reconstructions in real time during the repetition time (TR) of the acquisition sequence \cite{Miccai:2007,Med. Image Analysis -Vol 12, Issue 5, June 2008}. In this article, we first revisite and thoroughly analyze this approach and show it is actually sub-optimal and not recursively minimizing the intended criterion due to the Laplace-Beltrami regularization term. Then, we propose a new approach that implements the QBI reconstruction algorithm in real-time using a fast and robust Laplace-Beltrami regularization without sacrificing the optimality of the Kalman filter. We demonstrate that our method solves the correct minimization problem at each iteration and recursively provides the optimal QBI solution. We validate with real QBI data that our proposed real-time method is equivalent in terms of QBI estimation accuracy to the standard off-line processing techniques and outperforms the existing solution. Last, we propose a fast algorithm to recursively compute gradient orientation sets whose partial subsets are almost uniform and show that it can also be applied to the problem of efficiently ordering an existing point-set of any size. Our work allows to start an acquisition just with the minimum number of gradient directions and an initial estimate of the q-ball and then all the rest, including the next gradient directions and the q-ball estimates, are recursively and optimally determined, allowing the acquisition to be stopped as soon as desired or at any iteration with the optimal q-ball estimate. This opens new and interesting opportunities for real-time feedback for clinicians during an acquisition and also for researchers investigating into optimal diffusion orientation sets and, real-time fiber tracking and connectivity mapping