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)

Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

Left-invariant evolutions of wavelet transforms on the Similitude Group

Enhancement of multiple-scale elongated structures in noisy image data is relevant for many biomedical applications but commonly used PDE-based enhancement techniques often fail at crossings in an image. To get an overview of how an image is composed of local multiple-scale elongated structures we construct a multiple scale orientation score, which is a continuous wavelet transform on the similitude group, SIM(2). Our unitary transform maps the space of images onto a reproducing kernel space defined on SIM(2), allowing us to robustly relate Euclidean (and scaling) invariant operators on images to left-invariant operators on the corresponding continuous wavelet transform. Rather than often used wavelet (soft-)thresholding techniques, we employ the group structure in the wavelet domain to arrive at left-invariant evolutions and flows (diffusion), for contextual crossing preserving enhancement of multiple scale elongated structures in noisy images. We present experiments that display benefits of our work compared to recent PDE techniques acting directly on the images and to our previous work on left-invariant diffusions on orientation scores defined on Euclidean motion group.Comment: 40 page

Dynamic Denoising of Tracking Sequences

©2008 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.DOI: 10.1109/TIP.2008.920795In this paper, we describe an approach to the problem of simultaneously enhancing image sequences and tracking the objects of interest represented by the latter. The enhancement part of the algorithm is based on Bayesian wavelet denoising, which has been chosen due to its exceptional ability to incorporate diverse a priori information into the process of image recovery. In particular, we demonstrate that, in dynamic settings, useful statistical priors can come both from some reasonable assumptions on the properties of the image to be enhanced as well as from the images that have already been observed before the current scene. Using such priors forms the main contribution of the present paper which is the proposal of the dynamic denoising as a tool for simultaneously enhancing and tracking image sequences.Within the proposed framework, the previous observations of a dynamic scene are employed to enhance its present observation. The mechanism that allows the fusion of the information within successive image frames is Bayesian estimation, while transferring the useful information between the images is governed by a Kalman filter that is used for both prediction and estimation of the dynamics of tracked objects. Therefore, in this methodology, the processes of target tracking and image enhancement "collaborate" in an interlacing manner, rather than being applied separately. The dynamic denoising is demonstrated on several examples of SAR imagery. The results demonstrated in this paper indicate a number of advantages of the proposed dynamic denoising over "static" approaches, in which the tracking images are enhanced independently of each other

De-noising SPECT/PET Images Using Cross-Scale Regularization

De-noising of SPECT and PET images is a challenging task due to the inherent low signal-to-noise ratio of acquired data. Wavelet based multi-scale denoising methods typically apply thresholding operators on sub-band coefficients to eliminate noise components in spatial-frequency space prior to reconstruction. In the case of high noise levels, detailed scales of sub-band images are usually dominated by noise which cannot be easily removed using traditional thresholding schemes. To address this issue, a cross-scale regularization scheme is introduced, which takes into account cross-scale coherence of structured signals. Preliminary results show promising performance in denoising clinical SPECT and PET images for liver and brain studies. Wavelet thresholding was also compared to denoising with a brushlet expansion. The proposed regularization scheme eliminates the need for threshold parameter settings, making the denoising process less tedious and suitable for clinical practice