Continuous Ultrasound Speckle Tracking with Gaussian Mixtures

Speckle tracking echocardiography (STE) is now widely used for measuring strain, deformations, and motion in cardiology. STE involves three successive steps: acquisition of individual frames, speckle detection, and image registration using speckles as landmarks. This work proposes to avoid explicit detection and registration by representing dynamic ultrasound images as sparse collections of moving Gaussian elements in the continuous joint space-time space. Individual speckles or local clusters of speckles are approximated by a single multivariate Gaussian kernel with associated linear trajectory over a short time span. A hierarchical tree-structured model is fitted to sampled input data such that predicted image estimates can be retrieved by regression after reconstruction, allowing a (bias-variance) trade-off between model complexity and image resolution. The inverse image reconstruction problem is solved with an online Bayesian statistical estimation algorithm. Experiments on clinical data could estimate subtle sub-pixel accurate motion that is difficult to capture with frame-to-frame elastic image registration techniques

Total Variation Reconstruction From Quasi-Random Samples

Abstract-Pseudo-random numbers are often used for generating incoherent uniformly distributed sample distributions. However randomness is a sufficient -not necessary -condition to ensure incoherence. If one wants to reconstruct an image from few samples, choosing a globally optimized set of evenly distributed points could capture the visual content more efficiently. This work compares classical random sampling with a simple construction based on properties of the fractional Golden ratio sequence and the Hilbert space filling curve. Images are then reconstructed using a total variation prior. Results show improvements in terms of peak signal to noise ratio over pseudo-random sampling

Functions of bounded variation, signed measures, and a general Koksma-Hlawka inequality

In this paper we prove a correspondence principle between multivariate functions of bounded variation in the sense of Hardy and Krause and signed measures of finite total variation, which allows us to obtain a simple proof of a generalized Koksma--Hlawka inequality for non-uniform measures. Applications of this inequality to importance sampling in Quasi-Monte Carlo integration and tractability theory are given. Furthermore, we discuss the problem of transforming a low-discrepancy sequence with respect to the uniform measure into a sequence with low discrepancy with respect to a general measure $\mu$, and show the limitations of a method suggested by Chelson.Comment: 29 pages. Second version: some minor changes, typos fixed, etc. The manuscript has been accepted for publication by Acta Arithmetic

Attitude-trajectory estimation for forward looking multi-beam sonar based on acoustic image registration

This work considers the processing of acoustic data from a multi-beam Forward Looking Sonar (FLS) on a moving underwater platform to estimate the platform’s attitude and trajectory. We propose an algorithm to produce an estimate of the attitude-trajectory for a FLS based on the optical flow between consecutive sonar frames. The attitude-trajectory can be used to locate an underwater platform, such as an Autonomous Underwater Vehicle (AUV), to a degree of accuracy suitable for navigation. It can also be used to build a mosaic of the underwater scene. The estimation is performed in three steps. Firstly, a selection of techniques based on the optical flow model are used to estimate a pixel displacement map (DM) between consecutive sonar frames represented in the native polar (range/bearing) format. The second step finds the best match between the estimated DM and DMs for a set of modeled sonar sensor motions. To reduce complexity, it is proposed to describe the DM with a small parameter vector derived from the displacement distribution. Thus, an estimate of the incremental sensor motion between frames is made. Finally, using a weighted regularized spline technique, the incremental inter-frame motions are integrated into an attitude-trajectory for the sonar sensor. To assess the accuracy of the attitude-trajectory estimate, it is used to register FLS frames from a field experiment dataset and build a high-quality mosaic of the underwater scene

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Image registration for sonar applications

This work develops techniques to estimate the motion of an underwater platform by processing data from an on-board sonar, such as a Forward Looking Sonar (FLS). Based on image registration, a universal algorithm has been developed and validated with in field datasets. The proposed algorithm gives a high quality registration to a fine (sub-pixel) precision using an adaptive filter and is suitable for both optical and acoustic images. The efficiency and quality of the result can be improved if an initial estimate of the motion is made. Therefore, a coarse (pixel-wide) registration algorithm is proposed, this is based on the assumption of local sparsity in the pixel motion between two images. Using a coarse and then fine registration, large displacements can be accommodated with a result that is to a sub-pixel precision. The registration process produces a displacement map (DM) between two images. From a sequence of DMs, an estimation of the sensor's motion is made. This is performed by a proposed fast searching and matching technique applied to a library of modelled DMs. Further, this technique exploits regularised splines to estimate the attitude and trajectory of the platform. To validate the results, a mosaic has been produced from three sets of in field data. Using a more detailed model of the acoustic propagation has the potential to improve the results further. As a step towards this a baseband underwater channel model has been developed. A physics simulator is used to characterise the channel at waymark points in a changing environment. A baseband equivalent representation of the time varying channel is then interpolated from these points. Processing in the baseband reduces the sample rate and hence reduces the run time for the model. A comparison to a more established channel model has been made to validate the results