Locating structural changes in a multiple scattering domain with an irregular shape

International audienceLocadiff is a method for imaging local structural changes in a random, heterogeneous medium. It relies on the combination of a forward model to calculate the sensitivity kernel of the source-receiver pairs, with an inversion method to determine the position of the changes. So far, the sensitivity kernel has been evaluated based on an analytical solution of the diffusion equation, which lacks the flexibility to handle problems where the domain has boundaries with an irregular shape. Moreover, the accuracy of the previous inversion method, based on linear algebra tools, was very sensitive to the values of the inversion parameters. This paper introduces a more generic approach to solve both these issues. The first problem is tackled by the implementation of numerical method as an alternative for solving the diffusion equation. The second problem is tackled by the introduction of enhanced optimization algorithms to improve the stability of the inversion. This improved version of Locadiff is validated via both numerical examples and experimental data from an actual civil engineering problem

Robust inversion and detection techniques for improved imaging performance

Thesis (Ph.D.)--Boston UniversityIn this thesis we aim to improve the performance of information extraction from imaging systems through three thrusts. First, we develop improved image formation methods for physics-based, complex-valued sensing problems. We propose a regularized inversion method that incorporates prior information about the underlying field into the inversion framework for ultrasound imaging. We use experimental ultrasound data to compute inversion results with the proposed formulation and compare it with conventional inversion techniques to show the robustness of the proposed technique to loss of data. Second, we propose methods that combine inversion and detection in a unified framework to improve imaging performance. This framework is applicable for cases where the underlying field is label-based such that each pixel of the underlying field can only assume values from a discrete, limited set. We consider this unified framework in the context of combinatorial optimization and propose graph-cut based methods that would result in label-based images, thereby eliminating the need for a separate detection step. Finally, we propose a robust method of object detection from microscopic nanoparticle images. In particular, we focus on a portable, low cost interferometric imaging platform and propose robust detection algorithms using tools from computer vision. We model the electromagnetic image formation process and use this model to create an enhanced detection technique. The effectiveness of the proposed technique is demonstrated using manually labeled ground-truth data. In addition, we extend these tools to develop a detection based autofocusing algorithm tailored for the high numerical aperture interferometric microscope

Compressive 3D ultrasound imaging using a single sensor

Three-dimensional ultrasound is a powerful imaging technique, but it requires thousands of sensors and complex hardware. Very recently, the discovery of compressive sensing has shown that the signal structure can be exploited to reduce the burden posed by traditional sensing requirements. In this spirit, we have designed a simple ultrasound imaging device that can perform three-dimensional imaging using just a single ultrasound sensor. Our device makes a compressed measurement of the spatial ultrasound field using a plastic aperture mask placed in front of the ultrasound sensor. The aperture mask ensures that every pixel in the image is uniquely identifiable in the compressed measurement. We demonstrate that this device can successfully image two structured objects placed in water. The need for just one sensor instead of thousands paves the way for cheaper, faster, simpler, and smaller sensing devices and possible new clinical applications

Real-time Regularized Tracking of Shear-Wave in Ultrasound Elastography

Elastography is a convenient and affordable method for imaging mechanical properties of tissue, which are often correlated with pathologies. An emerging novel elastography technique applies an external acoustic radiation force (ARF) to generate shear-wave in the tissue which are then tracked using ultrasound imaging. Accurate tracking of the small tissue motion (referred to as tissue displacement) is a critical step in shear-wave elastography, but is challenging due to various sources of noise in the ultrasound data. I formulate tissue displacement estimation as an optimization problem and propose two computationally efficient approaches to estimate the displacement field. The first algorithm is referred to as dynamic programming analytic minimization (DPAM), which utilizes first order Taylor series expansion of the highly nonlinear cost function to allow for its efficient optimization. DPAM was previously proposed for quasi-static elastography and I extend the approach to shear-wave elastography. The second algorithm is a novel technique that exploits second-order Taylor expansion of the non-linear cost function. I call the new algorithm as second-order analytic minimization elastography (SESAME). I compare DMAP and SESAME to the standard normalized Cross Correlation (NCC) approach in the context of estimating displacement and elasticity of the medium for shear-wave elastography (SWE). The results of micrometer-order displacement estimation in a uniform simulation phantom illustrate that SESAME outperforms DPAM, which in turn outperforms NCC in terms of signal to noise ratio (SNR) and jitter. In addition, the relative difference between true and reconstructed shear modulus (averaged over several excitations focusing at different focal depths with different scatterers realizations at each depth) is approximately 3.41%, 1.12% and 1.01%, respectively, for NCC, DPAM and SESAME. The performance of the proposed methods is also assessed with real data acquired using a tissue-mimicking phantom, wherein, in comparison to NCC, DPAM and SESAME improve the SNR of displacement by 7.6 dB and 9.5 dB, respectively. Experimental results on a tissue-mimicking phantom also show that shear modulus reconstruction is more accurate with DPAM and SESAME in comparison with NCC

Inverse Problems in Wave Scattering and Impedance Tomography

[no abstract available

スパースアレイ・レーダにおける信号処理技術

Tohoku University佐藤源之課

Computational Inverse Problems for Partial Differential Equations

The problem of determining unknown quantities in a PDE from measurements of (part of) the solution to this PDE arises in a wide range of applications in science, technology, medicine, and finance. The unknown quantity may e.g. be a coefficient, an initial or a boundary condition, a source term, or the shape of a boundary. The identification of such quantities is often computationally challenging and requires profound knowledge of the analytical properties of the underlying PDE as well as numerical techniques. The focus of this workshop was on applications in phase retrieval, imaging with waves in random media, and seismology of the Earth and the Sun, a further emphasis was put on stochastic aspects in the context of uncertainty quantification and parameter identification in stochastic differential equations. Many open problems and mathematical challenges in application fields were addressed, and intensive discussions provided an insight into the high potential of joining deep knowledge in numerical analysis, partial differential equations, and regularization, but also in mathematical statistics, homogenization, optimization, differential geometry, numerical linear algebra, and variational analysis to tackle these challenges