9,619 research outputs found
Sparsity driven ultrasound imaging
An image formation framework for ultrasound imaging from synthetic transducer arrays based on sparsity-driven regularization functionals using single-frequency Fourier domain data is proposed. The framework involves the use of a physics-based forward model of the ultrasound observation process, the formulation of image formation as the solution of an associated optimization problem, and the solution of that problem through efficient numerical algorithms. The sparsity-driven, model-based approach estimates a complex-valued reflectivity field and preserves physical features in the scene while suppressing spurious artifacts. It also provides robust reconstructions in the case of sparse and reduced observation apertures. The effectiveness of the proposed imaging strategy is demonstrated using experimental data
Distributed shape derivative via averaged adjoint method and applications
The structure theorem of Hadamard-Zol\'esio states that the derivative of a
shape functional is a distribution on the boundary of the domain depending only
on the normal perturbations of a smooth enough boundary. Actually the domain
representation, also known as distributed shape derivative, is more general
than the boundary expression as it is well-defined for shapes having a lower
regularity. It is customary in the shape optimization literature to assume
regularity of the domains and use the boundary expression of the shape
derivative for numerical algorithms. In this paper we describe several
advantages of the distributed shape derivative in terms of generality, easiness
of computation and numerical implementation. We identify a tensor
representation of the distributed shape derivative, study its properties and
show how it allows to recover the boundary expression directly. We use a novel
Lagrangian approach, which is applicable to a large class of shape optimization
problems, to compute the distributed shape derivative. We also apply the
technique to retrieve the distributed shape derivative for electrical impedance
tomography. Finally we explain how to adapt the level set method to the
distributed shape derivative framework and present numerical results
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