Sparsity constrained contrast source inversion

Abstract

Ultrasound imaging is used for detecting and characterizing breast lesions. A state of the art imaging method is the contrast source inversion (CSI), which solves the full wave nonlinear inverse problem. However, when the measurements are acquired in noisy environments, CSI can diverge from the correct solution after several iterations. Problems associated with noisy data were originally solved by including total variation (TV) regularization. Unfortunately, for very noisy data, TV regularization alone is not sufficient. In this work, compressed sensing ideas are used to regularize the inversion process by restricting the solution of the CSI method to be sparse in a transformation domain. The proposed method estimates the contrast source and contrast function by minimizing the mean squared error between the measured and modeled data. An extra penalty term is added to measure sparsity in the transformation domain. A second method that combines sparsity of the contrast source and minimal TV in the contrast function is also presented. The proposed methods are tested on noise-free and noisy synthetic data sets representing a scan of a cancerous breast. Numerical experiments show that, for measurements contaminated with 1% noise, the sparsity constrained CSI improves the normalized mean squared error of the reconstructed speed-of-sound profiles up to 36% in comparison with traditional CSI. Also, for measurements contaminated with 5% noise, the proposed methods improve the quality of the reconstruction up to 70% in comparison with the traditional CSI method. Experimental results also show that the methods remain convergent to the correct speed-of-sound profile as the number of iterations increases.

Integral modelling of propagation of incident waves in a laterally varying medium: An exploration in the frequency domain

“…Anyhow, the analytic expressions for the incident pressure waves may be written as a functional part FP, and an integral part IP. Although similar approximations can be found in the literature (see [16]), we provided an approximated analytic solution for the incident wave and applied it to the problem of propagation of seismic waves. Computational implementations were developed in order to compute, for different velocity profiles, the functional and the integral parts, which constitute the incident wave, q j inc .…”

“…The contrast term has been introduced by [13] and [14] in the context of the Contrast Source Inversion (CSI) method. χ(⃗ x,ω) has been recently used in medical applications [15]- [16]. The χ(⃗ x,ω) term can be a good choice for wavefield inversion in seismic exploration, since iterative inversion methods, like FWI [17]- [18], use schemes that start with a guess of the velocity profile, which is updated at each step of the method.…”

Redatuming of 2-D Wave Fields Measured on an Arbitrary-Shaped Closed Aperture

“…2) Experimental results: Contrast source inversion (CSI) is applied to the data from the DBUS system [6], [21], [27]. Five frequency components between 0.25 MHz and 0.3 MHz are used for the inversion.…”

Multi-parameter inversion with the aid of particle velocity field reconstruction

“…In both cases similar results are obtained and the four small lesions have almost the correct parameter values. The ripples seen in the background are caused by the coarse discretization of the domain and can be solved by using a finer spatial discretization or additional regularization based on total variation or sparsity constraints 21,28 . Integral equation formulations have the advantage that they perform well with relatively coarse sampling because of having a bounded operator.…”