Imaging from Echoes: On Inverse Problems in Ultrasound

Ultrasound (US) imaging is currently living a revolution. On the one hand, ultrafast US imaging, a novel way of acquiring and producing US images, has paved the way to several advanced imaging modes, e.g. shear-wave elastography, ultrafast Doppler imaging and ultrafast contrast imaging. On the other hand, the mass adoption of mobile commodity devices pushes towards portable US imaging. These new paradigms require to rethink the imaging pipeline and come with a myriad of new challenges in terms of data rate, power considerations as well as software and hardware design. In this thesis, we explore several inverse problems related to these challenges, with an emphasis on data-rate reduction for imaging and localization. We follow the view of considering pulse-echo US imaging as a tomographic image reconstruction problem where sensor measurements can be seen as projections onto quadric surfaces. By appropriate parameterization of these surfaces, we devise efficient formulations of the measurement model associated with the image reconstruction problem and pave the way to large scale regularized US imaging. We introduce USSR, an UltraSound Sparse Regularization framework, which exploits the measurement model in the context of convex optimization algorithms. We describe three applications, namely sparsely regularized beamforming where high-quality images are obtained with few insonifications, compressed beamforming which aims to decrease the amount of data collected per insonification, and image restoration which exploits a model of non-stationary blur to enhance already reconstructed images. We suggest a compressive multiplexing approach for US signals. Such a technique achieves high-quality imaging with significantly fewer coaxial cables connecting the probe to the imaging system than existing methods. The compression is based on the compressive multiplexer, an analog compressed-sensing architecture, and the reconstruction relies on convex optimization algorithms. We propose two methods which exploit different low-dimensional models of US signals, namely the bandpass signal model and the pulse-stream model. We tackle the problem of localizing strong reflectors, with potential application in non-destructive evaluation and contrast-enhanced US imaging. We suggest a threefold approach composed of a time-of-flight (TOF)-sensing step, a TOF-labeling step and a localization step, which is capable of recovering the locations of strong reflectors with significantly fewer transducer elements and less sensor measurements than existing techniques. By exploring innovative methods for imaging and localization, this work contributes to a next generation of US imaging devices which will benefit from ultrafast US imaging to integrate advanced imaging modes into more and more compact systems.

Ultrafast ultrasound imaging as an inverse problem: Matrix-free sparse image reconstruction

Marcel Arditi, Adrien Georges Jean Besson, Rafael Eduardo Carrillo Rangel, Florian Martinez, Dimitris Perdios, Jean-Philippe Thiran, Yves Wiaux

Conventional ultrasound (US) image reconstruction methods rely on delay-and-sum (DAS) beamforming, which is a relatively poor solution of the image reconstruction problem. An alternative to DAS consists in using iterative techniques which require both an accurate measurement model and a strong prior on the image under scrutiny. Towards this goal, much effort has been deployed in formulating models for US imaging which usually require a large amount of memory to store the matrix coefficients. We present two different techniques which take advantage of fast and matrix-free formulations derived for the measurement model and its adjoint, and rely on sparsity of US images in well-chosen models. Sparse regularization is used for enhanced image reconstruction. Compressed beamforming exploits the compressed sensing framework to restore high quality images from fewer raw-data than state-of-the-art approaches. Using simulated data and in vivo experimental acquisitions, we show that the proposed approach is three orders of magnitude faster than non-DAS state-of-the-art methods, with comparable or better image quality.

2017

Sparse regularization methods in ultrafast ultrasound imaging

Olivier Bernard, Adrien Georges Jean Besson, Rafael Eduardo Carrillo Rangel, Jean-Philippe Thiran, Yves Wiaux

Ultrafast ultrasound (US) imaging based on plane wave (PW) insonification is a widely used modality nowadays. Two main types of approaches have been proposed for image reconstruction either based on classical delay-and-sum (DAS) or on Fourier reconstruction. Using a single PW, these methods lead to a lower image quality than DAS with multi-focused beams. In this paper we review recent beamforming approaches based on sparse regularization methods. The imaging problem, either spatial-based (DAS) or Fourier-based, is formulated as a linear inverse problem and convex optimization algorithms coupled with sparsity priors are used to solve the ill-posed problem. We describe two applications of the framework namely the sparse inversion of the beamforming problem and the compressed beamforming in which the framework is combined with compressed sensing. Based on numerical simulations and experimental studies, we show the advantage of the proposed methods in terms of image quality compared to classical methods.

Ieee2016

Data-driven Measurement Designs for Magnetic Resonance Imaging

Baran Gözcü

Despite being a powerful medical imaging technique which does not emit any ionizing radiation, magnetic resonance imaging (MRI) always had the major problem of long scanning times that can take up to an hour depending on the application. It also requires uncomfortable breath-holds due to the slow acquisition, sedation of children and repeated scans in the cases of degraded image quality due to body motion. Recent years have seen new image reconstruction techniques that need less amount of acquired data (i.e., accelerated scans) for reconstructing MRI images: parallel imaging and compressed sensing (CS). Although much work has been done on the reconstruction side, there has been relatively less work on experimental design, i.e., which parts of the Fourier domain to acquire during the scan, an essential factor that considerably affects the performance of image reconstructions. The state-of-the-art experimental designs use random subsampling either based on parametric models or heuristical adaptive models. The requirement of extensive parameter tuning and the random nature of the performance render these methods impractical and unreliable for clinical use. Can we systematically use the data acquired during past MRI scans for the design of accelerated scans with a reliable image quality? This problem is the focus of this thesis which proposes a data-driven scan design approach and training procedures which efficiently and effectively learn the structure inherent in the data, and accordingly, design the scans that directly acquire only the most relevant information during acquisition given an acceleration rate constraint. As a result, this boosts the performance of the existing state-of-the-art compressive sensing techniques on real-world datasets. Moreover, this approach provides strong theoretical guarantees by using tools from statistical learning theory. The intensive computational training procedures of our approach are made feasible by large-scale implementations on a parallel computing cluster. In return, this approach avoids any dependence on parametric or heuristic models and provides a reliably consistent image reconstruction performance for accelerated scans. Our approach is flexible and capable of giving deterministic scan designs specific to the anatomy, to the acceleration rate in use, to the reconstruction algorithm and the scan settings such as static/dynamic and parallel imaging. Apart from measurement designs for MRI, this thesis also considers the reconstruction problem. In particular, we focus on the inverse problems that involve a mixture of regularizers in the objective function, exploiting multiple structures at the same time. For these problems, we propose a reliable and systematic optimization framework and illustrate its effectiveness. Finally, in the last part of the thesis, we present a data-driven model and an optimization method for the design of nearly isometric, linear and dimensionality reducing embeddings.

EPFL2019

Data-driven Measurement Designs for Magnetic Resonance Imaging

Baran Gözcü

EPFL2019