Learning the weight matrix for sparsity averaging in compressive imaging

We propose to map the fast iterative shrinkage-thresholding algorithm to a deep neural network (DNN), with a sparsity prior in a concatenation of wavelet bases, in the context of compressive imaging. We exploit the DNN architecture to learn the optimal weight matrix of the corresponding reweighted l1-minimization problem. We later use the learned weight matrix for the image reconstruction process, which is recast as a simple l1-minimization problem. The approach, denoted as learned extended FISTA, shows promising results in terms of image quality, compared to state-of-the-art algorithms, and significantly reduces the reconstruction time required to solve the reweighted l1-minimization problem.

Imaging from Echoes: On Inverse Problems in Ultrasound

Adrien Georges Jean Besson

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.

EPFL2019

Compressive Multiplexing of Ultrasound Signals

Marcel Arditi, Adrien Georges Jean Besson, Dimitris Perdios, Jean-Philippe Thiran, Yves Wiaux

High-quality 3D ultrasound (US) imaging requires dense matrix-array probes with thousands of elements and necessitates an unrealistic number of coaxial cables to connect such probes to back-end systems. To address this issue, many techniques have been developed such as sparse arrays, mechanical scanning, multiplexing and micro-beamforming, which permit to achieve 3D imaging with existing 2D imaging systems but with a degradation in image quality. We propose a novel multiplexing method which relies on compressed-sensing (CS) principles to significantly reduce the number of coaxial cables. We exploit the compressive multiplexer (CMUX) introduced for radio-frequency signals to multiplex US signals in the probe head. The CMUX considers a set of signals as inputs, modulates them with chipping sequences and sums them to form a single output. On the reconstruction side, we propose two methods: one solving a CS-based problem exploiting sparsity of US signals in a pulse-stream model (CS-PS) and another one solving a least-squares problem in the Fourier domain based on bandlimited signal properties of US signals. We demonstrate through simulations and in vivo experiments that the proposed techniques lead to high-quality reconstruction with significantly fewer coaxial cables, up to 12x less with CS-PS.

IEEE2018

3D Reconstruction of Optical Diffraction Tomography Based on a Neural Network Model

Morteza Hasani Shoreh

Optical tomography has been widely investigated for biomedical imaging applications. In recent years, it has been combined with digital holography and has been employed to produce high quality images of phase objects such as cells. In this Thesis, we look into some of the newest optical Diffraction Tomography (DT) based techniques to solve Three-Dimensional (3D) reconstruction problems and discuss and compare some of the leading ideas and papers. Then we propose a neural-network-based algorithm to solve this problem and apply it on both synthetic and biological samples. Conventional phase tomography with coherent light and off axis recording is performed. The Beam Propagation Method (BPM) is used to model scattering and each x-y plane is modeled by a layer of neurons in the BPM. The network's output (simulated data) is compared to the experimental measurements and the error is used for correcting the weights of the neurons (the refractive indices of the nodes) using standard error back-propagation techniques. The proposed algorithm is detailed and investigated. Then, we look into resolution-conserving regularization and discuss a method for selecting regularizing parameters. In addition, the local minima and phase unwrapping problems are discussed and ways of avoiding them are investigated. It is shown that the proposed learning tomography (LT) achieves better performance than other techniques such as, DT especially when insufficient number or incomplete set of measurements is available. We also explore the role of regularization in obtaining higher fidelity images without losing resolution. It is experimentally shown that due to overcoming multiple scattering, the LT reconstruction greatly outperforms the DT when the sample contains two or more layers of cells or beads. Then, reconstruction using intensity measurements is investigated. 3D reconstruction of a live cell during apoptosis is presented in a time-lapse format. At the end, we present a final comparison with leading papers and commercially available systems. It is shown that -compared to other existing algorithms- the results of the proposed method have better quality. In particular, parasitic granular structures and the missing cone artifact are improved. Overall, the perspectives of our approach are pretty rich for high-resolution tomographic imaging in a range of practical applications.