Restoration of ultrasonic images using non-linear system identification and deconvolution

This paper studies a new ultrasound image restoration method based on a non-linear forward model. A Hammerstein polynomial-based non-linear image formation model is considered to identify the system impulse response in baseband and around the second harmonic. The identification process is followed by a joint deconvolution technique minimizing an appropriate cost function. This cost function is constructed from two data fidelity terms exploiting the linear and non-linear model components, penalized by an additive-norm regularization enforcing sparsity of the solution. An alternating optimization approach is considered to minimize the penalized cost function, allowing the tissue reflectivity function to be estimated. Results on synthetic ultrasound images are finally presented to evaluate the algorithm performance

Inverse Problem Formulation and Deep Learning Methods for Ultrasound Beamforming and Image Reconstruction

Ultrasound imaging is among the most common medical imaging modalities, which has the advantages of being real-time, non-invasive, cost-effective, and portable. Medical ultrasound images, however, have low values of signal-to-noise ratio due to many factors, and there has been a long-standing line of research on improving the quality of ultrasound images. Ultrasound transducers are made from piezoelectric elements, which are responsible for the insonification of the medium with non-invasive acoustic waves and also the reception of backscattered signals. Design optimizations span all steps of the image formation pipeline, including system architecture, hardware development, and software algorithms. Each step entails parameter optimizations and trade-offs in order to achieve a balance in competing effects such as cost, performance, and efficiency. The current thesis is devoted to research on image reconstruction techniques in order to push forward the classical limitations. It is tried not to be restricted into a specific class of computational imaging or machine learning method. As such, classical approaches and recent methods based on deep learning are adapted according to the requirements and limitations of the image reconstruction problem. In other words, we aim to reconstruct a high-quality spatial map of the medium echogenicity from raw channel data received from piezoelectric elements. All other steps of the ultrasound image formation pipeline are considered fixed, and the goal is to extract the best possible image quality (in terms of resolution, contrast, speckle pattern, etc.) from echo traces acquired by transducer elements. Two novel approaches are proposed on super-resolution ultrasound imaging by training deep models that create mapping functions from observations recorded from a single transmission to high-quality images. These models are mainly developed to resolve the necessity of several transmissions, which can potentially be used in applications that require both high framerate and image quality. The remaining four contributions are on beamforming, which is an essential step in medical ultrasound image reconstruction. Different approaches, including independent component analysis, deep learning, and inverse problem formulations, are utilized to tackle the ill-posed inverse problem of receive beamforming. The primary goal of novel beamformers is to find a solution to the trade-off between image quality and framerate. The final chapter consists of concluding remarks on each of our contributions, where the strengths and weaknesses of our proposed techniques based on classical computational imaging and deep learning methods are outlined. There is still a large room for improvement in all of our proposed techniques, and the thesis is concluded by providing avenues for future research to attain those improvements

Semi-blind ultrasound image deconvolution from compressed measurements

The recently proposed framework of ultrasound compressive deconvolution offers the possibility of decreasing the acquired data while improving the image spatial resolution. By combining compressive sampling and image deconvolution, the direct model of compressive deconvolution combines random projections and 2D convolution with a spatially invariant point spread function. Considering the point spread function known, existing algorithms have shown the ability of this framework to reconstruct enhanced ultrasound images from compressed measurements by inverting the forward linear model. In this paper, we propose an extension of the previous approach for compressive blind deconvolution, whose aim is to jointly estimate the ultrasound image and the system point spread function. The performance of the method is evaluated on both simulated and in vivo ultrasound data

A Physical Model of Non-stationary Blur in Ultrasound Imaging

Conventional ultrasound (US) imaging relies on delay-and-sum (DAS) beamforming which retrieves a radio- frequency (RF) image, a blurred estimate of the tissue reflectivity function (TRF). Despite the non-stationarity of the blur induced by propagation effects, most state-of-the-art US restoration approaches exploit shift-invariant models and are inaccurate in realistic situations. Recent techniques approximate the shift- variant blur using sectional methods resulting in improved accuracy. But such methods assume shift-invariance of the blur in the lateral dimension which is not valid in many US imaging configurations. In this work, we propose a physical model of the non-stationary blur, which accounts for the diffraction effects related to the propagation. We show that its evaluation results in the sequential application of a forward and an adjoint propagation operators under some specific assumptions that we define. Taking into account this sequential structure, we exploit efficient formulations of the operators in the discrete domain and provide an evaluation strategy which exhibits linear complexity with respect to the grid size. We also show that the proposed model can be interpreted in terms of common simplification strategies used to model non-stationary blur. Through simulations and in vivo experimental data, we demonstrate that using the proposed model in the context of maximum-a-posteriori image restoration results in higher image quality than using state-of-the-art shift-invariant models. The supporting code is available on github: https://github.com/LTS5/us-non-stationary-deconv

Beamforming through regularized inverse problems in ultrasound medical imaging

Beamforming (BF) in ultrasound (US) imaging has significant impact on the quality of the final image, controlling its resolution and contrast. Despite its low spatial resolution and contrast, delay-and-sum (DAS) is still extensively used nowadays in clinical applications, due to its real-time capabilities. The most common alternatives are minimum variance (MV) method and its variants, which overcome the drawbacks of DAS, at the cost of higher computational complexity that limits its utilization in real-time applications. In this paper, we propose to perform BF in US imaging through a regularized inverse problem based on a linear model relating the reflected echoes to the signal to be recovered. Our approach presents two major advantages: 1) its flexibility in the choice of statistical assumptions on the signal to be beamformed (Laplacian and Gaussian statistics are tested herein) and 2) its robustness to a reduced number of pulse emissions. The proposed framework is flexible and allows for choosing the right tradeoff between noise suppression and sharpness of the resulted image. We illustrate the performance of our approach on both simulated and experimental data, with in vivo examples of carotid and thyroid. Compared with DAS, MV, and two other recently published BF techniques, our method offers better spatial resolution, respectively contrast, when using Laplacian and Gaussian priors

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1