### Recent advances in acquisition and reconstruction for Compressed Sensing MRI

Philippe Ciuciu – *CEA/NeuroSpin & CEA-INRIA Parietal team, Gif-sur-Yvette, France.
*Jeffrey Fessler –

*Dept. of EECS, College of Engineering, University of Michigan, Ann Arbor, MI, USA.*

Compressed Sensing (CS) MRI methods have led to accelerated data acquisition while preserving image quality by (i) massive under-sampling of existing k-space trajectories (e.g. Cartesian lines or radial spokes, spirals) and (ii) nonlinear reconstruction algorithms that promote either sparsity or low-rank models of the reconstructed MR image in some domain. Two recent complementary research directions are starting to supplant this classical CS setting: (1) the design of optimization-driven under-sampling schemes that maximize sampling efficiency, allow variable density sampling in multiple dimensions according to the acquisition setup (2D vs 3D imaging, single vs multishot acquisitions, etc.), and (2) the advent of machine learning tools (e.g., deep learning) for MR image reconstruction that are based on data-driven methods rather than mathematical models.

This course will focus on these new trends in CS MR acquisition and image reconstruction and is split in two parts accordingly. Demonstrations on both retrospectively under-sampled and prospectively compressed high-resolution ex-vivo and in-vivo human data will be provided to show the robustness of the proposed methodology against the classical acquisition artifacts (e.g., gradient errors, off-resonance effects) that occur in spiral imaging for instance.

Importantly, python and julia codes exemplified by jupyter notebooks will allow the participants/attendees to test the codes and practice by themselves. This will give them a deep insight on the exposed advanced methods both at the acquisition and reconstruction stages.

### Geodesic methods in Biomedical Image Analysis

Laurent D. Cohen – *CEREMADE, UMR CNRS 7534, University Paris Dauphine, PSL Research University, Paris, France*.

Tubular and tree structures appear very commonly in biomedical images like vessels, microtubules or neuron cells. Minimal paths have been used for long as an interactive tool to segment these structures as cost minimizing curves. The user usually provides start and end points on the image and gets the minimal path as output. These minimal paths correspond to minimal geodesics according to some adapted metric. They are a way to find a (set of) curve(s) globally minimizing the geodesic active contours energy. Finding a geodesic distance can be solved by the Eikonal equation using the fast and efficient Fast Marching method. Introduced first as a way to find the global minimum of a simplified active contour energy, we have recently extended these methods to cover all kinds of active contour energy terms. Also, various methods have been introduced that improve either the interactive aspects or their efficiency in order to make completely automatic or minimally interactive tools for image segmentation. For example, the metric can take into account both scale and orientation of the path. This leads to solving an anisotropic minimal path in a 2D or 3D+radius space (Figure 1). More recently, a new way to penalize the curvature in the framework of geodesic minimal paths was introduced, leading to more natural results in vessel extraction for example (Figure 2). In particular, much work has been applied to retina images like the automatic detection of vascular tree as well as the geometric analysis of these structures (Figure 3).

In this course we will present different methods based on geodesics from their basics to biomedical applications, in particular for blood vessel segmentation.

### Optimal Transport for machine learning

Rémi Flamary – *University Côte d’Azur, Lagrange Laboratory, Côte d’Azur Observatory, Nice, France.*

This tutorial aims at presenting the mathematical theory of optimal transport (OT) and providing a global view of the potential applications of this theory in machine learning, signal pro-cessing and biomedical data processing.

The ﬁrst part of the tutorial will present the theory of optimal transport and the optimization problems through the original formulation of Monge and the Kantorovitch formulation in the primal and dual. The algorithms used to solve these problems will be discussed and the problem will be illustrated on simple examples. We will also introduce the OT-based Wasserstein distance and the Wasserstein barycenters that are fundamental tools in data processing of histograms [Gramfort et al., 2015]. Finally we will present recent developments in regularized OT that bring eﬃcient solvers and more robust solutions [Cuturi, 2013].

The second part of the tutorial will present numerous recent applications of OT in the ﬁeld of machine learning and signal processing and biomedical imaging. We will see how the mapping inherent to optimal transport can be used to perform domain adaptation and transfer learning [Courty et al., 2016] with several biomedical applications [Gayraud et al., 2017]. Next we will discuss how the Wasserstein distance can be included in the learning and data processing for data seen as histograms with application in multi-label classiﬁcation and linear unmixing. Finally we will discuss its use on empirical datasets with applications such as generative adversarial networks, subspace estimation and domain adaptation.

### Deep Learning for Biomedical Image Reconstruction

Jong Chul Ye, Ph.D. *– KAIST Endowed Chair Professor; Professor of Dept. of Bio and Brain Engineering; Korea Advanced Inst. of Science & Technology (KAIST), **Daejeon, Republic of Korea*

Recently, deep learning approaches have achieved significant performance improvement over existing iterative reconstruction techniques in various biomedical image reconstruction problems. However, it is still unclear to the imaging community why these deep-learning architectures work for specific inverse issues. This tutorial will first discuss the latest state-of-the-art deep-learning image reconstruction algorithms for various imaging modalities such as X-ray CT, MRI, optical imaging, PET, ultrasound, and more. Subsequently, we also introduce recent theoretical results from signal processing community that combines deep learning approaches with the classical signal processing approach, such as compressed sensing, low-rank matrix completion, wavelets, non-local algorithms, etc. In particular, we will show that deep learning approach is a natural extension of compressed sensing theory.

### Breaking the Boundaries of Conventional Ultrasonography: Ultrasound Elastography and Photoacoustic Imaging for Characterization of Tissue Biomechanics, Function, and Molecular Compositions** **

Abbas Samani – *Department of Electrical and Computer Engineering, Biomedical Engineering Program, Department of Medical Biophysics, Robarts Research Institute, Western University, London, Ontario Canada
*Hassan Rivaz –

*Department of Electrical and Computer Engineering*,

*PERFORM Centre and Faculty of Engineering and Computer Science Concordia University*,

*Montreal, Quebec, Canada*

Mohammad Mehrmohammadi –

*Department of Biomedical/Electrical and Computer Engineering Wayne State University, Barbara Ann Karmanos Cancer Institute, Detroit, USA*

Elastography involves imaging the biomechanical properties of tissue. It is of significant interest in many disease (e.g. cancer) diagnosis applications and in guidance/monitoring of surgical operations. Elastography has evolved into several different techniques, but it can be broadly grouped into harmonic and quasi-static elastography. Harmonic elastography techniques include inducing shear or compressional waves in the tissue through external mechanical actuation. This is followed by imaging the induced waves before the tissue biomechanical properties are reconstructed and visualized. Quasi-static elastography involves inducing very low frequency deformation in the tissue using ultrasound probe or specialized mechanical actuation systems. Data characterizing tissue deformation are acquired using ultrasound imaging or magnetic resonance imaging (MRI) techniques in conjunction with signal processing. In general, this data is processed within an inverse problem algorithm before the tissue elasticity modulus (e.g. Young’s modulus or shear modulus) is reconstructed and visualized. The tutorial will involve presenting various image reconstruction algorithms, including Helmholtz inversion, strain imaging and full inversion based reconstruction techniques.

Central to all elastography methods is estimation of tissue motion from an imaging modality such as ultrasound. Motion data acquisition aiming at elastography applications is an active field of research. In general, such data acquisition is more difficult in ultrasound imaging due to several sources of signal decorrelation. Window-based techniques calculate motion for small windows (also known as kernels) of the raw ultrasound data (i.e. RF data), and can be categorized into amplitude- and phased-based. Amplitude-based methods maximize cross correlation or normalized cross correlation, whereas phase-based methods find the zero- crossing of the phase of the cross correlation. An alternative approach to correlation-based methods is minimization of a regularized cost function. These methods exploit a priori information pertaining to smoothness of tissue deformation, and therefore are robust to signal decorrelation. A disadvantage of these methods is their computational complexity, and as such, are not readily suitable for real-time implementation. In this part of the tutorial, state-of-the-art elastography techniques will be reviewed, and live demos on tissue displacement estimation and elastography image reconstruction will be presented.