Exposés

Giovanni S. Alberti	Disjoint sparsity for signal separation and applications to quantitative photoacoustic tomography
Abstract: This is joint work with H Ammari. The main focus of this talk is the reconstruction of the signals f and g_i, i=1,...,N, from the knowledge of their sums h_i=f+g_i, under the assumption that f and the g_is can be sparsely represented with respect to two different dictionaries Af and Ag. This generalises the well-known ``morphological component analysis'' to a multi-measurement setting. The main result states that f and the g_is can be uniquely and stably reconstructed by finding sparse representations of h_i for every i with respect to the concatenated dictionary [A_f,A_g], provided that enough incoherent measurements g_is are available. The incoherence is measured in terms of their mutual disjoint sparsity. This method finds applications in the reconstruction procedures of several hybrid imaging inverse problems, where internal data are measured. These measurements usually consist of the main unknown multiplied by other unknown quantities, and so the disjoint sparsity approach can be directly applied. In this case, the feature that distinguishes the two parts is the different level of smoothness. As an example, I will show how to apply the method to the reconstruction in quantitative photoacoustic tomography, also in the case when the Grüneisen parameter, the optical absorption and the diffusion coefficient are all unknown.

Mark A. Anastasio	Iterative Image Reconstruction Methods for Photoacoustic Computed Tomography with Application to Experimental Data
Abstract: Photoacoustic computed tomography (PACT) is an emerging soft-tissue imaging modality that has great potential for a wide range of preclinical and clinical imaging applications. It can be viewed as a hybrid imaging modality in the sense that it utilizes an optical contrast mechanism combined with ultrasonic detection principles, thereby combining the advantages of optical and ultrasonic imaging while circumventing their primary limitations. In this talk,we review our recent advancements in practical image reconstruction approaches for PACT. Such advancements include physics-based models of the measurement process and associated optimization-based inversion methods for reconstructing images from limited data sets in acoustically heterogeneous media. Applications of PACT to transcranial brain imaging and breast cancer detection will be discussed.

Maïtine Bergounioux	Quantitative Thermoacoustic Tomography with microwaves sources : the inverse model
Abstract: The talk is the companion talk of the one of Amélie Litman. Once the forward model has been set we consider the inverse problem in a finite dimensional framework wia an optimal control approach. Joint work with Hassan Akhouayri, Maïtine Bergounioux, Anabela Da Silva, Peter Elbau & Leonida Mindrinos

Elie Bretin	Time reversal method in the case of non Dirac delta source approximation
Abstract: We consider in this work the problem of reconstructing a source s(x,t) = \partial_t f(t) H(x) in acoustic media. In the case of a Dirac pulse f approximation, this problem is well known and conduces to a Cauchy problem for which, the initial data H can be reconstructed using a time reversal algorithm or inverse spherical Radon transform. The novelty here is to consider a general pulse f and we explain why this problem can be still expressed as an equivalent Cauchy problem with perturbed the initial data. More precisely, we see that the initial conditions are now obtained with a convolution product of the ideal source H with an explicit kernel K_f. This inverse source problem can then be solved using a classical time reversal technique coupled with a deconvolution algorithm. Some numerical experiments highlight the efficiency of this approach. This is joint work with Carine Lucas and Yannick Privat.

Emmanuel Bossy	Exploiting light coherence for photoacoustic
Abstract: Since its introduction in the mid-nineties, photoacoustic imaging of biological tissue has been one of the fastest growing biomedical imaging modality, and its basic principles are now considered as well established. The general principle of photoacoustic imaging is the following: the sample to be imaged is illuminated by pulsed light (for most implementations), and acoustic waves generated from illuminated absorbing regions are detected by acoustic sensors. One major interest of this technique is that it allows imaging optical absorption at large depth inside optically scattering media, with the resolution of ultrasound, much better than the resolution provided by purely optical techniques. Lasers are generally used as sources, as powerful and flexible sources of light energy, and light propagation in photoacoustic imaging is generally considered from the perspective of transport theory. However, coherence properties of lasers also provide specific properties for multiple scattering of light, such as the formation of optical speckle patterns or the possibility of manipulating scattered light with optical wavefront shaping, not described within the framework of the transport theory. In this presentation, I will show that light coherence therefore provides many degrees of freedom that can be exploited in photoacoustic imaging. I will first illustrate how multiple speckle illumination provide 1) a way to compensate for reconstruction artefacts caused by limited-view and limited-bandwidth measurements 2) a way to obtain super-resolution photoacoustic images, beyond the acoustic diffraction limit. I will then illustrate how the manipulations of the various degrees of freedom of coherent light can be manipulated by optical wavefront shaping in the context of photoacoustic imaging.

Ben Cox	Quantitative estimation of concentrations using multiwavelength photoacoustic imaging
Abstract: Optical imaging modalities offer high contrast but at depths beyond the ballistic regime in tissue light is strongly scattered leading to a loss of image resolution. Photoacoustic imaging overcomes this by encoding the information about the absorption contrast on an ultrasonic wave. It therefore has the potential to provide high resolution 3D images at multiple optical wavelengths, and has attracted considerable attention for preclinical applications in recent years. However, unlike many purely optical techniques, using multiwavelength photoacoustic image data for spectroscopy - and more generally for quantitative estimation - has proved non-trivial. These reasons for this, and potential ways to overcome them, will be discussed.

Anabela Da Silva	Improved Localization and Quantification in Photoacoustic Tomography by Using Intrinsic Acoustic Information Content
Abstract: Due to the diffusing and absorbing nature of the surrounding tissues, the major part of the optical fluence is deposited at the periphery of the tissue, generating an intense acoustic pressure wave that hides the photoacoustic signal of interest. We propose a method for improving the localization and the quantification of the optical parameters in photoacoustic tomography of biological tissues, that are intrinsically heterogeneous in both optical and acoustic properties. It is based on the exploitation of both the photoacoustic signal, generated by the heterogeneous optical structures, and the secondary acoustic echoes due to the interaction between a primary photoacoustic wave generated near the tissues surface region and the heterogeneous acoustic structures. These secondary echoes can also be collected through proper measurements of the photoacoustic signals. The experimental procedure is presented as well as the method to filter the signal and the reconstruction algorithm accounting for the acoustic information. Joint work with Charles Handschin, Christophe Riedinger, Amélie Litman, Serge Mensah & Hassan Akhouayri

Peter Elbau	Simultaneous Reconstruction of Absorption Coefficient, Speed of Sound, and Density with Photoacoustic Sectional Imaging.
Abstract: We would like to study weakly scattering objects where it is possible to apply photoacoustic sectional imaging; which is a photoacoustic measurement setup where the initial laser pulse is focused in such a way that only a single slice of the object is illuminated. By doing such measurements for every choice of illumination plane, it was shown in a paper by Kirsch and Scherzer in 2012 that it is possible to recover not only the absorption coefficient, but also the speed of sound of the medium. We want to demonstrate that this result can be extended to samples where the mass density cannot be considered to be constant (for example if there are inclusions filled with air). Then, the acoustic equation will contain the mass density as an additional unknown material parameter and it turns out that it can be also reconstructed (together with the absorption coefficient and the speed of sound) from the photoacoustic sectional maging measurements.

Josselin Garnier	The random paraxial wave equation and application to correlation-based imaging
Abstract: We analyze wave propagation in random media in the so-called paraxial regime, which is a special high-frequency regime in which the wave propagates along a privileged axis. We show by multiscale analysis how to reduce the problem to the Ito-Schrodinger stochastic partial differential equation. We also show how to close and solve the moment equations for the random wave field. Based on these results we propose to use correlation-based methods for imaging in complex media and consider several examples in seismology and nondestructive testing.

Thomas Glatz	Photoacoustic tomography with spatially varying compressibility and density
Abstract: We investigate photoacoustic tomography with two spatially varying acoustic parameters, the compressibility and the density. We consider the reconstruction of the absorption density with complete and partial measurement data. We investigate and analyze three different numerical methods suitable for this wave model, and compare the results. The standard reconstruction procedure for photoacoustic tomography accounting for sound speed variations is time reversal. It consists in solving a time-reversed wave equation on a bounded domain, usually assuming vanishing final values, which leads to an approximation error. The measurements serve as Dirichlet boundary data. A Neumann series approach based on time reversal gives a convergent reconstruction method in the case of exact data and non-trapping speed. In contrast, we formulate the photoacoustic problem as an operator equation. A Landweber iteration allows to stably reconstruct a regularized solution. Different to time reversal, this gives convergence to such a regularized solution also in cases where the photoacoustic inversion is ill-posed, like in the presence of noise or when the underlying speed of sound is trapping. The back-propagation, that can in some sense be found in all treated reconstruction techniques, is now encoded in the adjoint operator.

Thomas Haberkorn	An optimal control approach to Photoacoustic Tomography
Abstract: We will give a mathematical model for photoacoustic tomography, a hybrid imaging technique for soft tissues. It consists in exposing a body to a light source (laser) that diffuses in the body. The energy of the diffused light is then inhomogeneously absorbed which results in the expansion of the body and ultimately in the generation of an acoustic wave. The inverse problem is then to reconstruct the absorption and diffusion coefficients from the measurements of the acoustic wave. After taking into account the different time-scales of the phenomemon, we neglect the thermal diffusion and model it with a diffusion equation (for the light) and a wave equation. This inverse problem is written as an optimal control problem in which the controls are the absorption and the diffusion coefficients. We show the well-posedness of this optimal control problem and provide first order necessary conditions for a control to be optimal. We then give some numerical results for the reconstruction of the absorption coefficient in the case where there is only a small number of measurements.

Philippe Jaming	Radon transforms of thin objects
Abstract: In this talk, we investigate the Radon transform of measures supported on curves in the plane or surfaces in the 3-dimensional space. We will show how those objects are defined and then investigate how many measurements are needed to uniquely determine the measure when the curve or surface has some specific shapes (circular, parabolic,...). The results can also be interpreted in terms of unique continuation properties of some PDEs. The talk is based on joint work with K. Kellay (Bordeaux) and ongoing work with K. Gröchenig (Vienna)

Alain Le Pape	Photo-Acoustic Imaging: Present and future for pre-clinical research and medical practice

Thibault Liard	Non-localization of eigenfunctions for Sturm-Liouville operators
Abstract: We focus our attention on a non-localization property of the eigenfunctions of Sturm- Liouville operators A_\alpha = - \partial_{xx}+a (\cdot) Id, where 0 \leq a\leq M on (0,L) with L>0 and M>0. More precisely, we address the extremal spectral problem of minimizing the L²-norm of a function e on a measurable subset \omega \subset (0,L), where e runs over all eigenfunctions of A_\alpha, at the same time with respect to all subsets \omega having a prescribed measure and all nonnegative L^\infty potential functions a having a prescribed essentially upper bound. We provide some existence and qualitative properties of the minimizers, as well as precise lower and upper estimates on the optimal value. Numerous consequences in control and stabilization theory are then highlighted, both theoretically and numerically.

Amélie Litman	Quantitative Thermoacoustic Tomography with microwaves sources : the forward model
Abstract:In photo-acoustic tomography (PAT), an electromagnetic (EM) wave in the optical range is sent through a biological object (e.g., a woman's breast in mammography) with the aim of triggering a thermo-elastic response in the tissue. In thermo-acoustic tomography (TAT), the same principle is applied except that the EM waves are chosen in the radiofrequency range. For these centimetric waves, the radiation pattern of the antenna is spatially wide with respect to the illuminated target and the whole object is more or less irradiated. As human tissues are known to be lossy, parts of the absorbed EM energy is transformed into a thermo-elastic expansion. This in turn results in a pressure wave which can be measured with transducers placed around the object. The TAT approach adequately combines the high resolution of the ultrasound diagnostics and the penetration depth of the EM waves. In PAT, the EM illumination is described thanks to the diffusion equation or the light transport model. In TAT, it is the electromagnetic field itself which is the quantity of interest and thus, three-dimensional Maxwell equations must come in full play. In this talk, we will present a mathematical description of the various relations which link the polarized EM waves, the temperature variations and the acoustic pressure. The correct definition of these various equations is a prerequisite step before tackling a joint quantitative inversion procedure where the parameters of interest will be related to the electromagnetic (refractive indices), thermal (temperature rise) or acoustic (acoustic velocities) waves. Joint work with Hassan Akhouayri, Maïtine Bergounioux, Anabela Da Silva, Peter Elbau & Leonida Mindrinos

Felix Lucka	4D PAT based on Sparse Variational Methods
Abstract:The acquisition time of current high-resolution 3D photoacoustic tomography (PAT) devices limits their ability to image dynamic processes in living tissue (4D PAT). In our work, we try to overcome this limitation by combining recent advances in spatio-temporal sub-sampling schemes, variational regularization and convex optimization with the development of tailored data acquisition systems. We first show that images with acceptable spatial resolution can be obtained from suitably sub-sampled PAT data if sparsity-constrained image reconstruction techniques such as total variation regularization enhanced by Bregman iterations are used. A further increase of the dynamic frame rate can be achieved by exploiting the temporal redundancy of the data through the use of sparsity-constrained dynamic models such as optimal transport models. While simulated data from numerical phantoms will be used to illustrate the potential of the developed methods, we will also discuss the results of their application to different measured data sets. Furthermore, we will outline how to combine GPU computing and state-of-the-art optimization approaches to cope with the immense computational challenges imposed by 4D PAT. Joint work with: Marta Betcke, Simon Arridge, Ben Cox, Nam Huynh, Edward Zhang and Paul Beard.

Pierre Millien	Magnetoacoustic tomography with magnetic induction
Abstract: We provide a mathematical analysis and a numerical framework for magnetoacoustic tomography with magnetic induction. The imaging problem is to reconstruct the conductivity distribution of biological tissue from measurements of the Lorentz force induced tissue vibration. We begin with reconstructing from the acoustic measurements the divergence of the Lorentz force, which is acting as the source term in the acoustic wave equation. Then we recover the electric current density from the divergence of the Lorentz force. To solve the nonlinear inverse conductivity problem, we introduce an optimal control method for reconstructing the conductivity from the electric current density. We prove its convergence and stability. We also present a fixed point approach and prove its convergence to the true solution. A new direct reconstruction scheme involving a partial differential equation is then proposed based on viscosity-type regularization to a transport equation satisfied by the electric current density field. We prove that solving such an equation yields the true conductivity distribution as the regularization parameter approaches zero. Finally, we test the three schemes numerically in the presence of measurement noise, quantify their stability and resolution, and compare their performance.

Léonidas Mindrinos	Inverse Problems of Quantitative Coupled Physics Imaging techniques
Abstract: We consider the combined system of Photoacoustic and Optical Coherence Tomography. We present a unified model to describe the experiment starting from the microscopic Maxwell's equations. Since a single modality does not provide unique solvability of all the optical parameters under no assumptions about the medium, we address the question if the additional information from the combined system makes the inverse problem feasible.

Daniel Razanski	Computational and visualization challenges in multi-dimensional optoacoustic tomography
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John C. Schotland	Inverse problems in acousto-optic imaging
Abstract: A method to reconstruct the optical properties of a highly-scattering medium from acousto-optic measurements is proposed. The method is based on the solution to an inverse problem for the radiative transport equation with internal data. A stability estimate and a direct reconstruction procedure are described.

Erica Schwindt	On the uniqueness and stability of an inverse problem in photo-acoustic tomography
Abstract: In this talk, I will present an inverse problem in photo-acoustic tomography. The aim is to recover and characterize the absorption coefficient of a soft body. The inverse problem is formulated as a problem of optimal control in which the control variable is the coefficient to retrieve. The result of existence of at least one optimal control was proved in `` An optimal control problem in photo-acoustic tomography " by M. Bergounioux et al. (2014). In this presentation, I will deal with the problem of the uniqueness of the optimal solution (absorption coefficient) and also I will present a study on the sensitivity of this solution with respect to variations of the source of illumination and with respect to observation.

Tanja Tarvainen	Bayesian approach to quantitative photoacoustic tomography
Abstract: Quantitative photoacoustic tomography is an emerging imaging technique aimed at estimating the (absolute) quantitative values of optical parameters inside tissue from photoacoustic images which are formed by combining optical information and ultrasound propagation. This is an ill-posed problem, and therefore it needs to be approached within the framework of inverse problems. In this talk, it is shown how the problem can be approached in the framework of Bayesian inverse methods. Results of recent developments using this approach are shown and discussed.

Roger Zemp	Photoacoustic imaging of oxygen metabolism, gene expression and porphyrin nanodroplets
Abstract:Photoacoustic imaging is used to sense optical absorption with ultrasonic spatial resolution or better. We report on recent developments in using photoacoustic imaging to image oxygen flux and metabolism, imaging of gene expression using dark reporters optimized for photoacoustics, and directed evolution strategies to achieve smart photoswitchable behavior for such reporters. We additionally report on hybrid imaging strategies for magnetic trapping and detection of circulating tumor cells with single-cell detection capabilities, and novel porphyrin nanodroplets for photoacoustic targeted imaging and blood biomarker enhancement.

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