Wavelet based deconvolution method in ultrasonic tomography

International audienceThis paper deals with the quantitative and qualitative ultrasonic imaging of media contrasting strongly with the background (bones, for example). The wave propagation in these structures, which involves on several phenomena, generates ultrasound signals forming packages with different time and frequency signatures. To correlate the complex physical processes involved with the various packets forming the signals, it is advisable to separate the useful information (about the various packages, for example) from the parasite information (electronic noise). After testing several possible methods (filtering, deconvolution) with variable levels of success, it was proposed here to increase the resolution of the ultrasound signals, using a method of processing which was optimized by simultaneously analyzing the time and frequency parameters. For this purpose, algorithms based on the wavelet decomposition of the signals were used and suitable transmitted signals correlated with the parameters of the experimental device and the incident wave, were selected. The mathematical properties of the transmitted signal could be adapted themselves well to this time and frequency based approach. This method, which we have called the "wavelet based deconvolution method", makes it possible to determine the transfer function of the scatterer, which we attempted to reconstruct

Ultrasonic discrimination and modelling for crack-tip echoes

International audienceThe problem of discriminating between the acoustical signatures of an open crack tip and an interface is approached by modelling the various ultrasonic signatures and by a signal processing method. In the modelling study, the Kirchhoff approximation (the physical optics approximation) is used to describe the far field scattered by an arbitrary object with non-negligible dimensions in comparison with the wavelength, and to express this field depending on the incident field. It is established that, under this condition, the impulse response of an open crack tip is proportional to the first-order derivative of the impulse response of the transmitter. In the signal processing study, spectral and wavelet analyses were applied to the discrimination problem. The basic idea was to discriminate signatures simultaneously in time and in frequency (scale) domain. This method was found to be an effective means of testing models for the interactions between waves and flaws. Both aspects (modelling and signal processing) were studied numerically and experimentally, and the validity of the results was tested on an industrial sample

Simultaneous assessment of bone thickness and velocity for ultrasonic computed tomography using transmission-echo method

International audienceThe robustness and accuracy of the transmissionecho (TE) method is investigated on simultaneous thickness and velocity estimation of double-layered thin bone samples. Twentytwo pairs of bovine cortical samples were assembled and measured by two pairs of immersion transducers with nominal frequencies of 1MHz and 2.25MHz. For each measurement, the TOF of six pulses contained by one transmission and two echo signals were detected and then used for the calculation. The mean relative errors of effective samples for 1MHz and 2.25MHz transducers are 4.87% and 7.13% on cortical thickness estimation, and 4.65% and 5.88% on velocity assessment, respectively. For both thickness and velocity measurement, the experiments in low frequency provide more accurate estimations, and the velocity measurement shows more stability. It is demonstrated that the TE method has the potential to simultaneously estimate the cortical thickness and ultrasonic wave velocity for the mimic model of long bones

Non-linear ultrasonic tomography of high-contrasted materials

International audienceThis study focuses on the ultrasonic characterization and imaging of elastic materials like cylinders or tubes. In this case, ultrasonic wave propagation is greatly perturbed by the difference in the acoustic impedance between the scatterer and the surrounding medium (soft tissues, water or coupling gel), which results in considerable parasite events such as the refraction, attenuation and scattering of the waves. The aim of this work is then to solve a non-linear inverse scattering problem. Analytical or algebraic approaches may be applied generally involving in a "classical" problem of minimization of the differences between modeling data and measurements. Several strategies can be used to model the forward problem and to solve the inverse problem simply, efficiently and accurately. The distorted diffraction tomography is an inversion iterative method and belongs to the class of algebraic reconstruction algorithms. This method was developed to increase the order of application of the Born approximation (in the case of weakly contrasted media) to higher orders. The iterations are performed numerically by solving the forward and inverse problems at every iteration after calculating an appropriate Green's function; the previous iteration serves in each case to define the surrounding medium with a variable background. This yields quantitative information about the scatterer, such as the speed of sound and the attenuation. Quantitative ultrasonic imaging techniques of this kind are of great potential value in fields such as medicine, underwater acoustics and non-destructive testing

Numerical modeling in quantitative ultrasonic tomography of standing trees

International audienceThe aim of this project is to develop an ultrasonic device for parametric imaging of standing trees. The device is designed to perform both transmission and reflection measurements that can be therefore used for quantitative tomographic imaging. It allows various automatic acquisitions, since the angular position of the transducers could be adjusted. This makes possible to scan the wave propagation occurring in all directions inside the medium. The associated electronic set-up allows mainly measuring the slowness (and therefore the velocity) and the attenuation of the ultrasonic waves. Tomograms were computed by fast algebraic algorithms: (1) using the filtered backprojection algorithm with fan beam geometry, (2) using a new algorithm that we are developing based on a "layer-stripping" method. Our first numerical results on an academic and realistic phantom of tree are presented in this paper

An alternative ultrasonic method for measuring the elastic properties of cortical bone

We studied the elastic properties of bone to analyze its mechanical behavior. The basic principles of ultrasonic methods are now well established for varying isotropic media, particularly in the field of biomedical engineering. However, little progress has been made in its application to anisotropic materials. This is largely due to the complex nature of wave propagation in these media. In the present study, the theory of elastic waves is essential because it relates the elastic moduli of a material to the velocity of propagation of these waves along arbitrary directions in a solid. Transducers are generally placed in contact with the samples which are often cubes with parallel faces that are difficult to prepare. The ultrasonic method used here is original, a rough preparation of the bone is sufficient and the sample is in rotation. Moreover, to analyze heterogeneity of the structure we measure velocities in different points on the sample. The aim of the present study was to determine in vitro the anisotropic elastic properties of cortical bones. For this purpose, our method allowed measuring longitudinal and transversal velocities (CL and CT) in longitudinal (fiber direction) and radial directions (orthogonal to the fiber direction) of compact bones. Young's modulus E and Poisson's ratio Ν, were then deduced from the velocities measured considering the compact bone as transversely isotropic or orthotropic. The results are in line with those of other methods

Assessing the cortical thickness of long bone shafts in children, using two-dimensional ultrasonic diffraction tomography

International audienceEchography is one of the first-line techniques used in clinical practice to diagnose osteoarticular diseases in children. However, this technique involves the use of standard equipment, which is not adapted to the morphology or the acoustical properties of children's bones. In this study, we developed an ultrasonic tomography method for measuring the cortical thickness of children's long bones. Ultrasonic tomography gives cross-sectional images showing the spatial distribution of some of the physical components of an object, based on scattered ultrasound measurements. These measurements are carried out using variably dense sets of transmitter and receiver positions and various the wave frequencies. We solved this inverse scattering problem using a Born approximation, which yields an attractively simple linear relation between the object function and the scattered field, particularly in the far field. Experiments with a 2D-ring antenna show the applicability of the method and its various improvements to bone thickness imaging

Traitement du signal par transformation en ondelettes : application au contrôle non destructif par ultrasons

Le contrôle non destructif des matériaux par ultrasons pose essentiellement un problème de discrimination entre les signaux utiles (ceux qui proviennent par exemple de petits diffuseurs) des signaux parasites (ceux qui proviennent par exemple des interfaces). On espère pouvoir effectuer cette discrimination sur les signatures temps-échelle, c'est a dire grâce à l'analyse en ondelettes utilisée ici comme technique de traitement du signal (Pré-traitement des données avant injection dans les algorithmes de construction d'images) [ 1 ]. Nous avons mis au point un algorithme basé sur l'analyse en ondelettes orthogonales de S.Jaffard et Y.Meyer [2] [3] pour élaborer, ensuite, un algorithme d'analyse surabondante en échelles qui présente les avantages de l'analyse continue (présentation des résultats sous forme d'images) tout en conservant ceux de l'analyse discrète. Nous avons développé ensuite des logiciels rapides à base de procédures de transformée de Fourier rapide que nous avons testé sur des exemples simples, avant de traiter un certain nombre de problèmes. Nous nous sommes d'abord servi de cet algorithme pour mettre au point un réjecteur automatique de certains signaux parasites, comme les signaux d'interfaces à fort contraste (interfaces eau-acier et acier-eau par exemple), en utilisant l'apparition de sous-harmoniques et la notion de cône d'influence. Le second problème que nous avons étudié, a été la détection de défaut dans une pièce en acier massive munie d'un revêtement épais d'acier inoxydable, une fissure pouvant prendre naissance à l'interface entre les deux aciers. Les analyses en ondelettes comparées d'échogrammes de zones saines et de ceux de zones malsaines laissent apparaître des différences aussi bien sur les analyses surabondantes que sur les analyses discrètes. C'est cette finesse d'analyse que nous avons utilisée ensuite pour vérifier le bien fondé de nôtre modélisation. L'analyse en ondelettes s'avère être un excellent outil pour ce type de problème