Nonlinear Imaging using Time Reversal and Array Transducers
Context and problem. Nowadays, ultrasound imaging is largely used in biomedical diagnosis (echography) and in Non-Destructive Evaluation (NDE). In NDE, sensitivity of ultrasound imaging systems has been improved the detection of flaws, over the past twenty years. In biomedical applications, ultrasound imaging has the advantage over other imaging methods, such as Computed Tomography (CT) or Magnetic Resonance Imaging (MRI), of being relatively cheap and portable. The resolution and contrast of ultrasound imaging is determined by various factors, including transducer design, type of waveform, and frequency of operation. Significant advances have been made in the recent years on super-resolution and ultrafast 3D imaging using 2D arrays. To maximize the imaging resolution, high operating frequencies (> 1 MHz) and multi-element transducers are usually employed, leading to two major limitations. First, the penetration depth is limited by the large attenuation of the ultrasonic waves in the propagating medium and by the aberration and reverberation associated with the interfaces at high frequencies. Second, the complexity of the signal processing associated with a large number of transducer elements still limits the achievable frame rate for a given image quality. In this work, two complementary strategies are proposed to address these limitations: waveform design for non-linear excitation and parallel processing for accelerated computing of advanced algorithms such as correlation-based imaging.
Waveform design. The waveform design enables to improve the contrast and/or of the spatial resolution of ultrasound image. Beamforming can be seen as the first kind of waveform design using multi-element probe design. The second kind of waveform design is directly related to the time-domain series transmitted to the ultrasound probe and has enabled the development of harmonic imaging techniques based on the nonlinear mechanical behaviour of the wave propagation or of the cracks in the medium. Indeed, when ultrasound sinusoidal waves of frequency f0 propagate, the echoes received are also composed of harmonic components (2f0, 3f0,...). By extracting each harmonic component, it is possible to obtain ultrasound images with high contrast compared to standard beamforming algorithm. Given this success, harmonic imaging has become the native imaging modality in conventional ultrasound scanners by using discrete encoding techniques with multiple transmissions. Since the backscattered nonlinearities are a function of the transmitted signal, enhancing the image quality in harmonic imaging is equivalent to finding the best transmitted wave. Waveform design can be decomposed in two ways: optimizing the wave in space or optimizing the wave in time. In the first way, beamforming has improved the contrast and the resolution. Whereas this spatial beamforming can be obtained from an optimal and adaptive process, all solutions of the encoding excitations are non-optimal. The question of waveform design remains open. Therefore the second way consists in finding the temporal waveform. In our opinion, the settings of the excitation must consider the targeted medium and they must derive from an optimal command process. Therefore, the optimal command problem consists of seeking the optimal excitation which provides the best image quality. Several studies have proposed a solution for nonlinear imaging, based on iterative algorithms that are related to the features of the wave or directly the values of the samples.
Correlation-based imaging. While the NDE industry is still defining a framework for the use of Total Focusing Method (TFM), a small number of super-resolution signal processing algorithms are proposed such as multi-modal plane wave imaging. In medical imaging, Synthetic Aperture Focusing Technique (SAFT), similar to TFM, has led to super-resolution algorithms such as coherent compounding, using plane or diverging waves, and phase coherence imaging. The correlation-based patented algorithm Excitelet proposed by Masson and Quaegebeur allows super-resolution imaging at much lower frequencies (0,1 to 1 MHz) as compared to conventional NDE or medical imaging, for larger penetration depths. Excitelet inherently considers a detailed model of the full wave propagation path, including the transducer dynamics, the coupling interfaces and the propagation in the medium. Excitelet has already demonstrated better resolution and robustness to the number of transducers than standard TFM/SAFT beamforming approaches. In medical imaging, experimental validation on a simple phantom has shown potential improvement for diagnostic.
In a very similar way, time reversal optimizes the signal-to-noise ratio (SNR) by combining a waveform design in space and in time, thanks to a physical matched filter. It enables focusing the incident wavefield on small inhomogeneities, without information on the medium and even if the medium is aberrating. Its principle consists in sending a first wave at the frequency f0 and in retro-propagating the time reversed echoes. Nevertheless, as the wave is retro-propagated, the harmonic components are neglected. This property has been used to reduce the tissue harmonic components in ultrasound contrast imaging or to analyze the nonlinear features. Therefore, this method is not designed to maximize the harmonics components from propagation in tissue. However, other approaches based on the time reversal principle have been proposed, as for instance the method combining time reversal and harmonic imaging, exploiting the second harmonics at 2f0 is extracted by filtering. A direct time reversal of second harmonics is not the matched filter which optimizes the SNR for harmonic components, since the propagation at 2f0 is linear. To understand it, one way consists in modelling the ultrasound system by simple parallel subsystems such Hammerstein decomposition. Then time reversal can be applied for each subsystems of the model. However, this solution was only applied on simple medium. Moreover, it was only tested by considering a high number of elements of the ultrasound probe. These two conditions are limitations imposed on the application of this optimization.
Scope of the project. The aim of the project is to exploit waveform design and correlation-based imaging in the design of multi-element arrays. The methods will be applied to soft nonlinear medium, as in biomedical field or in agrifood. In order to limit the number of signals to transmit in a second time, a probe will be manufactured with sparse elements. This project has the following specific objectives:
is a collaboration between the lab LAUM (Le Mans, France) and Université de Sherbrooke (Sherbrooke, Canada).
Signal processing and ultrasound imaging.This part will be dedicated to developing new methods of signal processing to enhance the quality of ultrasound image. The method will consider the nonlinear features of the echoes composed of harmonics.
In the first part, the transmitted waveform will be designed from time reversal techniques (pre-processing). Since a direct time-reversal of second harmonics is not the matched filter which optimizes the SNR for harmonic components, the ultrasound system will be modelled by simple parallel subsystems. In this work, a simple Hammerstein model will be used for the modelling of the nonlinear behaviour. Thus, the system will be decomposed by parallel subsystems where the nonlinearity is separated of the linearity. In standard time reversal technique, only the first channel describing linearity is considered. However, finding the optimal wave for harmonic generation means to create a matched filter for the second channel and its solution is not trivial. Indeed, after the transmission of the time reversed second harmonics at 2f0, the new 2f0 retro-propagated component is due to a linear process and so not optimal (since it is different to the time reversal solution). The matched filter for the second harmonics is thus disrupted by the nonlinear effect. The time reversal technique for harmonics will have to consider the frequency doubling and without increasing the transmit power. By assuming that the ultrasound system can be modelled as a Hammerstein decomposition, the matched filter for harmonics will be obtained by reversing time and by annihilating the harmonic effects. A new step will be added based on demodulation. However, it will consider the geometry of the probe to keep the coherence of the phases between echoes.
In the second part, the SNR of harmonic echoes will be enhanced in post-processing. The coherence between the echoes and the transmitted wave can be applied in post-processing using correlation-based imaging. However, as for transmitted waveform design, the correlation has to consider the nonlinear propagation of waves in the considered medium. Both methods in pre-processing and in post-processing will be first validated numerically. Then the method will be applied in a simple experiment with a limited number of transducers. Finally, the method will be implemented in the Verasonics prototyping platform at Université de Sherbrooke. Both methods will be compared and mixed to maximize SNR.
Probe design and fabrication. This part will be dedicated to the design and fabrication of arrays of piezoceramic transducers adapted to the ultrasound imaging approaches developed in the first part.
In the first part, a single-element probe will be fabricated using laser machining for the piezoelectric transducer and use of additive manufacturing (AM) to fabricate the other components. This will build upon the laser micro-machining techniques developed by Masson and Quaegebeur over the past 15 years for electrode patterning and piezoceramic (PZT) cutting. The second strategy will employ AM techniques using lithography-based ceramic manufacturing available at the Interdisciplinary Institute for Technological Innovation (3IT) of Université de Sherbrooke.
In the second part, multiple elements will be integrated to create probes made of sparse arrays, and fabricated with all the components considered (piezoelectric transducer elements, matching and backing layers, lens, and flexible PCB for connections).Wire connections will be optimized to ensure robustness and durability using a custom PCB. A laser micro-vibrometer available at the 3IT will be used to assess the pattern of strain generated at the contact surface of transducers. Imaging algorithm will be implemented using a Verasonics prototyping platform available in Université de Sherbrooke ultrasound laboratory. The probes will be evaluated: 1) on a thick composite structure with hidden damage, for deep imaging in NDE, and 2) on ultrasound biomedical phantoms, mimicking properties of tissues and skull, for deep and fast imaging in medical applications.
Keywords. Ultrasound, transducers, multielement probes, non-linear, sparse arrays, waveform design
Location. Mainly in LAUM on the site of ESEO, Angers. Several long stays in Sherbrooke are to be expected.
Candidate. This thesis work will require good adaptability and communication skills within a multidisciplinary team. The postdoctoral fellow will have to show autonomy and creativity in the design and the experiments to be carried out. This project is intended for a candidate, motivated and curious, with a good knowledge in the fields: ultrasound imaging, signal processing and transducers. The postdoctoral position will start in March 2020.
Funding. Grant financed by Pays de la Loire region by the RFI WISE network for a period of one year.
Sébastien Ménigot (ESEO, LAUM, Angers): email@example.com
Patrice Masson (Université de Sherbrooke): Patrice.Masson@USherbrooke.ca
Nicolas Quaegebeur (Université de Sherbrooke): Nicolas.Quaegebeur@USherbrooke.ca
(c) GdR 720 ISIS - CNRS - 2011-2020.