High resolution Ultrasound Transmission Tomography
Final Report Abstract
Ultrasound computer tomography (USCT) is a novel imaging method with high potential for improving breast cancer diagnosis. First clinical studies with USCT already show the importance of transmission tomography to achieve a high sensitivity and specificity: sound speed and attenuation imaged in transmission tomography are expected to provide a quantitative tissue characterization. In this project, we proposed to increase the resolution of full 3D transmission images by an order of magnitude while being able to compute images on nowadays computers. For this purpose, we developed a more accurate forward modeling with the paraxial approximation of the wave equation. We tackled the inverse problem with sophisticated numerical optimization methods, preconditioning methods, and multi-grid approaches in order to guarantee a fast and reliable convergence. We developed and verified the fundamental methods for wave propagation in 3D with the paraxial approximation of the Helmholtz equation for arbitrary objects at a realistic size of the KIT 3D aperture. The forward model was implemented in MATLAB and ported to CUDA C for GPU processing reaching a speedup factor of approx. 20. In collaboration with the TU Delft, we developed a “Redatuming” technique based on Hankel function decomposition of the measured field in order to back project the measured pressure field from the sensors to the region of interest, which is reconstructed. For the inversion process, we analyzed several approaches to reduce the computational burden: Cholesky preconditioning was able to reduce the number of iterations by approx. 70 to 85%. The matrix-free quasi-Newton preconditioning method saves approx. 30% of the computation time on average. Furthermore, we developed a multigrid-scheme for stepping from low to high frequencies while adapting the discretization of the imaged region of interest. We showed that the conjugate gradient applied to normal equation (CGNE) method gives more reliable solutions for linearized systems than Tikhonov regularization methods. We showed that the L-BFGS algorithm could be used as a preconditioning technique for Gauss-Newton CG and nonlinear CG, and was able to give significant acceleration especially to nonlinear CG with up to 22.7-fold speedup in iteration and 21.4-fold speedup in computational time. The methods were evaluated with several software phantoms using simulated data. The reconstructed values of speed of sound and attenuation match the ground-truth values with a very high precision: a mean square error (MSE) of 3.4e-11 at the final iteration was achieved. We analyzed the convergence and robustness as a function of the starting frequency of the reconstruction. We were able to achieve convergence at a starting frequency of 1MHz, which matches the lowest frequencies of the measured data of the KIT 3D USCT system. In conclusion, we developed and analyzed a wave-based transmission image reconstruction for 3D-USCT at high frequencies and large field of views - an application that was not possible with existing methods until now. In contrast to full-wave solutions the paraxial approximation was applied, which suits the forward problem in particular since it considers wave propagation in a preferred direction. We showed that the resolution of the transmission images can be significantly improved over ray-based algorithms. In contrast to full-wave solutions, the computing time could be considerably reduced. Yet we showed that even the fastest methods still needed dozens or hundreds of forward model computations to finish. In future, we want to investigate deep learning based approaches as learned iterative reconstruction schemes have the potential to reduce the number of necessary forward model computations significantly via unrolling the iteration using deep neural networks and meanwhile without compromising the reconstruction quality or even with improved reconstruction quality.
Publications
- “Wave equation based transmission tomography,” In Proc. IEEE Int. Ultrason. Symp. (IUS), pp. 1-4, Sep. 2016
H. Gemmeke, L. Althaus, K. W. A. van Dongen, H. Egger, J. Hesser, J. Mayer, N.V. Ruiter, M. Zapf, T. Hopp
(See online at https://doi.org/10.1109/ULTSYM.2016.7728829) - “Proceedings of the International Workshop on Medical Ultrasound Tomography: 1. - 3. Nov. 2017, Speyer, Germany”,KIT Scientific Publishing, Karlsruhe, ISBN: 978-3-7315-0689-8, 2018
T. Hopp, N.V. Ruiter, J.C. Bamber, N. Duric, K.W.A. van Dongen (eds.)
(See online at https://doi.org/10.5445/KSP/1000071328) - “USCT Image Reconstruction: Acceleration using Gauss-Newton Preconditioned Conjugate Gradient”, Proceedings International Workshop on Medical Ultrasound Tomography, pp. 41-52, 2017
H. Wang, H. Gemmeke, T. Hopp, J. Hesser
(See online at https://doi.org/10.5445/IR/1000079815) - “Experimental evaluation of straight ray and bent ray phase aberration correction for USCT SAFT imaging”, Medical Imaging 2018: Ultrasonic Imaging and Tomography, volume 10580, pp. 105800M, 2018
T. Hopp, M. Zapf, H. Gemmeke, N.V. Ruiter
(See online at https://doi.org/10.1117/12.2292895) - “Multigrid Method for Solving Linearized Systems in Ultrasound Transmission Tomography”, 2018 IEEE Nuclear Science Symposium and Medical Imaging Conference Proceedings (NSS/MIC), pp. 1-3, 2018
H. Wang, H. Gemmeke, T. Hopp, J. Hesser:
(See online at https://doi.org/10.1109/NSSMIC.2018.8824337) - “Ultrasound Image Reconstruction Using Nesterov's Accelerated Gradient”, 2018 IEEE Nuclear Science Symposium and Medical Imaging Conference Proceedings (NSS/MIC), pp. 1-3, 2018
H. Wang, B. Dalkilic, H. Gemmeke, T. Hopp, J. Hesser:
(See online at https://doi.org/10.1109/NSSMIC.2018.8824531) - “Accelerating image reconstruction in ultrasound transmission tomography using L-BFGS algorithm”, Medical Imaging 2019: Ultrasonic Imaging and Tomography, Volume 10955, pp. 109550B, 2019
H. Wang, H. Gemmeke, T. Hopp, J. Hesser
(See online at https://doi.org/10.1117/12.2512654) - “Experimental analysis of ray-based sound speed reconstruction algorithms for phase aberration corrected USCT SAFT imaging”, Medical Imaging 2019: Ultrasonic Imaging and Tomography, volume 10955, pp 109550J, 2019
T. Hopp, F. Zuch, M. Zapf, H. Gemmeke, N.V. Ruiter
(See online at https://doi.org/10.1117/12.2512955) - “GPU Acceleration of Wave Based Transmission Tomography”, 2019 IEEE 16th International Symposium on Biomedical Imaging (ISBI 2019), pp. 1753-1756, 2019
H. Wang, T. Hoa Huynh, H. Gemmeke, T. Hopp, J. Hesser
(See online at https://doi.org/10.1109/ISBI.2019.8759453) - “Redatuming of 2-D Wavefields Measured on an Arbitrary Shaped Closed Aperture”, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 2019
U. Taskin, J. van der Neut, H.Gemmeke, K.W.A. van Dongen
(See online at https://doi.org/10.1109/TUFFC.2019.2942453) - (2021): Analysis of linearized inverse problems in ultrasound transmission imaging. In: Proceedings of the International Workshop on Medical Ultrasound Tomography: 14.-15. Oct. 2019, Wayne State University, Detroit, Michigan, USA, 2021. S. 155-163
H. Wang, H. Gemmeke, K. W. A. van Dongen, T. Hopp, J. Hesser
(See online at https://doi.org/10.5445/IR/1000135826)
