Pisarenko Class Beamformer Applied to Passive Acoustic Mapping of Ultrasound Cavitation

Cavitation induced by High Intensity Focused Ultrasound (HIFU) used in therapeutic ultrasound can be imaged passively using linear arrays and beamforming algorithms. A challenging purpose is to image both in spatial and temporal domain cavitation sources that are strongly involved in the tissue-ultrasound interaction, with a long-term objective of high image quality as well as real-time application. Recently, a formalism in the Fourier Domain using the Cross-Spectral Matrix (CSM), i.e. the spatial covariance matrix of the Fourier transform of received data, has been proposed to transpose adaptive algorithms currently used in array processing to this context. The strength of this formalism lies in combining the advantage of adaptive approaches in terms of image quality and enhancement of source localization, with a significant decrease of the numerical cost thanks to the use of Fourier Domain approaches. The present study focuses on an adaptive beamformer making use of the Pisarenko class methods, based on the p-th root compression of the CSM matrix. This method is compared to current state of the art in the context of passive cavitation imaging: The non-adaptive Frequency Domain Passive Cavitation Imaging (FD-PCI) and the adaptive Time Domain Robust Capon Beamformer (TD-RCB). The influence of the parameter p has been investigated on the resolution and the contrast of cavitation maps, and the parameter- free midway approach proposed by Stoica et al. is also considered. The performances of the method are illustrated using the simple case of single point-source simulations. The results show that it approaches the image quality of TD-RCB method, but with a computation time equivalent to FD-PCI. The Pisarenko class beamformer proves to be a promising tool combining good image quality characteristic of the adaptive approach with a significant reduction of the numerical computation time associated to the Fourier Domain implementation.