Efficient Convolutional Forward Model for Passive Acoustic Mapping and Temporal Monitoring

TL;DR

This work addresses the need for high-temporal-resolution, low-cost PAM to monitor time-evolving cavitation during therapeutic ultrasound. It presents a time-domain convolutional forward model (TD-CM-PAM) that expresses the forward operator as a linear convolution, enabling efficient computation via FFT, and formulates a regularized spatiotemporal inverse problem solved by ADMM with a joint sparsity and ReD prior. The approach achieves higher temporal fidelity with substantially reduced computation compared to iterative time-domain methods and outperforms frequency-domain beamformers, particularly in short temporal windows. By reconstructing cavitation activity as a 3D datacube and generating 2D spatial maps from temporal priors, the method offers improved localization (CNR) and shape accuracy (Dice) for evolving cavitation clouds. The framework is general and extensible to other passive beamforming and spatiotemporal source localization problems, with potential for real-time monitoring in clinical settings.

Abstract

Passive acoustic mapping (PAM) is a key imaging technique for characterizing cavitation activity in therapeutic ultrasound applications. Recent model-based beamforming algorithms offer high reconstruction quality and strong physical interpretability. However, their computational burden and limited temporal resolution restrict their use in applications with time-evolving cavitation. To address these challenges, we introduce a PAM beamforming framework based on a novel convolutional formulation in the time domain, which enables efficient computation. In this framework, PAM is formulated as an inverse problem in which the forward operator maps spatiotemporal cavitation activity to recorded radio-frequency signals accounting for time-of-flight delays defined by the acquisition geometry. We then formulate a regularized inversion algorithm that incorporates prior knowledge on cavitation activity. Experimental results demonstrate that our framework outperforms classical beamforming methods, providing higher temporal resolution than frequency-domain techniques while substantially reducing computational burden compared with iterative time-domain formulations.

Figures (3)

• Figure 1: Passive acquisition dynamics under the sensor–pitch to pixel–width matching configuration. (a) For a single temporal sample, the contributors set $\Omega_{m,k}$ forms a paraboloid-like delay pattern. Neighboring sensors exhibit identical patterns differing only by a lateral shift. (b) As time progresses, the delay pattern expands outward in the $(x,z)$ plane, so more distant pixels may contribute. Thus, patterns evolve over time, and recorded signals result from the cumulative superposition of contributions across successive temporal slices.
• Figure 2: Simulated scenario with three clouds evolving in time.
• Figure 3: Estimated Maps Qualitative comparison.