On the Fundamental Limits of Single-snapshot Compressive Ultrasound Imaging Using Random Aberrative Masks
Compressive sensing emerges as a paradigm shift to realize real-time volumetric ultrasound imaging using a single element transducer equipped with an aberrative mask. Such a coded aperture encodes each scatterer in the FoV as a specific echo signal, compressing each volumetric into a time sequence that are reconstructed into image via computational methods. Compressive imaging (CI) can greatly reduce the data rate and simplify the electronics. Despite this potential, the practical performance of single-snapshot CI remains unclear, especially how it is influenced by mask design, imaging task complexity, and reconstruction strategy. For this, we separate the information budget provided by the mask from the algorithm-dependent extraction of the encoded information. First, the spatial impulse responses of random masks with different pixel sizes and time-delay ranges were calibrated, and the entropy-based effective rank of their similarity matrix was used to quantify the available encoding capacity. Masks with pixel size of approx. half wavelength and a time-delay range of two carrier periods provided higher encoding capacities, reaching up to 1.1% of the total sampled voxels. Algorithm-dependent information extraction was further evaluated for both ULM-motivated particle localization and B-mode imaging. For particle localization, L1-norm regularized least-squares method reconstructed particles corresponding to approx. 10% of the available encoding capacity, outperforming the matched filter. A transition from successful to failed reconstruction was observed when the number of particles exceeded this value, revealing the upper limit of the present CI systems using random masks. For B-mode imaging, LSQR achieved the highest SSIM among the evaluated methods, of up to 0.12, although the encoding capacity of the current random masks remained insufficient for high-fidelity reconstruction.