Ultrasound Plane Wave Imaging as an Inverse Problem With Joint Sparse-Based Regularized Solution

To overcome the limitation of traditional sparse regularization methods in ultrasound imaging, which struggle to preserve speckle textures, and to enhance the resolution, contrast, and texture fidelity of plane wave imaging.

A joint sparse regularization model is proposed, combining the ℓ₁ (spatial sparsity) and ℓ_2,1 (joint sparsity in the frequency domain) regularization terms. The inverse problem is solved using the Alternating Direction Method of Multipliers (ADMM) optimization algorithm. Based on the PICMUS dataset (including simulated, experimental, and in vivo data), the proposed method is compared with traditional Delay-and-Sum (DAS), single sparse regularization (ℓ₁), and multi-plane wave compounding (75_PW) methods. The axial and lateral resolutions (Full Width at Half Maximum, FWHM), Contrast-to-Noise Ratio (CNR), generalized CNR (gCNR), and Kolmogorov-Smirnov (KS) test results are evaluated.

The joint sparse method achieved an axial FWHM of 0.28 mm and a lateral FWHM of 0.30 mm in simulated resolution (SR), and 0.30 and 0.47 mm in experimental resolution (ER), respectively. These results are superior to those of DAS (ER lateral FWHM of 0.97 mm) and ℓ₁ method (ER lateral FWHM of 1.16 mm). The simulated contrast (SC) CNR reached 12.34, and the experimental contrast (EC) CNR was 9.15, both passing the KS test (preserving speckle distribution). The computational efficiency was significantly improved, with a single-frame reconstruction time of only 5.3 s, much faster than the ℓ₁ method (363.2 s) and 75_PW (45.6 s), but slightly slower than the single-angle DAS method (1.9 s).

The joint sparse regularization model, by exploiting the correlation of image frequency-domain structures, effectively improves resolution (reducing FWHM by 26-61%) and contrast while preserving speckle textures. It provides an efficient and robust solution for ultrasound inverse problem reconstruction.