End-to-end optimization of sparse ultrasound linear probes

Abstract

Ultrasound imaging faces a trade-off between image quality and hardware complexity caused by dense transducers. Sparse arrays are one popular solution to mitigate this challenge. This work proposes an end-to-end optimization framework that jointly learns sparse array configuration and image reconstruction. The framework integrates a differentiable Image Formation Model with a HARD Straight Thought Estimator (STE) selection mask, unrolled Iterative Soft-Thresholding Algorithm (ISTA) deconvolution, and a residual Convolutional Neural Network (CNN). The objective combines physical consistency (Point Spread Function (PSF) and convolutional formation model) with structural fidelity (contrast, Side-Lobe-Ratio (SLR), entropy, and row diversity). Simulations using a 3.5\,MHz probe show that the learned configuration preserves axial and lateral resolution with half of the active elements. This physics-guided, data-driven approach enables compact, cost-efficient ultrasound probe design without sacrificing image quality, and it is expandable to 3-D volumetric imaging.

Figures (3)

• Figure 1: Overview of the proposed end-to-end ultrasound optimization framework. In the forward path, the simulator generates synthetic RF data based on the active elements selected by $\mathbf{P}$, which are then reconstructed by the unrolled ISTA and CNN modules to match a reference image. Gradients from the reconstruction loss propagate backward through the network and simulator to update both the reconstruction parameters and the selection mask, enabling physics-guided sparse-array learning directly from image-level supervision.
• Figure 2: Residual CNN reconstruction head combining a projection branch $b=\Pi(|\hat{\mathbf{x}}|)$ and a residual refinement branch $\mathcal{H}_\theta(\cdot)$. The fused feature $x_5+x_1$ is mapped to a residual image $r$ by the final convolutional block, and the final output is $\widehat{\mathbf{I}} = b + \eta r$.
• Figure 3: (Comparison between the learned sparse configuration and the full-aperture reference. (a) Learned binary mask from the matrix $\mathbf{\hat{P}}$ showing the active transmit/receive elements (left), its corresponding synthesized PSF $\bm\kappa_{\mathbf{c}}$ from the differentiable simulator using the optimized mask (center), and the full-aperture reference PSF $\bm\kappa_{\text{ref}}$ (right). All PSFs are displayed on a 40dB logarithmic dynamic range. (b) Ground-truth image $\mathbf{I_{ref}}$ (left), blurred measurement $\mathbf{Y_c}$ (middle), and reconstructed image $\widehat{\mathbf{I}}$ obtained after unrolled ISTA and CNN refinement (right). The learned configuration achieves comparable axial and lateral resolution while using only half of the active elements. (c) Lateral (top) and axial (bottom) profiles comparing the learned and reference PSFs, showing close main-lobe widths and reduced sidelobe levels for the learned design.