End-to-end optimization of sparse ultrasound linear probes

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.