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.

Learning Point Spread Function Invertibility Assessment for Image Deconvolution

Deep-learning (DL)-based image deconvolution (ID) has exhibited remarkable recovery performance, surpassing traditional linear methods. However, unlike traditional ID approaches that rely on analytical properties of the point spread function (PSF) to achieve high recovery performance - such as specific spectrum properties or small conditional numbers in the convolution matrix - DL techniques lack quantifiable metrics for evaluating PSF suitability for DL-assisted recovery. Aiming to enhance deconvolution quality, we propose a metric that employs a non-linear approach to learn the invertibility of an arbitrary PSF using a neural network by mapping it to a unit impulse. A lower discrepancy between the mapped PSF and a unit impulse indicates a higher likelihood of successful inversion by a DL network. Our findings reveal that this metric correlates with high recovery performance in DL and traditional methods, thereby serving as an effective regularizer in deconvolution tasks. This approach reduces the computational complexity over conventional condition number assessments and is a differentiable process. These useful properties allow its application in designing diffractive optical elements through end-to-end (E2E) optimization, achieving invertible PSFs, and outperforming the E2E baseline framework.