Optimization of array encoding for ultrasound imaging

TL;DR

The paper addresses the challenge of improving ultrasound image quality in synthetic aperture imaging by learning transmit encoding sequences that are parameterized by time delays $t_{MT}$ and apodization weights $w_{MT}$ within the REFoCUS framework. It introduces a differentiable end-to-end pipeline where a frequency-domain encoding matrix $\mathbf{H}(\omega)$ links the ground-truth multistatic data $\mathbf{U}(\omega)$ to the transmitted responses $\mathbf{S}(\omega)$, and a Tikhonov decoder reconstructs $\widehat{\boldsymbol{\mathcal{U}}}$ prior to delay-and-sum beamforming to form image $|\mathcal{B}(\boldsymbol{\mathcal{H}}_{\boldsymbol{\sigma}}^\dagger \boldsymbol{\mathcal{S}})|_{\text{Im}}$. By backpropagating through a differentiable DAS beamformer, the model learns encodings that minimize an image-based loss $\mathcal{L}$, demonstrated on Field II simulations and validated experimentally with a tissue-mimicking phantom and a wire target. Results show significant improvements in image quality metrics (e.g., $\mathcal{L}$ against ground-truth contrast, gCNR, and cystic resolution) over conventional planewave and Hadamard encodings, with robustness to noise when trained accordingly. The work reveals that common encoding schemes occupy only a subset of possible sequences and that jointly optimized delays and apodizations can generalize across imaging targets, offering a path toward higher SNR and more uniform PSFs in clinical ultrasound.

Abstract

Objective: The transmit encoding model for synthetic aperture imaging is a robust and flexible framework for understanding the effects of acoustic transmission on ultrasound image reconstruction. Our objective is to use machine learning (ML) to construct scanning sequences, parameterized by time delays and apodization weights, that produce high-quality B-mode images. Approach: We use a custom ML model in PyTorch with simulated RF data from Field II to probe the space of possible encoding sequences for those that minimize a loss function that describes image quality. This approach is made computationally feasible by a novel formulation of the derivative for delay-and-sum beamforming. Main Results: When trained for a specified experimental setting (imaging domain, hardware restrictions, etc.), our ML model produces optimized encoding sequences that, when deployed in the REFoCUS imaging framework, improve a number of standard quality metrics over conventional sequences including resolution, field of view, and contrast. We demonstrate these results experimentally on both wire targets and a tissue-mimicking phantom. Significance: This work demonstrates that the set of commonly used encoding schemes represent only a narrow subset of those available. Additionally, it demonstrates the value for ML tasks in synthetic transmit aperture imaging to consider the beamformer within the model, instead of purely as a post-processing step.

Figures (12)

• Figure 1: The training procedure for the proposed ML model for data acquisition and imaging, which is fully parameterized by an encoding sequence. Simulated multistatic training data is encoded and decoded according to our model parameters, and an image is formed using delay-and-sum beamforming. The resulting B-mode image is evaluated by comparison to a target image, or with some other data obtained during the simulation, i.e., target position.
• Figure 2: The types of simulated data and imaging target type on which the ML model is trained and/or evaluated. (a) Conventional imaging targets generated from the uniform responses of individual scatterers in an anechoic field. (b) Imaging targets for image-derived data, where the amplitude of each scatterer is weighted according to a grayscale image. While all categories are used for validation of the ML model, numerical experiments suggest that training on the class of data emphasized in red (ground-truth contrast, underdeveloped speckle) produces the best optimized encoding sequences.
• Figure 3: Three choices for 15-transmit encodings applied to different imaging targets. We compare to imaging using planewaves with 1 degree of separation (left), planewaves with 10 degrees of separation (middle), and our novel optimized sequence (right). In all types of simulated data, we see considerable improvements in contrast and resolution over the conventional transmit encodings.
• Figure 4: (a) The contrast of an anechoic cyst as a function of cyst size, with a vertical line indicating the value of the cystic resolution. (b) The centered point targets for which the cystic resolution is measured. From this, we can see that the optimized encoding results in cystic resolution comparable to that of narrow span planewaves.
• Figure 5: (top) We plot the average gCNR for anechoic lesions in each region of the viewing range, averaged over randomly located targets over 50 instances of simulated data. Values are displayed for one instance of randomly located targets. (bottom) We plot the cystic resolution throughout the domain. Observe that only our optimized encoding sequence is able to maintain the same quality measured by gCNR and cystic resolution throughout the imaging domain.