Uncertainty Estimation for Trust Attribution to Speed-of-Sound Reconstruction with Variational Networks

TL;DR

Uncertainty Estimation for Trust Attribution to Speed-of-Sound Reconstruction with Variational Networks addresses noisy ultra-sound frame data by integrating uncertainty estimates into a VN-based SoS reconstruction framework. It develops Monte Carlo Dropout and Bayesian Variational Inference to quantify frame-wise uncertainty and introduces a relative uncertainty metric to automatically select the most trustworthy acquisition among multiple frames for breast cancer differential diagnosis. The approach preserves reconstruction accuracy while providing interpretable trust signals that can guide clinical decisions, demonstrated on simulated data and in vivo BI-RADS 4 lesions distinguishing carcinoma from fibroadenoma. A tractable algebraic reformulation for the KL term in BVI enhances computational feasibility on standard hardware, supporting potential real-time clinical deployment.

Abstract

Speed-of-sound (SoS) is a biomechanical characteristic of tissue, and its imaging can provide a promising biomarker for diagnosis. Reconstructing SoS images from ultrasound acquisitions can be cast as a limited-angle computed-tomography problem, with Variational Networks being a promising model-based deep learning solution. Some acquired data frames may, however, get corrupted by noise due to, e.g., motion, lack of contact, and acoustic shadows, which in turn negatively affects the resulting SoS reconstructions. We propose to use the uncertainty in SoS reconstructions to attribute trust to each individual acquired frame. Given multiple acquisitions, we then use an uncertainty based automatic selection among these retrospectively, to improve diagnostic decisions. We investigate uncertainty estimation based on Monte Carlo Dropout and Bayesian Variational Inference. We assess our automatic frame selection method for differential diagnosis of breast cancer, distinguishing between benign fibroadenoma and malignant carcinoma. We evaluate 21 lesions classified as BI-RADS~4, which represents suspicious cases for probable malignancy. The most trustworthy frame among four acquisitions of each lesion was identified using uncertainty based criteria. Selecting a frame informed by uncertainty achieved an area under curve of 76% and 80% for Monte Carlo Dropout and Bayesian Variational Inference, respectively, superior to any uncertainty-uninformed baselines with the best one achieving 64%. A novel use of uncertainty estimation is proposed for selecting one of multiple data acquisitions for further processing and decision making.

Figures (6)

• Figure 1: a) SoS reconstruction pipeline on a clinical example: Echo data from different transmit events are beamformed, between pairs of which the displacements are estimated. Using multiple displacement maps, a SoS map is reconstructed by solving an inverse problem with VN. b) The VN posterior is learned using Bayesian variational inference or Monte Carlo Dropout. At inference, samples are drawn from each posterior, with their mean being the reconstructed SoS image and the standard deviation the uncertainty estimate. c) Data from the same lesion is collected multiple times. Reconstruction uncertainty is used to select an optimal acquisition, later used for breast cancer differential diagnosis.
• Figure 2: Reconstruction errors in a) the k-Wave test data, and b) the RB test data. (Left) RMSEs of the different reconstruction methods, and (right) image-wise differential RMSEs with respect to VN.
• Figure 3: Examples reconstructions of four simulated ray-based numerical phantoms using each method (a-d), compared to the corresponding ground truth SoS maps (e).
• Figure 4: The $\Delta c$ distributions and ROC curves for CA vs. FA classification, for the uncertainty estimation approaches selecting the frames using (a) SI$^\text{rel}_\text{MCD}$ for MCD-reconstructed frames and (b) SI$^\text{rel}_\text{BVI}$ for BVI-reconstructed frames. The ROC curves display the classification criterion, sensitivity, and specificity at the point that maximizes the cumulative sensitivity and specificity.
• Figure 5: The displacement generation pipeline for the three datasets in this project. The first two simulation pipelines are for ray-based and k-wave data, where the ground truth is the starting point. The last row is for the in vivo data, where the RF recordings are the starting point as the ground truth is unknown.