Joint localization and classification of breast masses on ultrasound images using an auxiliary attention-based framework

. Author manuscript; available in PMC: 2023 Dec 1.

Published in final edited form as: Med Image Anal. 2023 Sep 14;90:102960. doi: 10.1016/j.media.2023.102960

Algorithm 1: Minibatch training of the proposed framework

\begin{matrix} Input : Training dataset X with a total of N images, of which N_{f} images have both class and location labels and N_{s} images only have \\ class labels (N = N_{f} + N_{s}) . A data subset with N_{f} fully-labeled samples is denoted as X_{f}, and the other data subset with N_{s} \\ partly-labeled samples is denoted as X_{s}; \\ Networks with parameters : FEX with Θ_{F}; AC with Θ_{C}; LA-Net with Θ_{D}; \\ Training hyper - parameters : Minibatch size (m); the number of stage 1 training epochs (t_{1}); the number of stage 2 training epochs (t_{2}); \\ Stage 1: Pre-train the LA-Net with fully-labeled subset X_{f} \\ Start training \\ Initialize training iteration: i = 1 \\ while i \leq t_{1} do \\ ⌊ \begin{matrix} Initialize the count of trained images in the current epoch: n; Set n = 0 \\ while n \leq N_{f} do \\ ⌊ \begin{matrix} 1 . Sample a batch of m images {X_{l}^{(1)}, \dots, X_{l}^{(m)}} from input data and their corresponding lesion location labels \\ {{\bar{Y}}_{p i x e l}^{(1)}, \dots, {\bar{Y}}_{p i x e l}^{(m)}} \\ 2 . Forward the batched data through the FEX and LA-Net and output mask prediction {P_{p i x e l}^{(1)}, \dots, P_{p i x e l}^{(m)}} \\ 3 . Calculate the loss L_{f l o c} using Eq . (6) \\ 4 . Update the parametes of FEX and LA-Net by ascending their stochastic gradients: \nabla_{(Θ_{F}, Θ_{D})} L_{f l o c} \\ 5 . Increment the count: n = n + m \end{matrix} \\ Increment iteration i = i + 1 \end{matrix} \\ End training \\ Output : Trained LA-Net with parameters {\bar{Θ}}_{D} \\ Stage 2: Train all three networks with the entire dataset X \\ Start training \\ Load the LA-Net parameters {\bar{Θ}}_{D} trained in Stage 1 \\ Initialize training iterator: i = 1 \\ while i \leq t_{2} do \\ ⌊ \begin{matrix} Initialize the count of trained images in the current epoch: n; Set n = 0 \\ while n \leq N do \\ ⌊ \begin{matrix} 1 . Sample a batch of m images {X^{(1)}, \dots, X^{(m)}} from input data . Among these, m_{f} images are from the subset X_{f}, and the \\ remaining m_{s} images are from the subset X_{s} . Thus, m_{f} images have GT class labels {{\bar{Y}}_{c l s}^{(1)}, \dots, {\bar{Y}}_{c l s}^{(m_{f})}} and GT location \\ labels {{\bar{Y}}_{p i x e l}^{(1)}, \dots, {\bar{Y}}_{p i x e l}^{(m_{f})}}, while the m_{s} images only have GT class labels {{\bar{Y}}_{c l s}^{(m_{f} + 1)}, \dots, {\bar{Y}}_{c l s}^{(m_{f} + m_{s})}} \\ 2 . Forward the batched data through the FEX, AC, and LA-Net . Predict lesion-types {P_{c l s}^{(1)}, \dots, P_{c l s}^{(m)}} on all m images . \\ Predict lesion locations {P_{p i x e l}^{(1)}, \dots, P_{p i x e l}^{(m_{f})}} for fully-labeled m_{f} images, which have annotated GT locations . Predict \\ lesion locations {P_{p i x e l}^{'^{(m_{f} + 1)}}, \dots, P_{p i x e l}^{'^{(m_{f} + m_{s})}}} for partly-labeled m_{s} images, which have unknown GT locations . Generate \\ pseudo location labels {{\bar{Y}}_{p i x e l}^{'^{(m_{f} + 1)}}, \dots, {\bar{Y}}_{p i x e l}^{'^{(m_{f} + m_{s})}}} using the binarize function applied to {P_{p i x e l}^{'^{(m_{f} + 1)}}, \dots, P_{p i x e l}^{'^{(m_{f} + m_{s})}}} described \\ in Eq. (7) \\ 3 . Calculate the hybrid loss L_{h y b} using Eq. (7) \\ 4 . Update the parameters of FEX, AC, and LA-Net by ascending their stochastic gradients: \nabla_{(Θ_{F}, Θ_{C}, Θ_{D})} L_{h y b} \\ 5 . Increment the count: n = n + m \end{matrix} \\ Increment iteration i = i + 1 \end{matrix} \\ End training \\ Output : Trained model weights of the FEX, AC, and LA-Net \end{matrix}