The increase of available large clinical and experimental datasets has contributed to a substantial amount of important contributions in the area of biomedical image analysis. Image segmentation, which is crucial for any quantitative analysis, has especially attracted attention. Recent hardware advancement has led to the success of deep learning approaches. However, although deep learning models are being trained on large datasets, existing methods do not use the information from different learning epochs effectively. In this work, we leverage the information of each training epoch to prune the prediction maps of the subsequent epochs. We propose a novel architecture called feedback attention network (FANet) that unifies the previous epoch mask with the feature map of the current training epoch. The previous epoch mask is then used to provide hard attention to the learned feature maps at different convolutional layers. The network also allows rectifying the predictions in an iterative fashion during the test time. We show that our proposed feedback attention model provides a substantial improvement on most segmentation metrics tested on seven publicly available biomedical imaging datasets demonstrating the effectiveness of FANet. The source code is available at https://github.com/nikhilroxtomar/FANet.

Analyzing multi-way measurements with variations across one mode of the dataset is a challenge in various fields including data mining, neuroscience and chemometrics. For example, measurements may evolve over time or have unaligned time profiles. The PARAFAC2 model has been successfully used to analyze such data by allowing the underlying factor matrices in one mode (i.e., the evolving mode) to change across slices. The traditional approach to fit a PARAFAC2 model is to use an alternating least squares-based algorithm, which handles the constant cross-product constraint of the PARAFAC2 model by implicitly estimating the evolving factor matrices. This approach makes imposing regularization on these factor matrices challenging. There is currently no algorithm to flexibly impose such regularization with general penalty functions and hard constraints. In order to address this challenge and to avoid the implicit estimation, in this paper, we propose an algorithm for fitting PARAFAC2 based on alternating optimization with the alternating direction method of multipliers (AO-ADMM). With numerical experiments on simulated data, we show that the proposed PARAFAC2 AO-ADMM approach allows for flexible constraints, recovers the underlying patterns accurately, and is computationally efficient compared to the state-of-the-art. We also apply our model to a real-world chromatography dataset, and show that constraining the evolving mode improves the interpretability of the extracted patterns.