Elisha Dayag

Elisha Dayag, Nhat Thanh Tran, Jack Xin

Accurate medical image segmentation is an integral part of the medical image analysis pipeline that requires the ability to merge local and global information. While vision transformers are able to capture global interactions using vanilla self-attention, their quadratic computational complexity in the input size remains a struggle for medical image segmentation tasks. Motivated by the dispersion property of vanilla self-attention and recent development of Mamba form of attention, Scalable and Efficient Mamba like Attention (SEMA) utilizes token localization via local window attention to avoid dispersion and maintain focusing, complemented by theoretically consistent arithmetic averaging to capture global aspect of attention. In this work, we present USEMA, a hybrid UNet architecture that merges the local feature extraction ability of convolutional neural networks (CNNs) with SEMA attention. We conduct experiments with USEMA across a variety of modalities and image sizes, demonstrating improved computational efficiency compared to transformer based models using full self-attention, and superior segmentation performance relative to purely convolution and Mamba-based models.

Elisha Dayag, Nhat Thanh Van Tran, Jack Xin

Transformer-based models are at the forefront in long time-series forecasting (LTSF). While in many cases, these models are able to achieve state of the art results, they suffer from a bias toward low-frequencies in the data and high computational and memory requirements. Recent work has established that learnable frequency filters can be an integral part of a deep forecasting model by enhancing the model's spectral utilization. These works choose to use a multilayer perceptron to process their filtered signals and thus do not solve the issues found with transformer-based models. In this paper, we establish that adding a filter to the beginning of transformer-based models enhances their performance in long time-series forecasting. We add learnable filters, which only add an additional $\approx 1000$ parameters to several transformer-based models and observe in multiple instances 5-10 \% relative improvement in forecasting performance. Additionally, we find that with filters added, we are able to decrease the embedding dimension of our models, resulting in transformer-based architectures that are both smaller and more effective than their non-filtering base models. We also conduct synthetic experiments to analyze how the filters enable Transformer-based models to better utilize the full spectrum for forecasting.

Elisha Dayag, Kevin Bui, Fredrick Park et al.

Based on transformed $\ell_1$ regularization, transformed total variation (TTV) has robust image recovery that is competitive with other nonconvex total variation (TV) regularizers, such as TV$^p$, $0<p<1$. Inspired by its performance, we propose a TTV-regularized Mumford--Shah model with fuzzy membership function for image segmentation. To solve it, we design an alternating direction method of multipliers (ADMM) algorithm that utilizes the transformed $\ell_1$ proximal operator. Numerical experiments demonstrate that using TTV is more effective than classical TV and other nonconvex TV variants in image segmentation.