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We show that an optimal finite element mesh refinement algorithm for a prototypical elliptic PDE can be learned by a recurrent neural network with a fixed number of trainable parameters independent of the desired accuracy and the input…

Many unsupervised domain adaptation (UDA) methods have been proposed to bridge the domain gap by utilizing domain invariant information. Most approaches have chosen depth as such information and achieved remarkable success. Despite their…

Deep unfolding methods---for example, the learned iterative shrinkage thresholding algorithm (LISTA)---design deep neural networks as learned variations of optimization methods. These networks have been shown to achieve faster convergence…

Deep learning is a very promising technique for low-dose computed tomography (LDCT) image denoising. However, traditional deep learning methods require paired noisy and clean datasets, which are often difficult to obtain. This paper…

A major challenge in X-ray computed tomography (CT) is reducing radiation dose while maintaining high quality of reconstructed images. To reduce the radiation dose, one can reduce the number of projection views (sparse-view CT); however, it…

This work studies the theoretical rules of feature selection in linear discriminant analysis (LDA), and a new feature selection method is proposed for sparse linear discriminant analysis. An $l_1$ minimization method is used to select the…

Alternating gradient-descent-ascent (AltGDA) is an optimization algorithm that has been widely used for model training in various machine learning applications, which aims to solve a nonconvex minimax optimization problem. However, the…

In clinical examinations and diagnoses, low-dose computed tomography (LDCT) is crucial for minimizing health risks compared with normal-dose computed tomography (NDCT). However, reducing the radiation dose compromises the signal-to-noise…

Compressed Sensing using $\ell_1$ regularization is among the most powerful and popular sparsification technique in many applications, but why has it not been used to obtain sparse deep learning model such as convolutional neural network…

This paper presents a hybrid morphological neural network for regression tasks called linear dilation-erosion regressor ($\ell$-DER). An $\ell$-DER is given by a convex combination of the composition of linear and morphological operators.…

Single-Photon Emission Computed Tomography (SPECT) is widely applied for the diagnosis of coronary artery diseases. Low-dose (LD) SPECT aims to minimize radiation exposure but leads to increased image noise. Limited-view (LV) SPECT, such as…

Training deep neural networks (DNNs) efficiently is a challenge due to the associated highly nonconvex optimization. The backpropagation (backprop) algorithm has long been the most widely used algorithm for gradient computation of…

Recently, the study on learned iterative shrinkage thresholding algorithm (LISTA) has attracted increasing attentions. A large number of experiments as well as some theories have proved the high efficiency of LISTA for solving sparse coding…

Building extraction $-$ needed for inventory management and planning of urban environment $-$ is affected by the misalignment between labels and off-nadir source imagery in training data. Teacher-Student learning of noise-tolerant…

Supervised topic models simultaneously model the latent topic structure of large collections of documents and a response variable associated with each document. Existing inference methods are based on variational approximation or Monte…

Deep neural networks have a great potential to improve image denoising in low-dose computed tomography (LDCT). Popular ways to increase the network capacity include adding more layers or repeating a modularized clone model in a sequence. In…

Linear discriminant analysis (LDA) is a fundamental classification and dimension reduction method that achieves Bayes optimality under Gaussian mixture, but often struggles in high-dimensional settings where the covariance matrix cannot be…

Histologic examination plays a crucial role in oncology research and diagnostics. The adoption of digital scanning of whole slide images (WSI) has created an opportunity to leverage deep learning-based image classification methods to…

Deep-learning methods have shown promising performance for low-dose computed tomography (LDCT) reconstruction. However, supervised methods face the problem of lacking labeled data in clinical scenarios, and the CNN-based unsupervised…

Linear discriminant analysis (LDA) is a popular technique to learn the most discriminative features for multi-class classification. A vast majority of existing LDA algorithms are prone to be dominated by the class with very large deviation…