Ting‐Li Chen

Shan Huang, Xiaohong Liu, Tao Tan et al.

Magnetic resonance images (MRI) acquired with low through-plane resolution compromise time and cost. The poor resolution in one orientation is insufficient to meet the requirement of high resolution for early diagnosis of brain disease and morphometric study. The common Single image super-resolution (SISR) solutions face two main challenges: (1) local detailed and global anatomical structural information combination; and (2) large-scale restoration when applied for reconstructing thick-slice MRI into high-resolution (HR) iso-tropic data. To address these problems, we propose a novel two-stage network for brain MRI SR named TransMRSR based on the convolutional blocks to extract local information and transformer blocks to capture long-range dependencies. TransMRSR consists of three modules: the shallow local feature extraction, the deep non-local feature capture, and the HR image reconstruction. We perform a generative task to encapsulate diverse priors into a generative network (GAN), which is the decoder sub-module of the deep non-local feature capture part, in the first stage. The pre-trained GAN is used for the second stage of SR task. We further eliminate the potential latent space shift caused by the two-stage training strategy through the self-distilled truncation trick. The extensive experiments show that our method achieves superior performance to other SSIR methods on both public and private datasets. Code is released at https://github.com/goddesshs/TransMRSR.git .

Ting-Li Chen, Dawei D. Chang, Su-Yun Huang et al.

The singular value decomposition (SVD) of large-scale matrices is a key tool in data analytics and scientific computing. The rapid growth in the size of matrices further increases the need for developing efficient large-scale SVD algorithms. Randomized SVD based on one-time sketching has been studied, and its potential has been demonstrated for computing a low-rank SVD. Instead of exploring different single random sketching techniques, we propose a Monte Carlo type integrated SVD algorithm based on multiple random sketches. The proposed integration algorithm takes multiple random sketches and then integrates the results obtained from the multiple sketched subspaces. So that the integrated SVD can achieve higher accuracy and lower stochastic variations. The main component of the integration is an optimization problem with a matrix Stiefel manifold constraint. The optimization problem is solved using Kolmogorov-Nagumo-type averages. Our theoretical analyses show that the singular vectors can be induced by population averaging and ensure the consistencies between the computed and true subspaces and singular vectors. Statistical analysis further proves a strong Law of Large Numbers and gives a rate of convergence by the Central Limit Theorem. Preliminary numerical results suggest that the proposed integrated SVD algorithm is promising.

Ting-Li Chen, Su-Yun Huang, Yanyuan Ma et al.

We consider an enlarged dimension reduction space in functional inverse regression. Our operator and functional analysis based approach facilitates a compact and rigorous formulation of the functional inverse regression problem. It also enables us to expand the possible space where the dimension reduction functions belong. Our formulation provides a unified framework so that the classical notions, such as covariance standardization, Mahalanobis distance, SIR and linear discriminant analysis, can be naturally and smoothly carried out in our enlarged space. This enlarged dimension reduction space also links to the linear discriminant space of Gaussian measures on a separable Hilbert space.

Ting-Li Chen

The mean-shift algorithm is a popular algorithm in computer vision and image processing. It can also be cast as a minimum gamma-divergence estimation. In this paper we focus on the "blurring" mean shift algorithm, which is one version of the mean-shift process that successively blurs the dataset. The analysis of the blurring mean-shift is relatively more complicated compared to the nonblurring version, yet the algorithm convergence and the estimation consistency have not been well studied in the literature. In this paper we prove both the convergence and the consistency of the blurring mean-shift. We also perform simulation studies to compare the efficiency of the blurring and the nonblurring versions of the mean-shift algorithms. Our results show that the blurring mean-shift has more efficiency.