RTG Student Presentations

Presentation #1

Speaker: Guangting Yu, ASU SoMSS

Title: Kronecker Product Decomposition with applications in image deblurring

Abstract: Blurred images are caused by both systematic error such as lens defect and random noise. By some reasonable assumptions, the blurring effect can be modeled as a linear map of the true image, namely Ax = b, where x is the (vectorized) true image and b is the (vectorized) blurred image. Naive methods to invert the system will be both costly (high space & time complexity) and noisy (random noise amplified to dominate signal). Fast algorithms inspired by Kronecker product approximation of A are developed to reduce the complexity, and pseudoinverse by singular value decomposition is also applied to prevent inverting random noises. Numerical experiments are conducted to illustrate the efficiency and effectiveness of the algorithm.

Presentation #2

Speaker:  Ping-Han Huang, ASU SoMSS

Title: Optimal Sampling Designs for Functional Regression

Abstract: Functional data analysis is useful for intrinsically high-dimensional data. In many applications, the number of repeated measures per subject is however limited due to practical constraints such as costs. In light of this limitation, studies have been done in finding an optimal sampling design for sparse observations to precisely recover the trajectory of the underlying predictor function and predict a response with functional regressions. To help expand the dimension of such research from linear to quadratic regression, our study dives into simulations of an increased number of eigenpairs and applies the Probabilistic Subset Search algorithm (Rha et al., 2020) to obtain insights on the difference between dense and sparse data. Our finding suggests that optimal sampling locations tend to become more stable and consistent as the number of eigenpairs used in the PSS algorithm increases. For the dense dataset, the sampling locations are closer to the true design, whereas the sparse dataset could generate designs that are further away from the true design.