9 citations · 17 across the 14 of their papers we have counts for
15 papers
Provable wavelet-based neural approximation
Youngmi Hur, Hyojae Lim, Mikyoung Lim
In this paper, we develop a wavelet-based theoretical framework for analyzing the universal approximation capabilities of neural networks over a wide range of activation functions.…
Simplifying Formal Proof-Generating Models with ChatGPT and Basic Searching Techniques
Sangjun Han, Taeil Hur, Youngmi Hur +3
The challenge of formal proof generation has a rich history, but with modern techniques, we may finally be at the stage of making actual progress in real-life mathematical problems…
Design of Wavelet Filter Banks for Any Dilation Using Extended Laplacian Pyramid Matrices
Youngmi Hur, Sungjoo Kim
In this paper, we present a new method for designing wavelet filter banks for any dilation matrices and in any dimension. Our approach utilizes extended Laplacian pyramid matrices…
New Tight Wavelet Frame Constructions Sharing Responsibility
Youngmi Hur, Hyojae Lim
Tight wavelet frames (TWFs) in \(L^2(\mathbb{R}^n)\) are versatile, and are practically useful due to their perfect reconstruction property. Nevertheless, existing TWF construction…
Wavelet series expansion in Hardy spaces with approximate duals
Youngmi Hur, Hyojae Lim
In this paper, we provide sufficient conditions for the functions and to be the approximate duals in the Hardy space for all . Based on these co…
Laplacian Pyramid-like Autoencoder
Sangjun Han, Taeil Hur, Youngmi Hur
In this paper, we develop the Laplacian pyramid-like autoencoder (LPAE) by adding the Laplacian pyramid (LP) concept widely used to analyze images in Signal Processing. LPAE decomp…
Tight Wavelet Filter Banks with Prescribed Directions
Youngmi Hur
Constructing tight wavelet filter banks with prescribed directions is challenging. This paper presents a systematic method for designing a tight wavelet filter bank, given any pres…
Invertibility of circulant matrices of arbitrary size
Jeong-Ok Choi, Youngmi Hur
In this paper, we present sufficient conditions to guarantee the invertibility of rational circulant matrices with any given size. These sufficient conditions consist of linear com…
Deep Scattering Network with Max-pooling
Taekyung Ki, Youngmi Hur
Scattering network is a convolutional network, consisting of cascading convolutions using pre-defined wavelets followed by the modulus operator. Since its introduction in 2012, the…
Multivariate Tight Wavelet Frames with Few Generators and High Vanishing Moments
Youngmi Hur, Zachary Lubberts, Kasso A. Okoudjou
Tight wavelet frames are computationally and theoretically attractive, but most existing multivariate constructions have various drawbacks, including low vanishing moments for the…
Scaling Laplacian Pyramids
Youngmi Hur, Kasso A. Okoudjou
Laplacian pyramid based Laurent polynomial (LP) matrices are generated by Laurent polynomial column vectors and have long been studied in connection with Laplacian pyramidal al…
Generalizations of the Maillet Determinant
Youngmi Hur, Zachary Lubberts
We consider several extensions of the Maillet determinant studied by Malo, Turnbull, and Carlitz and Olson, and derive properties of the underlying matrices. In particular, we comp…
Prime Coset Sum: A Systematic Method for Designing Multi-D Wavelet Filter Banks with Fast Algorithms
Youngmi Hur, Fang Zheng
As constructing multi-D wavelets remains a challenging problem, we propose a new method called prime coset sum to construct multi-D wavelets. Our method provides a systematic way t…
Committee Algorithm: An Easy Way to Construct Wavelet Filter Banks
Youngmi Hur
Given a lowpass filter, finding a dual lowpass filter is an essential step in constructing non-redundant wavelet filter banks. Obtaining dual lowpass filters is not an easy task. I…
Coset Sum: an alternative to the tensor product in wavelet construction
Youngmi Hur, Fang Zheng
A multivariate biorthogonal wavelet system can be obtained from a pair of multivariate biorthogonal refinement masks in Multiresolution Analysis setup. Some multivariate refinement…