Related papers: Gabor frames and higher dimensional boundaries in …
Gabor frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. Finding general and verifiable conditions which imply…
While the last five years have seen considerable progress in understanding the internal representations of deep learning models, many questions remain. This is especially true when trying to understand the impact of model design choices,…
Graph Neural Networks (GNNs) have gained popularity in various learning tasks, with successful applications in fields like molecular biology, transportation systems, and electrical grids. These fields naturally use graph data, benefiting…
Time-frequency analysis, such as the Gabor transform, plays an important role in many signal processing applications. The redundancy of such representations is often directly related to the computational load of any algorithm operating in…
The construction of finite tight Gabor frames plays an important role in many applications. These applications include significant ones in signal and image processing. We explore when constant amplitude zero autocorrelation (CAZAC)…
We investigate the problem of constructing sparse time-frequency representations with flexible frequency resolution, studying the theory of nonstationary Gabor frames in the framework of decomposition spaces. Given a painless nonstationary…
In this paper, a color edge detection method is proposed where the multi-scale Gabor filter are used to obtain edges from input color images. The main advantage of the proposed method is that high edge detection accuracy is attained while…
Representing data residing on a graph as a linear combination of building block signals can enable efficient and insightful visual or statistical analysis of the data, and such representations prove useful as regularizers in signal…
Mapping complex input data into suitable lower dimensional manifolds is a common procedure in machine learning. This step is beneficial mainly for two reasons: (1) it reduces the data dimensionality and (2) it provides a new data…
Understanding low-dimensional structures within high-dimensional data is crucial for visualization, interpretation, and denoising in complex datasets. Despite the advancements in manifold learning techniques, key challenges-such as limited…
Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…
This manuscript focuses on the construction of compactly supported dual Gabor frames in $L^2(\mathbb{R})$. The performance of the constructed dual frames is analysed for Gabor systems generated by B-splines and exponential B-splines of…
Manifold learning techniques have become increasingly valuable as data continues to grow in size. By discovering a lower-dimensional representation (embedding) of the structure of a dataset, manifold learning algorithms can substantially…
Graph signal processing (GSP) is a framework to analyze and process graph-structured data. Many research works focus on developing tools such as Graph Fourier transforms (GFT), filters, and neural network models to handle graph signals.…
This work developes a quantitative framework for describing the overcompleteness of a large class of frames. A previous paper introduced notions of localization and approximation between two frames $\mathcal{F} = \{f_i\}_{i \in I}$ and…
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…
Efficient and accurate detection of subtle motion generated from small objects in noisy environments, as needed for vital sign monitoring, is challenging, but can be substantially improved with magnification. We developed a complex Gabor…
The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
Modern machine learning algorithms have been adopted in a range of signal-processing applications spanning computer vision, natural language processing, and artificial intelligence. Many relevant problems involve subspace-structured…