Cosine Series Representation

TL;DR

This paper introduces a functional data analysis framework using explicit orthonormal basis expansion for modeling and denoising biomedical signals, enabling flexible smoothing, regularization, and hypothesis testing.

Contribution

It presents a novel FDA approach based on basis expansion that improves interpretability and scalability in biomedical signal analysis.

Findings

Effective denoising of EEG signals demonstrated.

Application to diffusion tensor imaging shows improved modeling.

Framework allows transparent statistical inference on basis coefficients.

Abstract

We present a functional data analysis (FDA) framework based on explicit orthonormal basis expansion for modeling and denoising complex biomedical signals. Observed functional data are represented as smooth functions in a Hilbert space, and statistical inference is performed directly on their basis coefficients. This formulation provides a transparent and flexible approach to smoothing, regularization, and hypothesis testing. Applications to diffusion tensor imaging tract modeling and EEG denoising demonstrate the advantages of explicit basis representations for scalable and interpretable functional modeling.