Exploring multiscale methods: reviews and insights

This paper aims to provide a comprehensive review of multiscale methods and techniques, which represent data (or signals) at different scales (or resolutions) to extract richer information from them. Over the past few decades, multiscale methods have been widely applied in various fields, such as statistics and signal processing. In this paper, we provide an overview of conventional multiscale methods, including the Fourier transform, the short-time Fourier transform, and the wavelet transform. In addition, we focus on more recently developed data-adaptive multiscale methods, such as the empirical mode decomposition, the SiZer, the thick-pen transform, and the elastic-band transform. To better understand multiscale methods, we demonstrate various applications using several simulated and real-world datasets. We are confident that this review offers a comprehensive understanding of multiscale methods and identifies potential areas for further research.