Applied Wavelet Analysis: Denoising, Trend Extraction, and Compression

This volume continues the progression established in Volume I by focusing on the applied use of wavelet transforms for practical signal and image processing tasks. While the mathematical foundations and core discrete wavelet framework have already been introduced, the emphasis here is on how wavelets are used in practice—to suppress noise, compress data, extract trends, and evaluate performance within real analytical workflows. Wavelet-based denoising and compression are among the most widely deployed applications of multiscale analysis. They appear in domains ranging from speech and audio processing to sensing, imaging, and time-series analysis. The Volume II-A, Applied Wavelet Analysis: Denoising, Trend Extraction, and Compression presents these techniques systematically, with attention to **method selection, parameter tuning, and quantitative evaluation**, rather than purely theoretical derivation. Throughout the book, one-dimensional signals (including time series, sensor measurements, and speech) and two-dimensional data (such as images and spatial fields) are treated within a unified multiresolution framework. Comparisons with classical and industry-standard approaches are included where appropriate, highlighting both the strengths and limitations of wavelet-based methods. Rather than presenting wavelets as abstract mathematical constructs, this volume emphasizes their role as tools within reproducible analytical pipelines. All examples are implemented in Python and are designed to support experimentation, validation, and adaptation to real-world applications.