Cubic B-Spline Wavelet Decomposition and Reconstruction Algorithm with Implementation

We have successfully developed and comprehensively tested the cubic B-spline wavelet decomposition and reconstruction algorithm program, ensuring its stability and reliability. The implementation utilizes cubic B-spline scaling functions with optimized filter coefficients for multi-resolution analysis. The decomposition process employs a pyramid algorithm with downsampling operations, while reconstruction performs exact inverse operations with upsampling and synthesis filters. This program is designed for immediate use and requires minimal configuration. Users can directly apply it to various signal processing tasks including noise reduction, feature extraction, and data compression. The algorithm maintains perfect reconstruction properties through carefully designed dual filter banks that preserve signal integrity across decomposition levels. We are pleased to offer this program to fellow researchers and engineers. It includes core functions for wavelet transformation, coefficient thresholding, and inverse transformation with error checking mechanisms. We believe this implementation will be valuable for your computational projects and research endeavors. Thank you for your interest and support! For any technical inquiries or assistance with integration, please don't hesitate to contact us. The code includes detailed comments explaining key parameters such as decomposition levels, boundary handling, and coefficient storage formats.