Implementation of 2D Discrete Wavelet Transform Using Mallat Pyramid Algorithm

This source code implements the 2D Discrete Wavelet Transform using the Mallat pyramid algorithm. The algorithm is widely employed in signal and image processing for decomposing signals or images into frequency components at different scales, enabling better capture of local signal characteristics. The discrete wavelet transform finds applications in numerous fields including image compression, image enhancement, and signal denoising. The Mallat pyramid algorithm represents a classical wavelet transformation approach whose core concept involves iterative multi-scale decomposition and reconstruction of signals through successive filtering operations. The implementation typically utilizes complementary high-pass and low-pass filters (such as Haar, Daubechies, or other wavelet families) applied along both horizontal and vertical directions for 2D data processing. Key implementation aspects include: - Row-wise and column-wise convolution operations with decomposition filters - Dyadic downsampling to create multi-resolution representations - Reconstruction through upsampling and inverse filtering - Support for multiple decomposition levels through iterative processing By utilizing this source code, users can efficiently implement 2D discrete wavelet transformations and apply them to various signal or image processing tasks. The code structure allows customization of wavelet types, decomposition levels, and boundary handling methods to suit specific application requirements.