Implementing 2D Discrete Wavelet Transform on Images with Custom Algorithms

To achieve more refined image processing, we can first perform a 2D discrete wavelet transform on the image, decomposing it into 3 hierarchical levels. For implementation, we would create custom filter banks using wavelet coefficients (like Daubechies or biorthogonal filters) and apply them through convolution operations across both horizontal and vertical dimensions. Instead of directly calling MATLAB's dwt and idwt functions, we can utilize specific algorithms such as the Mallat algorithm (pyramid algorithm) for decomposition or the Cohen-Daubechies-Feauveau (CDF) biorthogonal wavelet algorithm for reconstruction. This approach involves iteratively applying low-pass and high-pass filters followed by downsampling for decomposition, and upsampling with filter application for reconstruction. Implementing these algorithms manually allows for deeper understanding of discrete wavelet transform principles and applications, while establishing a solid foundation for handling more complex image processing tasks in the future. The custom implementation would include functions for handling boundary conditions, managing subbands (LL, LH, HL, HH), and ensuring perfect reconstruction conditions.