Gray Image Three-Level Wavelet Decomposition

In this example, we perform a three-level wavelet decomposition on the grayscale Lena image. Wavelet decomposition is a widely used image processing technique that decomposes an image into frequency information at different scales. By applying wavelet decomposition to grayscale images, we can obtain both low-frequency and high-frequency components, which helps in better understanding image details and structures. The implementation typically involves using wavelet transform libraries like PyWavelets in Python. The key function `wavedec2()` performs multi-level 2D discrete wavelet decomposition, returning approximation coefficients (low-frequency components) and detail coefficients (horizontal, vertical, and diagonal high-frequency components) at each level. For a three-level decomposition, the algorithm recursively applies wavelet transforms to the approximation coefficients of the previous level. The decomposition process reveals image features at different resolutions: Level 1 captures fine details, Level 2 shows medium-scale structures, and Level 3 represents coarse image characteristics. This hierarchical representation is particularly useful for image compression, denoising, and feature extraction applications.