Wavelet Transform for Image Processing

Wavelet transform is a mathematical tool extensively used in digital signal processing and image processing fields. This technique decomposes signals or images into different frequency components, enabling multi-scale analysis and manipulation. In practical implementation, libraries like PyWavelets in Python or MATLAB's Wavelet Toolbox provide functions such as wavedec2() for 2D discrete wavelet decomposition, which separates images into approximation coefficients (low-frequency components) and detail coefficients (horizontal, vertical, diagonal high-frequency components). Key algorithms include Discrete Wavelet Transform (DWT) using filter banks like Haar, Daubechies, or Coiflet wavelets, where high-pass and low-pass filters are applied recursively. The transform enables data compression by thresholding detail coefficients (e.g., using wthresh() function), significantly reducing storage and transmission requirements while preserving visual quality. Therefore, wavelet transform is crucial for practical image processing, allowing granular control over image features through techniques like wavelet denoising (wdenoise()) and multi-resolution analysis for applications in medical imaging, satellite imagery, and digital photography.