Wavelet Transform-Based Image Compression and Encoding

Image compression and encoding using wavelet transform represents a widely adopted methodology in digital image processing. This technique effectively reduces image data volume by decomposing images into distinct frequency components through wavelet analysis. Wavelet transform serves as a mathematical framework that breaks down signals or images into multi-resolution frequency representations, enabling efficient compression and encoding procedures. In MATLAB implementation, key functions like wavedec2 perform 2D discrete wavelet decomposition, while appcoef2 and detcoef2 extract approximation and detail coefficients respectively. The compression algorithm typically involves: 1. Multi-level wavelet decomposition using Daubechies or similar wavelets 2. Threshold-based coefficient quantization (wthresh function) 3. Entropy encoding of significant coefficients 4. Reconstruction via waverec2 with compressed coefficients This approach maintains critical image information while achieving substantial data reduction through: - Energy compaction in low-frequency subbands - Negligible high-frequency coefficient elimination - Adaptive quantization strategies - Progressive reconstruction capabilities The MATLAB implementation allows parameter optimization for compression ratio versus quality trade-offs, with psnr calculations validating reconstruction fidelity.