SPIHT Image Compression Using Wavelet and Bandelet Transforms

In this document, we discuss the SPIHT (Set Partitioning in Hierarchical Trees) image compression algorithm based on wavelet and bandelet transforms. The SPIHT algorithm represents a widely-used image compression methodology that leverages wavelet and bandelet transformations to achieve efficient image compression. Wavelet and bandelet are mathematical tools that decompose images into different frequency components, enabling effective image compression through multi-resolution analysis. The algorithm implementation typically involves three key stages: wavelet transformation using functions like 'dwt2' in MATLAB, bandelet transformation for geometric representation, and the SPIHT encoding process that manages hierarchical tree structures through significance testing and bitplane coding. By combining these two transformation methods, SPIHT achieves superior compression performance while maintaining critical image information. Through the SPIHT algorithm implementation, we can significantly reduce image file size while preserving essential image details and structural information. The core algorithm operates by progressively encoding wavelet coefficients through bitplane processing, where the coder sequentially processes significance maps using coordinates sorting and refinement passes. Therefore, SPIHT image compression based on wavelet and bandelet transforms serves as a valuable technology with widespread applications in computer vision, image processing, and communication systems, particularly suitable for implementations requiring progressive transmission and quality scalability.