Image Compression Reimagined through Frequency domain to Wavelet Trees

Abstract

As the demand for efficient image storage and transmission grows across domains such as medical imaging, web development, and satellite communication, image compression has become a critical focus in digital media processing. This paper explores fundamental image compression principles and evaluates two prominent approaches: Fast Fourier Transform (FFT) and wavelet-based techniques, including Haar and Set Partitioning in Hierarchical Trees (SPIHT). While FFT leverages global frequency analysis for high-speed compression with moderate detail preservation, wavelet transforms provide superior localization in both time and frequency domains, allowing for better edge preservation and scalability. Experimental comparisons using grayscale images reveal that SPIHT achieves higher Peak Signal-to-Noise Ratio (PSNR) and compression ratio, whereas Haar excels in speed and simplicity. The findings emphasize the complementary nature of these techniques and highlight emerging hybrid approaches that combine FFT’s efficiency with the adaptive precision of wavelets to meet diverse compression needs.