Análise do algoritmo de compressão de imagem utilizando SVD truncado

Abstract

This study investigates grayscale image compression using truncated singular value decomposition, aiming to measure the balance between file size reduction and visual quality retention. A dataset of twenty‑nine images with varying resolutions and texture complexities was assembled. Each image was converted to grayscale and processed through truncated singular value decomposition, then reconstructed by varying the number of significant singular values. For each configuration, compression ratio, mean squared error, and peak signal‑to‑noise ratio in decibels were computed. Experiments were conducted in a Python environment with standard linear algebra libraries and no hardware optimizations. The findings detail how the number of components impacts both compression effectiveness and visual fidelity, presenting tables and graphics that depict the performance curve of the method. The study concludes that truncated singular value decomposition is a viable approach for academic purposes, suggesting future work on color image applications and optimized implementations.