In this paper, we present an optimized approach for compressing multispectral satellite images (MSSI) using Discrete Wavelet Transforms (DWT) combined with machine learning-based band classification. Traditional methods often lead to information loss or inefficiencies when applied to multispectral imagery. To overcome this, we classify MSSI bands into high and low-information categories by analyzing wavelet coefficients using Histogram of Oriented Gradients (HOG) and K-means clustering. High-information bands are compressed using Huffman coding, while low-information bands leverage Principal Component Analysis (PCA) to reduce dimensionality without significant data loss. Experimental results on Landsat 8 and Sentinel 2 datasets demonstrate the superiority of our method, achieving Peak Signal-to-Noise Ratios (PSNR) of up to 39.97 dB for Landsat 8 and 70.72 dB for Sentinel 2, with Structural Similarity Index (SSIM) values as high as 0.95. Additionally, our method improved compression ratios by up to 74.4%, outperforming conventional techniques. These results validate the efficiency of our approach in reducing storage and transmission costs while maintaining high image fidelity, offering a robust solution for satellite image compression.