Nowadays image compression is a task that has been more necessary than ever. Some techniques for image compression are investigated in this article. The first one is the well-known JPEG that is the most widely used technique for image compression. The second is Principal Component Analysis (PCA), also called Karhunen-Loeve transform, that is a statistical method applied for multivariate data analysis and feature extraction. In the latter, two approaches are being considered. The first approach uses the classical statistical method and the other one, artificial neural networks. In a comparative study, the results obtained by PCA neural network for compressing medical images are analyzed together with those obtained by using the classical statistical method and the JPEG compression standard technique.