Exponential B-spline functions are more flexible than cardinal B-spline polynomials due to the extra degrees of freedom inherited by the arbitrary choice of its parameters. In this paper, independent simple proofs of some of the important features of Exponential B-spline functions are given. A novel efficient technique has also been proposed for decomposing a signal in terms of its exponential B-spline expansion. Applications of Exponential B-spline functions in spatial image compression are demonstrated. Our illustrative results show that Exponential B-splines outperform cardinal B-splines in image compression.