B-splines caught interest of many engineering applications due to their merits of being flexible and provide a large degree of differentiability and cost/quality trade off relationship. However they have less impact with continuous time applications as they are constructed from piecewise polynomials. On the other hand, Exponential spline polynomials (E-splines) represent the best smooth transition between continuous and discrete domains as they are made of exponential segments. In this paper we present a complete analysis for an E-spline based subband coding (wavelet) perfect reconstruction (PR) system. Derivations for the scaling and wavelet functions are presented, along with application of the proposed system in image compression and image denoising. In image compression, a comparison of the proposed technique compared with the B-spline based PR system as well as the basic wavelet subband system with the SPIHT image codec, is presented. In image denoising, we report the enhancement achieved with the proposed E-spline based denoising approach compared with B-spline based denoising and another basic denoising technique. In both applications, E-splines show superior performance as will be illustrated.