Exponential spline perfect reconstruction, decomposition and reconstruction with applications in compression and denoising

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.