New Sampling Expansion Related to Derivatives in Quaternion Fourier Transform Domain

The theory of quaternions has gained a firm ground in recent times and is being widely explored, with the field signal image processing no exception. However, many important aspects quaternionic signals are yet to be particularly formulation Generalized Sampling Expansions (GSE). In present article, our aim formulate GSE realm one-dimensional quaternion Fourier transform. We have designed filters reconstruct signal, using its derivative. Since derivatives contain information about edges curves appearing images, therefore, such sampling formula substantial importance for processing, super-resolution procedures. Moreover, presented expansion can applied enhancement, color restoration compression filtering, etc. Finally, an illustrative example demonstrate efficacy proposed technique vivid simulations MATLAB.