Splines: a perfect fit for signal and image processing

TLDR

The article argues that splines offer a theoretically sound and practically advantageous alternative to traditional signal‑processing methods, retaining classical theory as a special case and leveraging familiar filter and recursive‑algorithm tools while linking to wavelet multiresolution theory. The authors aim to provide a tutorial, compile essential properties and computational tools, and review primary applications of splines for signal and image processing. They achieve this by presenting a pedagogical overview, summarizing mathematical and computational techniques, and surveying key application domains.

Abstract

The article provides arguments in favor of an alternative approach that uses splines, which is equally justifiable on a theoretical basis, and which offers many practical advantages. To reassure the reader who may be afraid to enter new territory, it is emphasized that one is not losing anything because the traditional theory is retained as a particular case (i.e., a spline of infinite degree). The basic computational tools are also familiar to a signal processing audience (filters and recursive algorithms), even though their use in the present context is less conventional. The article also brings out the connection with the multiresolution theory of the wavelet transform. This article attempts to fulfil three goals. The first is to provide a tutorial on splines that is geared to a signal processing audience. The second is to gather all their important properties and provide an overview of the mathematical and computational tools available; i.e., a road map for the practitioner with references to the appropriate literature. The third goal is to give a review of the primary applications of splines in signal and image processing.