Least squares generalized B-spline signal and image processing

This paper presents generalized B-spline interpolation and approximation techniques. The first part of this paper describes a technique for the continuous representation of discrete signals in terms of generalized B-splines (direct B-spline transform) and for interpolative signal reconstruction (indirect B-spline transform) with an expansion factor m. The key to our approach is to use a family of generalized B-spline filters. It has been shown that the scale factor can be modified to tune the approximated filter bandwidths. The second part of this paper makes use of these results to describe an equivalent filtering interpretation (low-pass filtering followed by a generalized B-spline interpolator) of generalized B-splines together with least squares generalized B-spline signal approximation methods. This part also concern with new theoretical results showing factorization of the transfer functions of the higher degree (n>3) generalized B-spline filters. Experimentally, it is seen that data compression with reduced amount of error can be achieved using these least squares generalized B-spline filtering techniques.