Title :
A note on Unser-Zeruhia generalized sampling theory applied to the linear interpolator
Author :
Janssen, A. J E M ; Kalker, T.
Author_Institution :
Philips Res. Lab., Eindhoven, Netherlands
fDate :
8/1/1999 12:00:00 AM
Abstract :
In this correspondence, we calculate the condition number of the linear operator that maps sequences of samples f(2k), f(2k+a), k∈Z of an unknown continuous f∈L2 (R) consistently (in the sense of the Unser-Zeruhia generalized sampling theory) onto the set of continuous, piecewise linear functions in L2(R) with nodes at the integers as a function of a∈(0,2). It turns out that the minimum condition numbers occur at a=√2/3 and a=2-√2/3 and not at a=1 as we might have expected. The theory is verified using the example of video deinterlacing
Keywords :
image sampling; interpolation; piecewise linear techniques; video signal processing; Unser-Zeruhia generalized sampling theory; continuous piecewise linear functions; linear interpolator; linear operator; minimum condition numbers; video deinterlacing; Error analysis; Image reconstruction; Image sampling; Layout; Motion estimation; Nonuniform sampling; Piecewise linear techniques; Sampling methods; Stability; TV;
Journal_Title :
Signal Processing, IEEE Transactions on