Title :
Postfiltering versus prefiltering for signal recovery from noisy samples
Author :
Pawlak, Miroslaw ; Rafajlowicz, Ewaryst ; Krzyzak, Adam
Author_Institution :
Dept. of Electr. & Comput. Eng., Univ. of Manitoba, Winnipeg, Canada
Abstract :
We consider the extension of the Whittaker-Shannon (WS) reconstruction formula to the case of signals sampled in the presence of noise and which are not necessarily band limited. Observing that in this situation the classical sampling expansion yields inconsistent reconstruction, we introduce a class of signal recovery methods with a smooth correction of the interpolation series. Two alternative data smoothing methods are examined based either on a global postfiltering or a local data presmoothing. We assess the accuracy of the methods by the global L2 error. Both band-limited and non-band-limited signals are considered. A general class of correlated noise processes is taken into account. The weak and strong rates of convergence of the algorithms are established and their relative efficiency is discussed. The influence of noise memory and its moment structure on the accuracy is thoroughly examined.
Keywords :
bandlimited signals; convergence; correlation theory; error analysis; estimation theory; interpolation; noise; signal denoising; signal reconstruction; signal sampling; smoothing methods; WS sampling theorem; Whittaker-Shannon reconstruction formula; correlated noise processes; data smoothing methods; global L2 error; global postfiltering; interpolation series; local data presmoothing; noise memory; noisy samples; nonband-limited signals; prefiltering; sampling expansion; signal recovery methods; strong convergence rate; Convergence; Helium; Image reconstruction; Image sampling; Interpolation; Reconstruction algorithms; Sampling methods; Signal processing algorithms; Signal sampling; Smoothing methods;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2003.820013