NDLI: Statistical optimality of Hermite splines

Content Provider	IEEE Xplore Digital Library
Author	Uhlmann, V. Fageot, J. Gupta, H. Unser, M.
Copyright Year	2015
Description	Author affiliation: Biomed. Imaging Group, Ecole Polytech. Fed. de Lausanne (EPFL), Lausanne, Switzerland (Uhlmann, V.; Fageot, J.; Gupta, H.; Unser, M.)
Abstract	Hermite splines are commonly used for interpolating data when samples of the derivative are available, in a scheme called Hermite interpolation. Assuming a suitable statistical model, we demonstrate that this method is actually optimal for reconstructing random signals in Papoulis' generalized sampling framework. We focus on second-order Lévy processes - the integrated version of Lévy processes - and rely on cubic Hermite splines to approximate the original continuous-time signal from its samples and its derivatives at integer values. We statistically justify the use of this reconstruction scheme by demonstrating the equivalence between cubic Hermite interpolation and the linear minimum mean-square error (LMMSE) estimation of a second-order Lévy process. We finally illustrate the cubic Hermite reconstruction scheme on an example of a discrete sequence sampled from the realization of a stochastic process.
Starting Page	226
Ending Page	230
File Size	2483809
Page Count	5
File Format	PDF
ISBN	9781467373531
DOI	10.1109/SAMPTA.2015.7148885
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-05-25
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Interpolation Estimation Gaussian processes White noise Splines (mathematics) Image reconstruction
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
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9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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