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MOMS: maximal-order interpolation of minimal support
1Biomedical Imaging Group, Swiss Federal Institute of Technology Lausanne, CH-1015 Lausanne EPFL, Switzerland. thierry.blu@epfl.ch
Summary
We introduce maximal-order-minimal-support (MOMS) functions for signal interpolation, offering superior accuracy over B-splines. These functions achieve significant sampling gains, increasing with approximation order L, with an asymptotic gain of 2/(pi)L.
Area of Science:
- Numerical Analysis
- Signal Processing
- Approximation Theory
Background:
- Signal interpolation is crucial in digital signal processing.
- Traditional methods often use B-splines as basis functions.
- Optimizing basis functions can improve interpolation accuracy and efficiency.
Purpose of the Study:
- To derive and analyze novel basis functions for signal interpolation.
- To introduce maximal-order-minimal-support (MOMS) functions.
- To quantify the performance improvement over standard B-splines.
Main Methods:
- Derivation of MOMS functions as linear combinations of B-splines and their derivatives.
- Analysis of MOMS function properties, including support and regularity.
- Computation of sampling gains achieved by MOMS functions compared to B-splines.
- Experimental validation using image rotation.
Main Results:
- MOMS functions provide maximal approximation accuracy for minimal support.
- Significant sampling gains are observed, increasing with approximation order (L).
- Asymptotic sampling gain for large L is 2/(pi)L.
- Performance is high even for functions with limited regularity.
Conclusions:
- MOMS functions represent an optimal choice for signal interpolation.
- Approximation performance is not solely dependent on function regularity.
- These findings have practical implications for image processing and signal reconstruction.
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