Please use this identifier to cite or link to this item:
|Title:||A Fast Algorithm to Map Functions Forward||Authors:||Lawton, W.||Keywords:||Approximate expansions using moments
Daubechies orthonormal wavelet basis
Interpolation kernels and subdivision
Scattered data interpolation
|Issue Date:||1997||Citation:||Lawton, W. (1997). A Fast Algorithm to Map Functions Forward. Multidimensional Systems and Signal Processing 8 (1-2) : 219-227. ScholarBank@NUS Repository.||Abstract:||Mapping functions forward is required in image warping and other signal processing applications. The problem is described as follows: specify an integer d ≥ 1, a compact domain D ⊂ Rd, lattices L1, L2 ⊂ Rd, and a deformation function F : D → Rd that is continuously differentiable and maps D one-to-one onto F(D). Corresponding to a function J : F(D) → R, define the function I = J ○ F. The forward mapping problem consists of estimating values of J on L2 ∩ F(D), from the values of I and F on L1 ∩ D. Forward mapping is difficult, because it involves approximation from scattered data (values of I ○ F-1 on the set F(L1 ∩ D)), whereas backward mapping (computing I from J) is much easier because it involves approximation from regular data (values of J on L2 ∩ D). We develop a fast algorithm that approximates J by an orthonormal expansion, using scaling functions related to Daubechies wavelet bases. Two techniques for approximating the expansion coefficients are described and numerical results for a one dimensional problem are used to illustrate the second technique. In contrast to conventional scattered data interpolation algorithms, the complexity of our algorithm is linear in the number of samples.||Source Title:||Multidimensional Systems and Signal Processing||URI:||http://scholarbank.nus.edu.sg/handle/10635/111126||ISSN:||09236082|
|Appears in Collections:||Staff Publications|
Show full item record
Files in This Item:
There are no files associated with this item.
checked on Sep 22, 2022
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.