Name
Title | ||
|---|---|---|
Variational image reconstruction from arbitrarily spaced samples: a fast multiresolution spline solution. |
Abstract | ||
|---|---|---|
We propose a novel method for image reconstruction from nonuniform samples with no constraints on their locations. We adopt a variational approach where the reconstruction is formulated as the minimizer of a cost that is a weighted sum of two terms: (1) the sum of squared errors at the specified points and (2) a quadratic functional that penalizes the lack of smoothness. We search for a solution that is a uniform spline and show how it can be determined by solving a large, sparse system of linear equations. We interpret the solution of our approach as an approximation of the analytical solution that involves radial basis functions and demonstrate the computational advantages of our approach. Using the two-scale relation for B-splines, we derive an algebraic relation that links together the linear systems of equations specifying reconstructions at different levels of resolution. We use this relation to develop a fast multigrid algorithm. We demonstrate the effectiveness of our approach on some image reconstruction examples. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1109/TIP.2004.841203 | IEEE Transactions on Image Processing |
Keywords | Field | DocType |
computational advantage,nonuniform interpolation,multiresolution reconstruction,variational approach,spaced sample,weighted sum,multigrid algorithm,fast multiresolution spline solution,radial basis functions rbfs,variational image reconstruction,image reconstruction,two-scale relation,linear system,algebraic relation,image reconstruction example,variational reconstruction.,thin-plate splines,analytical solution,linear equation,index terms—b-splines,b splines,computer simulation,cost function,differential algebraic equations,helium,radial basis function,thin plate splines,linear systems,spline,image resolution,nonuniform sampling,algorithms,artificial intelligence,sample size,interpolation,sum of squares,analytic solution,linear system of equations,indexing terms,thin plate spline | B-spline,Spline (mathematics),Applied mathematics,Thin plate spline,Linear system,Multiresolution analysis,Artificial intelligence,Iterative reconstruction,Mathematical optimization,System of linear equations,Pattern recognition,Mathematics,Multigrid method | Journal |
Volume | Issue | ISSN |
14 | 4 | 1057-7149 |
Citations | PageRank | References |
32 | 2.43 | 15 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Muthuvel Arigovindan | 1 | 128 | 17.90 |
| Michael Sühling | 2 | 109 | 17.77 |
| Patrick Hunziker | 3 | 79 | 5.07 |
| Unser, M. | 4 | 3438 | 442.40 |