Name
Title | ||
|---|---|---|
Analysis and Exploitation of Matrix Structure Arising in Linearized Optical Tomographic Imaging |
Abstract | ||
|---|---|---|
We present a novel method by which the large dense forward matrix $\mathbf{A}$ involved in a linear inverse diffusion problem can be decomposed into a number of sparse easily computed matrices. We begin by introducing an errorless decomposition which is applicable to a wide array of such imaging problems. Next, we incorporate interpolation into the construction of the matrices to reduce the computational complexity involved in the matrix-vector multiplications necessary to obtain an inverse solution. Error and computational complexity analysis are provided to support these developments. We then present numerical results that illustrate the gain in computational efficiency when the approximation is used in the Tikhonov regularized inverse problem, and show that the use of the approximation has virtually no negative effect on the quality of the reconstructed images. Finally, we discuss applicability to other imaging problems. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1137/060657285 | SIAM J. Matrix Analysis Applications |
Keywords | Field | DocType |
linear inverse diffusion problem,imaging problem,matrix structure arising,computed matrix,linearized optical tomographic imaging,present numerical result,computational efficiency,inverse problem,errorless decomposition,computational complexity analysis,computational complexity,inverse solution,image reconstruction,tikhonov regularization | Tikhonov regularization,Matrix analysis,Matrix (mathematics),Mathematical analysis,Interpolation,Algorithm,Inverse problem,Numerical analysis,Mathematics,Calculus,Sparse matrix,Computational complexity theory | Journal |
Volume | Issue | ISSN |
29 | 4 | 0895-4798 |
Citations | PageRank | References |
1 | 0.35 | 6 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Damon Hyde | 1 | 29 | 8.47 |
| Misha E. Kilmer | 2 | 41 | 6.13 |
| Dana H Brooks | 3 | 215 | 61.52 |
| Eric Miller | 4 | 15 | 2.16 |