Name
Abstract | ||
|---|---|---|
We describe a variational framework for the tomographic reconstruction of an image from the maximum likelihood (ML) estimates of its orthogonal moments. We show how these estimated moments and their (correlated) error statistics can be computed directly, and in a linear fashion from given noisy and possibly sparse projection data. Moreover, thanks to the consistency properties of the Radon transform, this two-step approach (moment estimation followed by image reconstruction) can be viewed as a statistically optimal procedure. Furthermore, by focusing on the important role played by the moments of projection data, we immediately see the close connection between tomographic reconstruction of nonnegative valued images and the problem of nonparametric estimation of probability densities given estimates of their moments. Taking advantage of this connection, our proposed variational algorithm is based on the minimization of a cost functional composed of a term measuring the divergence between a given prior estimate of the image and the current estimate of the image and a second quadratic term based on the error incurred in the estimation of the moments of the underlying image from the noisy projection data. We show that an iterative refinement of this algorithm leads to a practical algorithm for the solution of the highly complex equality constrained divergence minimization problem. We show that this iterative refinement results in superior reconstructions of images from very noisy data as compared with the classical filtered back-projection (FBP) algorithm. |
Year | DOI | Venue |
|---|---|---|
1996 | 10.1109/83.491319 | IEEE Transactions on Image Processing |
Keywords | Field | DocType |
Radon transforms,computerised tomography,correlation methods,error statistics,image reconstruction,iterative methods,maximum likelihood estimation,minimisation,tomography,variational techniques,Radon transform,correlated error statistics,cost functiona,equality constrained divergence minimization,filtered back-projection algorithm,iterative refinement,moment based variational approach,moment estimation,noisy projection data,nonnegative valued images,nonparametric estimation,orthogonal moments,probability densities,sparse projection data,statistically optimal procedure,tomographic image reconstruction,variational algorithm,variational framework | Iterative refinement,Image processing,Artificial intelligence,Radon transform,Velocity Moments,Iterative reconstruction,Mathematical optimization,Tomographic reconstruction,Pattern recognition,Iterative method,Algorithm,Tomography,Mathematics | Journal |
Volume | Issue | ISSN |
5 | 3 | 1057-7149 |
Citations | PageRank | References |
21 | 2.67 | 11 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Peyman Milanfar | 1 | 700 | 52.20 |
| William Clement Karl | 2 | 399 | 49.51 |
| Alan S. Willsky | 3 | 7466 | 847.01 |