Graph Laplacian tomography from unknown random projections

被引：144

作者：

Coifman, Ronald R. ^{[1
]}

Shkolnisky, Yoel ^{[1
]}

Sigworth, Fred J. ^{[2
]}

Singer, Amit ^{[1
]}

机构：

[1] Yale Univ, Dept Math, Program Appl Math, New Haven, CT 06520 USA

[2] Yale Univ, Sch Med, Dept Cellular & Mol Physiol, New Haven, CT 06520 USA

来源：

IEEE TRANSACTIONS ON IMAGE PROCESSING | 2008年 / 17卷 / 10期

关键词：

dimensionality reduction; graph laplacian; tomography;

D O I：

10.1109/TIP.2008.2002305

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

We introduce a graph Laplacian-based algorithm for the tomographic reconstruction of a planar object from its projections taken at random unknown directions. A Laplace-type operator is constructed on the data set of projections, and the eigenvectors of this operator reveal the projection orientations. The algorithm is shown to successfully reconstruct the Shepp-Logan phantom from its noisy projections. Such a reconstruction algorithm is desirable for the structuring of certain biological proteins using cryo-electron microscopy.

引用

页码：1891 / 1899

页数：9

共 29 条

[1]

[Anonymous], 2005, Advances in Neural Information Processing Systems (NIPS)

[2] Feasibility of tomography with unknown view angles [J].

Basu, S ;

Bresler, Y .

IEEE TRANSACTIONS ON IMAGE PROCESSING, 2000, 9 (06) :1107-1122

[3] Uniqueness of tomography with unknown view angles [J].

Basu, S ;

Bresler, Y .

IEEE TRANSACTIONS ON IMAGE PROCESSING, 2000, 9 (06) :1094-1106

[4] Laplacian eigenmaps for dimensionality reduction and data representation [J].

Belkin, M ;

Niyogi, P .

NEURAL COMPUTATION, 2003, 15 (06) :1373-1396

[5] A review of image denoising algorithms, with a new one [J].

Buades, A ;

Coll, B ;

Morel, JM .

MULTISCALE MODELING & SIMULATION, 2005, 4 (02) :490-530

[6]

CODDINGTON EA, 1984, THEORY ORDINARY DIFF

[7]

COIFMAN R. R., 1995, Wavelets and statistics, P125, DOI DOI 10.1007/978-1-4612-2544-7_9

[8] Diffusion maps [J].

Coifman, Ronald R. ;

Lafon, Stephane .

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2006, 21 (01) :5-30

[9] Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps [J].

Coifman, RR ;

Lafon, S ;

Lee, AB ;

Maggioni, M ;

Nadler, B ;

Warner, F ;

Zucker, SW .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2005, 102 (21) :7426-7431

[10] Geometric diffusions as a tool for harmonic analysis and structure definition of data: Multiscale methods [J].