Abstract
A method is presented to calculate state space realizations of a three-dimensional image set. It is based on interpreting the image set as the impulse response of a 3D separable system. As an application it is shown how this method, combined with approximation steps, including balanced model reduction, can be used to suppress noise in three-dimensional image sets. The approach was motivated by a practical problem in the analysis of three-dimensional fluorescent microscopy image data of fluorescently labelled cells. The method is illustrated by an analysis of simulated data and experimental data. The proposed approach can also be applied to a two-dimensional image in a straightforward way.
Article PDF
Similar content being viewed by others
References
S. Inoue and K.R. Spring, Video Microscopy: The Fundamentals, Plenum Pub Corp., 1997.
D.A. Agard (1984) ArticleTitle“Optical Sectioning Microscopy: Cellular Architecture in Three Dimensions” Annual Review of Biomedical Engineering 13 191–216
D.A. Agard Y. Hiraoka J.W. Sedat (1989) ArticleTitle“Three-dimensional Microscopy: Image Processing for High Resolution Subcellular Imaging” SPIE 61 24–30
G.M.P. van Kempen L.J. van Vliet (2000) ArticleTitle“The Influence of the Regularization Parameter and the First Estimate on the Performance of Tikhonov Regularized Non-linear Image Restoration Algorithms” Journal of Microscopy 198 IssueID1 63–75
G.M.P. van Kempen L.J. van Vliet P.J. Verveer H.T.M. van der Voort (1997) ArticleTitle“A Quantitative Comparison of Image Restoration Methods for Confocal Microscopy” Journal of Microscopy 185 354–365
B. Roysam A.K. Bhattacharjya C. Srinivas D.H. Szarowski J.N. Turner (1992) ArticleTitle“Unsupervised Noise Removal Algorithms for Three-dimensional Confocal Fluorescence Microscopy” Micron and Microscopica Acta 23 IssueID4 447–461
A. Doi T. Hinamoto (2001) ArticleTitle“A Spatial-domain Technique for the Design of 3-D Separable-denominator State-space Digital Filters” Multidimensional Systems and Signal Processing 12 89–98
T. Hinamoto and A. Doi, “Design of Multidimensional Separable-denominator Digital Filters in the Spatial Domain”, in Proceedings of IEEE Asia Pacific Conference on Circuits and Systems, Seoul, Korea, 1996, pp. 219–222.
T. Hinamoto A. Doi K. Harada (1997) ArticleTitle“Design of Multidimensional Separable-denominator Digital Filters in the Spatial Domain” Multidimensional Systems and Signal Processing 8 273–293
K. Hirano M. Sakane M.Z. Mulk (1984) ArticleTitle“Design of Three-dimensional Recursive Digital Filters” IEEE Transactions on Circuits and Systems CAS-31 IssueID6 550–561
B. Lashgari L.M. Silverman J.F. Abramatic (1983) ArticleTitle“Approximation of 2-D Separable in Denominator Filters” IEEE Transactions on Circuits and Systems CAS-30 IssueID2 107–121
R.J. Ober (1996) NoChapterTitle S. Bittanti G. Picci (Eds) “Balanced Canonical Forms”, in Identification; Adaptation; Learning Springer-Verlag Berlin 120–179
M. Green D.J.N. Limebeer (1995) Linear Robust Control Prentice-Hall Inc. New Jersey
K Zhou J.C Doyle K. Glover (1996) Robust Optimal Control Prentice-Hall Inc. New Jersey
W.S Lu A. Antoniou (1992) Two-dimensional Digital Filters Marcel Dekker Inc. New York
P.S.K. Hansen P.C. Hansen S.D. Hansen J.A. Sorensen (1999) ArticleTitle“Experimental Comparison of Signal Subspace Based Noise Reduction Methods” Proceedings of International Conference on Acoustics Speech and Signal Processing 1 101–104
T. Lin M. Kawamata T. Higuchi (1987) ArticleTitle“Design of 2-D Separable-denominator Digital Filters Based on the Reduced-dimensional Decomposition” IEEE Transactions on Circuits and Systems CAS-34 IssueID8 934–941
T. Lin M. Kawamata T. Higuchi (1987) ArticleTitle“Decomposition of 2-D Separable-denominator Systems: Existence Uniqueness and Applications” IEEE Transactions on Circuits and Systems CAS-34 IssueID3 292–296
T. Kailath (1980) Linear Systems Prentice-Hall Inc. New Jersey
B. Moore (1981) ArticleTitle“Principal Component Analysis in Linear Systems: Controllability Observability and Model Reduction” IEEE Transactions on Automatic Control AC-26 IssueID1 17–32
S.Y. Kung, “A New Identification and Model Reduction Algorithm via Singular Value Decompositions”, in Proceedings of the 12th Asilomar Conference on Signals, Systems and Computers, 1978, pp. 705–714.
H.P. Zeiger and A.J. McEwen, “Approximate Linear Realizations of Given Dimension via Ho’s Algorithm”, IEEE Transactions on Automatic Control, vol. AC-19, no. 153, 1974.
J.M. Maciejowski (1995) ArticleTitle“Guaranteed Stability with Subspace Methods” Systems and Control Letters 26 153–156
T. Kailath A.H Sayed B. Hassibi (2000) Linear Estimation Prentice-Hall Inc. New Jersey
L. Pernebo L.M. Silverman (1982) ArticleTitle“Model Reduction via Balanced State Space Representations” IEEE Transactions on Automatic Control Ac-27 IssueID2 382–387
W.W.F. Pijnappel A. van den Boogaart R. de Beer D. van Ormondt (1992) ArticleTitle“SVD-Based Quantification of Magnetic Resonance Signals” Journal of Magnetic Resonance 97 122–134
R.J. Ober E.S. Ward (1995) ArticleTitle“Correcting for Phase Distortion of NMR Spectra Analyzed Using Singular-value Decomposition of Hankel Matrices” Journal of Magnetic Resonance A 114 120–123
R.J. Ober J. Caves E.S. Ward (2003) ArticleTitle“Analysis of Exponential Data Using a Noniterative Technique: Application to Surface Plasmon Experiments” Analytical Biochemistry 312 57–65
L.J. van Vliet, “Grey-Scale Measurements in Multi-Dimensional Digitized Images”, Ph.D. thesis, University of Delft, 1993.
H. Chen J.R. Swedlow M. Grote J.W. Sedat D.A. Agard (1995) “The Collection Processing and Display of Digital Three-Dimensional Images of Biological Specimens” J. B. Pawley (Eds) Handbook of Biological Confocal Microscopy EditionNumber2 Plenum Press New York 197–210
G.M.P. van Kempen and L.J. van Vliet, “Improving the restoration of textured objects with prefiltering”, in Proceedings of 3rd Annual Conference of the Advanced School for Computing and Imaging (ASCI’97) 1997, pp. 174–179.
V. Ghetie E.S. Ward (2000) ArticleTitle“Multiple Roles for the Major Histocompatibility Complex Class I Related Receptor FcRn” Annual Review of Immunology 18 739–766
Author information
Authors and Affiliations
Corresponding author
Additional information
Received July 9, 2003; Revised April 20, 2003; Accepted June 11, 2004; First online version published in December 2004
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Ober, R.J., Lai, X., Lin, Z. et al. State Space Realization of a Three-dimensional Image Set with Application to Noise Reduction of Fluorescent Microscopy Images of Cells. Multidim Syst Sign Process 16, 7–47 (2005). https://doi.org/10.1007/s11045-004-4737-0
Issue Date:
DOI: https://doi.org/10.1007/s11045-004-4737-0