Image Deconvolution for Microscopy

Thesis by: Thomas Kasper
Advisor: Prof. Dr. Nassir Navab
Supervision by: Thorsten Zerfaß (Fraunhofer IIS), Stephan Rupp (Fraunhofer IIS), Andreas Keil
Due date: 2006-10-12

Abstract

Image restoration deals with recovering the original scene from the raw data recorded by a flawed optical device subject to systematic and random degradations. Modelled as a (convolution-) integral equation, it belongs to the class of notoriously ill-posed inverse problems characterized by their pathologic sensitivity to perturbations in the data. Casting the problem in an abstract framework of (robust) parameter estimation, we elaborate the theoretical background and discuss different regularization techniques. A selection of algorithms is reviewed and adapted for microscopy. Finally their performance is evaluated on sets of both synthetically generated and real-world data.

Resources

Software

Matlab, Visual C++

Hardware

• Microscope: Zeiss Axio Imager M1, dry
• Lens: Zeiss Achroplan 63x (numerical aperture: 0.95)
• Lighting:  LED
• CCD-camera JAI Pulnix TMC-1402 CL (1392x1040 and 800x600)

Download

• Thesis
• Final Talk

Literature (selection)

• Image Restoration/Deconvolution:
  • A. K. Katsaggelos, Digital Image Restoration, Springer Verlag, Berlin, Heidelberg, 2nd ed., 1991. Springer Series in Information Sciences, No. 23.
  • R. Neelamani, H. Choi, and R. Baraniuk, ForWaRD: Fourier-Wavelet Regularized Deconvolution for Ill-Conditioned Systems, IEEE Transactions on Signal Processing, 52 (2004), pp. 418-433. http://www.dsp.rice.edu/publications/pub/neelshdecon.pdf
  • R. Vio, J. Bardsley, and W. Wamsteker, Least-Squares methods with Poissonian noise: an analysis and a comparison with the Richardson-Lucy algorithm, Astronomy and Astrophysics, (2005). http://web.math.umt.edu/bardsley/papers/Lspoisson04.pdf
• Robust Parameter Estimation/Inverse Problems:
  • A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation, SIAM, 1st ed., 2005.
  • C. R. Vogel, Computational Methods for Inverse Problems, SIAM, 2002.
  • D. MacKay, Information Theory, Inference, and Learning Algorithms, Cambridge Press, 2003.
• Microscopy:
  • S. F. Gibson and F. Lanni, Experimental test of an analytical model of aberration in an oil-immersion objective lens used in three-dimensional light microscopy, Journal of the Optical Society of America, 8 (1991), pp. 1601-1613.