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Lensfree On-chip Tomographic Microscopy Employing Multi-angle Illumination and Pixel Super-resolution

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Uniqueness of tomography with unknown view angles.

S Basu¹, Y Bresler

¹Gen. Electr. Corp. Res. and Dev. Center, Niskayuna, NY 12309, USA. basu@crd.ge.com

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society

|February 8, 2008

Summary

This study shows that projection data can uniquely determine unknown view angles in 2-D parallel beam tomography. This method also recovers random shifts, crucial for imaging applications like electron microscopy.

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Area of Science:

Image reconstruction
Computational imaging
Tomographic analysis

Background:

Standard 2-D parallel beam tomography assumes known projection angles.
Unknown or approximate angles arise in MRI of moving patients and 3-D electron microscopy of viral particles.

Purpose of the Study:

To develop a method for determining unknown view angles directly from projection data in 2-D parallel beam tomography.
To investigate conditions for unique angle recovery and simultaneous estimation of data shifts.

Main Methods:

Utilized Helgasson-Ludwig consistency conditions for the Radon transform.
Developed algorithms for joint estimation of view angles and random projection shifts.

Main Results:

Proved that view angles are uniquely determined by projection data under mild conditions.
Demonstrated the possibility of unique recovery for both view angles and random shifts.

Conclusions:

The developed method enables direct determination of view angles from projection data, overcoming limitations of standard tomographic approaches.
This technique is applicable to scenarios with unknown or approximately known angles, enhancing image reconstruction accuracy in various imaging modalities.