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Uniqueness and sampling conditions for image reconstruction from the Hartley-transform intensity
Optics Letters
|October 22, 2009
Summary
A real 2D image can be uniquely reconstructed from its Hartley transform intensity, even when sampled below the Nyquist rate. This demonstrates that Hartley transform intensity-based image reconstruction is generally overdetermined and sub-Nyquist sampled.
Area of Science:
- Digital image processing
- Fourier analysis
- Computational imaging
Background:
- The Hartley transform is an alternative to the Fourier transform for image analysis.
- Reconstructing images from transform domain information is a fundamental problem in imaging science.
Purpose of the Study:
- To determine if a 2D image is uniquely defined by its Hartley transform intensity.
- To investigate the sampling requirements for reconstructing images from Hartley transform intensity.
Main Methods:
- A constructive proof was employed to demonstrate the uniqueness of image determination.
- Analysis of Hartley transform intensity sampling density was performed.
Main Results:
- A real 2D image is uniquely determined by its Hartley transform intensity.
- The required sampling density is approximately half the Nyquist density for the intensity.
Conclusions:
- Image reconstruction from Hartley transform intensity is generally overdetermined.
- Sub-Nyquist sampling of Hartley transform intensity is feasible for unique image reconstruction.
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