In the FBP algorithm, the ramp filter |w| has the zero response for the 0-frequency, thus its output has zero for the DC component, i.e., the average value would be zero, then, there would be negative values to compensate the common positive values. Since the nagative values are introduced by the ramp filtering and the image is positive generally, how to perform the normalization before the quantitative evaluation against the reference image?
Thanks.
This question is related with my previous one:
https://www.researchgate.net/post/proper_image_normalization_for_quantitative_comparison
Thank you @Syed Amir Gilani. I will read the thesis carefully for my question.
One understanding Xiangguo is , normalization brackets [0,1] or [-1,1] the #s and their variances are measurable .
Secondly , by normalizing you are changing the actual interpretation too . So when you say +ve or -ve there has to be some correlation to the raw data , not 1 to 1 .
@Aparna Sathya Murthy, thank you!
I think my question includes:
(1) The FBP algorithm is based on multiple summation of discrete backprojections, there are normalization factors.
(2) In the simulation, the sinogram may be from the Radon transform of digital image or directly sampling the analytical expression (my previous question: https://www.researchgate.net/post/are_there_tools_in_Matlab_to_create_the_phantom_sinogram_from_the_analytical_expression_directly), and the normalization factors in (1) may be different.
(3) Comparison and evaluation are actually for the reconstruction noise level but the noise may affect the normalization factors.
This may sound a bit off -beat :
http://matlab.izmiran.ru/help/toolbox/signal/spectra3.html
Numerical calculations for estimators need scaling and a degree of linearity (say) . This is provided by normalization and (bias /unbiased) estimators .The most obvious and exact estimation can be done using a probability density function , and you know this has its advantages.
Coming to Radon or other BPs , pdf for reconstruction is very much needed for looking at margins (phase of signal /directions etc etc)
Noise effects- maybe , again since we are considering band-limited signals (FFTd) the projection theory in terms of band-limited [-pi , pi] filters it and then handling of projected samples /slices are carried out.
The DC component can be recovered based on the "volume conservation property" of the Radon transform. Please refer to:
https://web.eecs.umich.edu/~fessler/course/516/l/c-tomo.pdf
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