As I know, the Radon transform is a very important tool in CT by Beer's law. Thus, finding $f(x)$ of Radon transform $Rf(L):=\int_{L} f(x)dl(x)$ is helpful in CT. Nowaday, the Filtered back-projection formula (FBP) for all dimensions $n$ (which can find the $f(x)$) is obtained and is used already.

My question is here. Why is people studying 'Inverse Problem' in Radon transform although FBP is obtained?


Note that the original mathematical back-projection method assumes that the value of the Radon transform is known for all lines. This is an infinite amount of information, so it is pure mathematics at that level.

Since practical tomography works with a finite number of values of the Radon transform, the inversion is ill-posed. This cannot be ignored due to the finite precision of any numerical measurement and to the impact of noise.

In addition, since exposure to X-rays is harmful, it is imperative to continue to seek and develop algorithms that achieve results with fewer X-ray exposures.


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