Nov 16 2011

statistical estimation and hypotheses testing in x-ray imaging

Tag: Noise,Physics,softwareadmin @ 9:56 am

The last two articles discussed the use of energy information to increase the SNR of x-ray imaging systems. They assumed that the attenuation coefficient is a continuous function of energy and that the energy spectrum is measured with perfect resolution. But we know from my posts here, here, here, and here that the attenuation coefficient can be expressed as a linear combination of two functions of energy. In addition, as I discussed in my posts about deadtime, the extremely high count rates required for medical x-ray systems severely limit the energy resolution and the complexity of the signal processing.

My paper “Near optimal energy selective x-ray imaging system performance with simple detectors”, which is available for free download here, discusses the use of the two-function decomposition in the signal processing. By transforming the problem from infinite to finite dimensions, the decomposition allows us to get near ideal SNR using low energy-resolution measurements, which may be possible with high speed photon counting detectors.

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Nov 09 2011

Monte Carlo simulation of SNR with energy information

Tag: Implementation,Math,Noise,Physicsadmin @ 11:41 am

In this post, I continue the discussion of my paper “Near optimal energy selective x-ray imaging system performance with simple detectors”, which is available for free download here. I will describe a Monte Carlo simulation of the SNR with energy information discussed in my last post. The simulation traces the paths of individual photons. This is, perhaps, more fundamental than my previous simulations that relied on statistical models for the detector data. I develop models for the random path lengths and use them to simulate the imaging task for SNR described in my last post. The model is validated by comparing the energy spectrum of photons transmitted through an object to the theoretical formula. I also provide an estimate of the errors in the Monte Carlo results.

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Nov 07 2011

SNR with energy information

Tag: Implementation,Math,Noise,Physicsadmin @ 10:40 am

In the next posts I will discuss some of the results in my recent paper, which is available for free download here. The paper discusses fundamental limits on the signal to noise ratio of x-ray detectors with energy spectrum information. It also describes how we can design practical systems with low energy resolution detectors whose performance gets close to the optimal limit.

more –>;