Radiation detectors are the basis of many medical imaging techniques, yet I believe not much attention is being paid to them in terms of rethinking the way they are designed to include the new techniques developed on the compressive sensing framework. Let me give you an simple example. But first before thinking about a new technology, one really needs to see what has been done before. Probably not the extent of being an expert but at least to the point where one gets a sense of the gist of what is being performed. I am taking some of the figures from this presentation on Radiation Detection & Measurement II, Pulse height spectroscopy which takes most of its material from The Essential Physics of Medical Imaging by Jerrold Bushberg. As a nuclear engineer, one of the textbook I had and can recommend is Radiation Detection and Measurement by Glenn Knoll (the errata sheet is here ). If you recall I asked Glenn two years ago about coded aperture ( CS: Coded Mask Imagers: What are they good for ? The George Costanza "Do the Opposite" Sampling Scheme). These two books are a good starting point and provide a very good shelf book for practicing engineers and physicists alike. They definitely provide a good vocabulary if you end up talking to a radiation detector designer.
One of the simplest configuration for detecting radiation is detecting Gamma ray photons. As shown in the figure below, a photon source provides undirected gammas which interact with the NaI(TI) material which will transform a high energy photon (gamma) into a photon in the visible light range that can be converted into an electron and then into a electrical current.
One also notices that the gamma rays also interact with the rest of the detector. Some of the interaction processes were already described in These Technologies Do Not Exist: A Random Anger Coding Scheme for PET/SPECT cameras entry. The figure below lists all kinds of interactions the gamma source eventually have with the detector (A, B, C, D, E, F):
Specifically as mentioned in the text of the presentation and the associated book:
Interactions of photons with a spectrometer
•An incident photon can deposit its full energy by:
–A photoelectric interaction (A)
–One or more Compton scatters followed by a photoelectric interaction (B)
•A photon will deposit only a fraction of its energy if it interacts by Compton scattering and the scattered photon escapes the detector (C)
–Energy deposited depends on scattering angle, with larger angle scatters depositing larger energies
Even if the incident photon interacts by the photoelectric effect, less than its total energy will be deposited if the inner-shell electron vacancy created by the interaction results in emission of a characteristic x-ray that escapes the detector (D)
Detectors normally shielded to reduce effects of natural background radiation and nearby radiation sources
•An x-ray or gamma-ray may interact in the shield of the detector and deposit energy in the detector:
–Compton scatter in the shield, with the scattered photon striking the detector (E)
–A characteristic x-ray from the shield may interact with the detector (F)
In the end, the spectrogram for this source is shown in its ideal form on the left hand side of the next figure and its real shape in the real configuration.
In other words, the two diracs have now been transformed into a much smoother function as a result of the interaction of the source with the detector. It so happens that the past 60-70 years, most detectors have been built in order to get the real figure (on the right) as close as possible to the left one. In effect, any new improvement of the technology (for instance replacing the NaI material with Silicon Drift Detectors (SDD) as in HICAM) is trying to make the right peak as close to a dirac as possible ( I am sure some of you are already seeing where I am going to say but nevertheless let us continue.) How bad is the interaction with the rest of the detector ? It can be made very bad, as shown in the figure below where the difference between the two spectra is directly dependent on the shape of the container surrounding the detector.
Another important characteristics of these sensors is that in order to provide spectral resolution, a gating system is put in place. The result of these spectra is generally given on Multi Channel Analyzers (MCA) that are natural extension of Single Channel Analysers (SCA) shown below.
Given all this background, what would look like a Compressive MultiChannel Analyzer ? and what would be its purpose compared to current established technology ?
A natural compressive sensing approach to this problem would probably revolve around a stronger smoothing of the real dirac figure making the detector measurement a direct incoherent measurement of the spectrum. How would we go about this ? After some thoughts, there are probably two paths to be investigated:
- change the arrangement of the material in front of the detector so that more Compton scattering occur (recall in current radiation detector technology we want to so the opposite of that)
- change the \Delta E so that it is a random set as opposed to a unique value.
By changing the structure of the material in front of the detector, this new type of detector may be providing directional sensitivity for a similar energy resolution. By changing the \Delta E, one might also provide a better control over the noise of the scattered signal. A way to investigate all this phase space would be to use some forward modeling using codes like MCNP or GEANT. After having created a concept, one can check the design using the Random coding for forward modeling as recently presented by Justin Romberg recently. This entry will be added to the These Technologies Do Not Exist page.