Please, cite this online document as:
Sykora S., Vasini E.M.,
Realistic simulated MR data (virtual phantoms) and the development of Inverse-Problems algorithms,
Talk at AIP 2019, Applied Inverse Problems Conference, Grenoble (France), July 8-12, 2019.
Simulated data are very important for the development, testing, and comparisons of algorithms for inverse problems (IP) of all kinds. The many inverse problems encountered in magnetic resonance (MR) are no exception.
Examples of raw MR data to be evaluated in various ways include FID's, relaxation decays, relaxation rate dependences on magnetic field (NMRD profiles) and/or on temperature, MRI transient signals acquired compatibly with various k-space sampling approaches, etc.
There are various reasons why simulation of such data is useful, such as:
Acquisition of "real" signals implies (i) the availability of suitable "real samples" that might illustrate the limits of a tested algorithm and (ii) availability of the costly and complex instruments (possibly of a number of different types) needed to generate the signals. These requirements are often extremely hard to meet in practice. In addition, "real samples" are often poorly characterized in advance, or even not characterized at all, which gives rise to a situation where an evaluation algorithm is to be validated solely on the basis of results provided by itself - a kind of circular logic. "Real" samples also quite often exhibit unforeseen real-life complications which distract and shift the focus from the algorithm to the sample itself.
Moreover, the acquisition of "real" signals is often very slow compared to the rate with which one can generate simulated data. The latter are also much more flexible in terms of setting sample/acquisition parameters settings, freedom of adding well defined samples of random noise, etc. All this is particularly important when the IP algorithm needs to be numerically validated in terms of its bias and/or noise propagation, using techniques of Monte Carlo type.
The usefulness of simulated data is farther enhanced if their "generators" can be made sophisticated enough to include a controlled amount of typical experimental distortions (artefacts). With such data one can test the impact of various artefacts (both one-by-one and in various combinations) on the results obtained by means of the tested algorithm. The capability to generate realistic simulated data including equally realistic simulated artefacts implies a considerably deep physical knowledge, as well as a lot of engineering experience. This is becoming a science on its own, somewhat similar to (but more complex than) devising good and versatile noise generators.
As an example, we present such a generator for translational-magnetization transients computed for hypothetical poly-dispersed samples (virtual phantoms) obtained by various MR techniques (IR, SR, FFC) on various "virtual instruments" burdened by combinations of many possible artefacts (RF pulse imperfections, magnetic field imperfections, receiver imperfections, etc). Inverting such simulated data using, as an example, two different algorithms provides useful insights into what one can expect once they get deployed to real data.