A Hands-On Introduction to Motion Correction with Pilot Tone
Peter Speier1
1Siemens Healthcare GmbH, Germany

Synopsis

Keywords: Image acquisition: Motion correction, Body: Respiratory, Physics & Engineering: Hardware

Pilot Tone has emerged recently as a versatile motion correction method with minimum hardware requirements. The presentation gives a hands-on introduction to implementing Pilot Tone to any MR scanner that allows access to the raw MR data. It starts with a basic setup, discusses the frequency selection, PT signal detection and extraction of physiologic information. Then it describes how to take two common hurdles for general use: Eddy current effects and RF artefacts. Finally, the benefits of local PT generation will be described together with a few examples.

Pilot Tone Background

It has been shown many years ago, that electromagnetic fields at low frequencies that enter the chest are modulated by respiratory and cardiac activity (900 MHz [Moskalenko 1958], 100 kHz [Tarjan 1968], 170MHz [Wen 1995]). The interaction of electromagnetic fields with electrically conductive body tissues is well understood and by itself has been used as an imaging modality [Griffiths 1999, Ma 2017].
This phenomenon has already been used to characterize motion in an MRI environment in multiple setups: noise navigator [Andreychenko 2015, Navest 2020], transmit coil reflections [Buikman 1988, Jaeschke 2019], local coil loading [Kudielka 2016]. It has been shown that a multi-channel system can acquire rich information that allows separation of multiple motion modes [Schroeder 2016, Jaeschke 2019].
The idea of Pilot Tone (PT) based motion correction is to implement an (electro)magnetic motion sensor with minimal hardware (HW) effort by adding hardware just for the generation of a reference signal and reuse the existing MR system infrastructure for receiving and processing the modulation of this signals [Speier 2015].
It has been demonstrated previously that information from external sensors can be recorded together with the MR data [Hanson 2007]: if modulated onto a magnetic field carrier signal of the right amplitude and frequency, the information can be encoded in the oversampling region of the MR data. Therefore, our motion sensing reference signal could be used to characterize the variations of the carrier signal in Hanson’s experiment, thus in communication science lingo it would be called a pilot tone.

Usage Examples

The Pilot Tone method has been used to perform retrospective respiratory gating [Vahle 2020, Pruitt 2020, Huang SS 2021, Solomon 2022] and respiratory triggering [Huang YT 2023], as well as joint retrospective respiratory and cardiac gating [Chen 2021, Falcao 2022]. PT based prospective cardiac triggering has also been demonstrated [Bacher 2018] and has recently been evaluated in clinical settings [Hayes 2022, Lin 2023]. In addition, PT has been applied to prospective slice tracking [Ludwig 2021, Ludwig 2023], detection of head motion [Speier 2018], patient communication [Bacher 2022] and has been compared to and combined with data driven motion correction methods [Wilkinson 2021, Brackenier 2022, Huang YT 2022].

PT Signal Characteristics

In the range of typical MR frequencies [20…300MHz] the tissue interaction is weak, leading only to a weak modulation of the signal. Typical values at 3T are ~5 % for respiratory, and ~1 % for cardiac motion in the optimally placed receive channels.
As an aside, the characteristics of tissue-field interactions at these low frequencies are also leveraged in the field of magnetic induction tomography (MIT) to image the electromagnetic properties of tissues. Some of the signal characteristics discussed in this field also apply to PT. [Ma 2017]
On the positive side, this weak interaction ensures that the signal is not attenuated significantly with penetration depth and therefore enables motion encoding from deep inside the body. For example, this means that the cardiac component of the Pilot Tone signal changes in sync with the cardiac volume [Bacher 2021], i.e., one extremum of the modulation corresponds to end-diastole, the other to end-systole. Thus, the cardiac phase can be derived from the Pilot Tone signal alone.
One the negative side, the small modulation depth limits the achievable SNR because the PT amplitude is limited by the dynamic range of the MR receiver. Also, the stability of the PT signal must be high compared to the modulation depth. We will see below that some measures are necessary to reach this stability.
In addition to the electromagnetic tissue interaction, respiratory motion will also change the relative positions of receive coils and PT generator. If the generator is placed on or in the anterior coil, the generator moves relative to the posterior coils. This (in MIT unwanted) effect will create additional modulation of the PT signal thereby increasing its sensitivity to respiration and aids in separation of respiratory motion from other motions.
While the PT signal can be generated as a magnetic near field with a suppressed electric field component, for frequencies above 1 GHz electromagnetic waves are required due to the short wavelength. Higher order tissue interactions become relevant, and the interaction is better described by a radar wave model. Compared to PT, the modulation depth increases while the signal penetration into the body reduces [Neumann 2023]. Such methods are out of scope of this presentation, but I want to point out the interesting hybrid method published as “Beat Pilot Tone” that implements MR detected radar [Lustig 2021].

Step 1: A 1st Experiment

Getting started with the Pilot Tone is quite easy. The first results can be obtained on any MR scanner quite easily by following the steps in this section.
Use an off-the-shelf synthesizer and feed its signal with a long coax-cable into the RF cabin, e.g., through the filter plate or the wave guide of the MR installation. Then generate a controlled magnetic field leak at the end of the cable by ending it in an open loop and place it somewhere in the cabin, e.g., at the inner wall of the RF cabin or on the magnet cover near the bore. Take care to ensure that the loop is well fixed and does not shift or vibrate. Ensure that it is not too close to the RF coil to avoid that the MR pulses couple back into the synthesizer and damage it.
Place a water phantom in the scanner and run adjustments. Set the synthesizer to the current Larmor frequency, f_Larmor, of your scanner and dial it into Synthesizer. Pick an amplitude and activate the signal generation.
Run an MR measurement with a slice in iso-center. Now, there should be an artefact in the middle of the image in the readout direction and spread out along the phase‑encoding (PE) direction (the pattern along the PE direction depends on the kSpace sampling scheme). Adjust the PT amplitude so that this signal is well visible but does not saturate the receiver yet, i.e., there are no additional artefacts, the noise background should not increase, and the phantom signal should not drop when switching the signal on.
Now change the PT frequency until the artefact is outside of the phantom but still inside the FOV. Run a series of measurements where you keep the coil positions exactly the same (e.g., use spine coil only), but move the phantom between images. The intensity of the artefact will vary slightly with the position due to the local signal modulation created by the conductive water in the bottle. The effect will be more pronounced when observed in images of individual channels.
A next step could be to repeat the experiment with a volunteer with anterior and posterior coils in different breath‑hold positions for each image: the artefact intensity should reflect the respiratory phase. Again, depending on the selected receive channels, the net modulation in the combined image could be small. Therefore, output the images of the individual receive channels and analyze them separately.
If the volunteer then switches between chest and belly breathing, the modulation pattern over the receive channels will vary with the respiration type. This already indicates that the Pilot Tone can separate different motions due to the many receive channels.
The next step will be to shift the PT signal away from the image into the oversampling region. This means that the PT will not be visible anymore in the final image (unless it is output with preserved readout-oversampling). Therefore, the next step requires access to the “raw” MR data, i.e., the data at the input of the image reconstruction pipeline.

Step 2: Protocol Dependent Frequency Selection

The readout sample rate of the raw MR data at the input of the image reconstruction is usually twice the rate required for the field-of-view in readout direction to accommodate the roll-off of anti-aliasing filters. If you can program the image reconstruction of your scanner, you should be able to access this “raw” data. Please note that while this user accessible data is generally called “raw data”, it has already been preprocessed by the receive system.
We place the PT frequency at a fixed point in the oversampling region, e.g., halfway between image border frequency, f_ima_max, and the Nyquist-frequency, f_data_max. For an image without in-plane shifts this frequency is
f_PT = (f_data_max- + f_ima_max)/2
For an image bandwidth in readout (RO) direction, BW_ima, this becomes
f_PT = (f_Larmor + 3/4 BW_ima)
If you apply a Fourier transform in readout direction, the PT will appear as a sharp peak. For a base resolution of pxl_RO the (spectrum of the) raw data line is 2*pxl_RO long and the peak will be placed at
pxl_PT = 1.75* pxl_RO.

This frequency should be entered in the synthesizer.
When your scanner readjusts the frequency, the position of the PT peak can change. In this case, either again retrieve f_Larmor or fit the peak position.
In the general case, the center frequency of the image does not always equal the f_Larmor of the adjustment: A shift in readout direction by shift_RO_pxl will change the center frequency and the PT peak will appear at position
pxl_PT = 1.75 * pxl_RO - shift_RO_pxl
The above analysis assumes that the image is placed symmetrically around the center frequency of the slice, i.e., the center frequency falls between two pixels. However, standard FFT routines are asymmetric and place the zero frequency for a vector of samples [0…N-1] onto sample N/2. Therefore, one way or another you might encounter an additional half pixel shift that needs to be corrected.
If you run protocols with very different BW_ima, the PT signal frequency will likely need to be adjusted to keep the PT signal in the oversampling region. In the context of MR detected radar (“Beat Pilot Tone”) a system has been built to automatically set the required frequencies [Grelling 2022].

Step 3: Complex Valued PT Signal Detection

Given that in‑plane shifts are arbitrary and do not necessarily fall onto the pixel grid, the shape of the PT peak in the Fourier transformed raw data line will vary. If you detect the PT in the spectrum, this shape variation will affect your results. For a radial acquisitions off-iso-center, for example, the position of the PT peak will change from line to line with projection angle and even though you can exactly determine the peak position, the PT values will depend on the projection angle.
This problem can be avoided with a detection in the time domain: under the assumption that the physiologic variations are slow enough to be negligible during an MR readout, the PT signal during the readout has, in every receive channel, the form of a pure harmonic oscillation:
PT(t) = A *exp( i * 2 * Pi * f * t),
with the amplitude A being a complex valued number. In general, the PT signal is modulated in both phase and amplitude. However, analyzing the phase of the PT signal is more challenging than analyzing its amplitude. Therefore, it is advisable to first focus on the PT amplitude abs(A).

Step 4: Using the PT Phase Information

In order to maximize SNR and information content, the complete complex valued PT information must be processed. However, this requires keeping the phase of the PT stable in the raw data. The first option is to determine the receiver phase for each measured raw data line from protocol information and subtract it from the measured PT phase. The phase of the readout is affected by MR phase cycles, e.g., quadratic RF spoiling, and by off-center-shifts in phase encode direction. This analytic option requires that the PT synthesizer is phase locked to the MR-scanner and that the phase relation between the PT signal at f_PT and the receiver reference signal at f_Larmor is calculated for the readout events. An alternative is to restrict the analysis to relative phases: Select a reference channel, preferably one with high SNR for the PT and little modulation. Determine the phase phi_ref of the complex amplitude A_ref in this channel and remove it from the amplitudes A_i of other channels. If you simply divide all A_i by A_ref, you can remove signal modulations caused by instabilities on the PT generation side or slightly incorrect PT peak position as well. Note that by these operations the physiologic modulation in the reference channel is copied to all other channels. Modern receivers acquire a wide signal band at a fixed frequency and in the digital domain reduce and shift the signal band to the one requested by the application. Steps 2, 3 & 4 are not required if your scanner allows you to place the PT detection before these processing steps and your PT generator is phase‑locked with the scanner’s receiver.

Improvement: Local PT Generation

The global PT generation outside the magnet bore has the disadvantage that all body parts are “illuminated”. The result is that motion of all body parts will contribute to the signal modulation even if they are outside the volume “seen” by the local coils. Therefore, when using a global PT with local coils around the chest for respiratory motion detection, even head or foot motion will contribute to the modulation.
The solution is to generate the PT close to the body part of interest in order to reduce the illuminated volume. If multiple motion modes are present the contributions of weakly modulating motions can be enhanced by positioning the PT generator close to the physical motion. For example, placing the PT generator on the chest on top of the heart enhances contributions by cardiac motion and makes them detectable in the presence of respiratory modulation [Schroeder 2016B].
The PT generator must of course be non-magnetic and must be hardened against the RF pulses of the MR measurement, i.e., it must neither be destroyed nor heated by them.
Possible solutions are:
  • transmission of the PT signal from a remote synthesizer into the bore. If the transmission is electric, the cable must be secured against sheath waves and the synthesizer should be protected against RF pulses coupling into the PT generating loop.
  • a battery powered stand-alone device like the one that is advertised by NYU for 3T on https://cai2r.net/resources/3t-pilot-tone/. While being easy to use it is currently limited to one PT frequency and is not synchronized with the scanner.
  • Integration of PT signal generation into the scanner HW and control SW, e.g., into a body array or spine coil.

Step 5: Extract Physio Data

The simplest way to extract physiologic motion information from the raw PT multi-channel data, vec_P, is to select the receive channel where the signal modulation is strongest. This approach works quite well for respiration, which typically is the dominating modulation but discards most of the measured data. We can optimize the quality of the resulting physio signal, PT_phys, by forming a weighted sum over all channels. Weight values, vec_W_M, are determined on training data with the goal to maximize the modulation created by the target motion, M, in the combined signal, PT_phys_M, while suppressing all other sources of modulation. It is useful to view the set of all possible weights as a vector space of dimension C, where C is the number of active receive coil elements. In that vector space a combination vector forms a base vector for a one-dimensional subspace. Unless two combination vectors are parallel, they belong to different subspaces. A set n of non-parallel combination vectors forms an n-dimensional subspace. Complex physiologic motions like respiration are not confined to one dimension but create significant modulation in at least two dimensions. To completely remove respiratory contributions to the signal PT_phys_M of another motion, M, that is measured in the presence of respiratory motion, its combination vector must be chosen to be orthogonal to the respiratory subspace. Optimal weights can be found by comparing training data with simultaneously measured motion ground truth, e.g., from MR navigators or images [Schroeder 2016], if available. Such ground truth data can be used to assign a length scale to PT_phys [ Ludwig 2021]. If ground truth is not available, weights can be found by “blind” source separation using Principal Component Analysis (PCA) or Independent Component Analysis (ICA) methods. These methods separate the input signal into components that are statistically independent using different criteria. After the algorithms have identified the major components, these components must be assigned to the different physiologic motion modes that are expected to be present. This is done by analyzing the components using previous knowledge about the motion, e.g., its frequency range, shape, or component amplitude. Also, the sign of the components is arbitrary and must also be determined using previous knowledge, e.g., knowledge about the wave form or expected distribution of correlation signs in the receive coil geometry [Bacher 2017, Bacher 2021, Chen 2022]. ICA methods [Sahonero 2017] have been used to detect motion components in PT data in a single step after preprocessing the data with PCA for dimensionality reduction [Bacher 2017]. However, these methods solve a non-convex problem iteratively and thus are computation intensive and in difficult cases their results vary with starting conditions. Contrary to ICA, PCA solves a convex problem and therefore is fast and robust but provides only orthogonal weight vectors. In general, the weights for different motion modes are not orthogonal. Thus, the separation of motion modes in the PCA output is often not optimal and weak components corresponding to small motion modes are often contaminated by other motion modes that correspond to strong components. The separation can be optimized by avoiding subspaces of unwanted motion modes in the weights vector [Zhang 2020, Speier 2022, Huang YT 2023]. These subspaces are approximated by PCA of filtered input data. Filtering is again based on previous knowledge about the unwanted motion mode to enhance its contribution to the data and suppress other motion modes. The resulting first (few) principal components span a subspace that contains the bulk of the enhanced motion mode. This subspace can then be avoided in the final coil combination. If necessary, this process can be repeated for other modulation sources, potentially using separate training data, to avoid additional unwanted signal contributions.
Blind source separation algorithms and coil combination require zero-mean input data. In the case of PT signals, the offset is large compared to the modulated part and must be carefully determined and removed, so that only the signal modulation due to motion is left in the input signal. This can be done in two ways:
  • Learn the signal average for each channel and subtract it on the input data. This training can be done once on the training data, and in case of signal drifts be repeated or updated continuously.
  • Treat the offset as unwanted signal contribution: Calculate the subspace of weights, vec_W_ 0, where vec_W_ 0 * mean(vec_PT_training) = 0 and project the input data into this subspace. This approach has the advantage that it is more robust against signal drifts and does not require a separate offset removal step.

Hurdle 1: Eddy Current Compensation

Gradient switching generates eddy currents in the conductive structures of an MR scanner. While decaying, these eddy currents generate magnetic fields with various spatial distributions, among them a spatially independent component. This dynamic B0 variation is compensated by following the Larmor frequency with the receiver reference, which in turn shifts the PT peak position in the raw MR data. The problem can be provoked, e.g., by interleaving image acquisitions with orthogonal slices back-to-back. If this frequency shift is not considered in the PT signal model, it can result in PT signal variations.
The problem can be fixed the following approaches:
  1. If your scanner supports it, you can retrieve the current value of the Larmor frequency and adapt the PT signal model.
  2. If you have an estimate for the maximum size of the frequency shift, you can filter the raw data before PT detection with a bandpass filter that provides a sufficiently flat response in the expected frequency band (albeit sacrificing some SNR).
  3. You can fit the peak position for each line but be careful not to introduce additional noise.
  4. For repetitive sequences learn the peak position as a function of sequence timing.
  5. If your scanner supports it, detect the PT before the B0 correction is applied.

Hurdle 2: RF Correction

The receive system of an MR scanner is actively decoupled during the RF pulses of an MR measurement. At the end of the pulse the receive system is recoupled and ready to receive signals again. The recoupling is not instantaneous, but the receiver gain takes some time to settle to its undisturbed value. MR spin signals change smoothly with distance from RF pulses. Thus, to avoid artefacts, MR acquisition schemes are designed to be tolerant against these variations, which also makes them tolerant against small variations in the effective receiver gain after recoupling. Therefore, small and fast variations do not disturb MR measurements. However, the PT signal, due to its weak physiologic modulation is sensitive even to very small receiver gain variations. The settling receiver gain generates transient artefacts in the PT signal following an RF pulse. This can be seen, e.g., in the PT data acquired with every echo of a multi-echo GRE measurement: The data will show a saw tooth pattern that repeats with every RF pulse.
The following approaches can be used alone or in combination to remove these artefacts:
  1. blank out the PT signal for some time after RF. This is applicable only for long pulse spacings.
  2. Average the PT signal from pulse to pulse. This can be used for cine type sequences.
  3. Process PT signals for each echo time TE (or in more general terms “time after recoupling”) separately and learn the conversion factors between them.
  4. Learn the shape of the artefact and compensate it. This requires knowledge about “time after recoupling”. Correction can be done by artefact subtraction or by gain multiplication as both are equivalent for small corrections.
  5. Learn the subspace occupied by RF pulse artefacts and avoid it during coil combination [Zhang 2020, Speier 2022, Huang YT 2023]

Summary

The Pilot Tone method
… can be implemented without scanner modification.
… requires access to oversampled “raw” MR data.
… position in MR raw data varies with protocol, off center shift and eddy currents.
… observes tissue conformation without delay and can therefore be self-calibrating.
… signal quality benefits from local signal generation.
… requires coil combination training.
… in general requires RF calibration.
… is versatile.
… there are a lot of yet unexplored applications!
… is fun, try it out!

Acknowledgements

I want to thank my colleagues Mario Bacher, Carmel Hayes and Yan Tu Huang for reviewing the manuscript.

References

[Andreychenko 2015]
Andreychenko A, Crijns S, Raaijmakers A, Stemkens B, Luijten P, Lagendijk J, et al. Noise variance of an RF receive array reflects respiratory motion: a novel respiratory motion predictor. ISMRM 2014 Milan, #0092

[Bacher 2017]
Bacher M. Cardiac Triggering Based on Locally Generated Pilot-Tones in a Commercial MRI Scanner: A Feasibility Study. [master’s thesis. Graz: Graz University of Technology; 2017. 103 p.]
https://diglib.tugraz.at, linked via
https://graz.pure.elsevier.com/de/publications/cardiac-triggering-based-on-locally-generated-pilot-tones-in-a-co

[Bacher 2018]
Bacher M SP, Bollenbeck J, Fenchel M, and Stuber M. Pilot Tone Navigation Enables Contactless Prospective Cardiac Triggering: Initial Volunteer Results for Prospective Cine. ISMRM 2018 Paris, #2960

[Bacher 2018B]
Bacher M, Speier P, Bollenbeck J, Fenchel M, and Stuber M. Model-Based Lag Free Processing of Pilot Tone Navigator Data Enables Prospective Cardiac Triggering. ISMRM, Paris 2018, #4913

[Bacher 2021]
Bacher M, Dornberger B, Bollenbeck J, Stuber M, and Speier P. Listening in on the Pilot Tone: A Simulation Study. ISMRM 2021 Online, #1364

[Bacher 2022]
Bacher M, Speier P, and Bollenbeck J. A Wireless Pilot Tone Based Patient Squeeze-Ball (P2TSB). ISMRM 2022 London, #2004

[Brackenier 2022]
Brackenier Y, Wilkinson T, Cordero-Grande L, Tomi-Tricot R, Bridgen P, Giles S, De Vita E, Malik SJ, and Hajnal JV. Pilot Tone meets DISORDER: Improved data-driven motion-corrected brain MRI by leveraging Pilot Tone signal variations. ISMRM 2022 London, #0859

[Buikman 1988]
Buikman D, Helzel T, Röschmann P. The rf coil as a sensitive motion detector for magnetic resonance imaging. Magnetic Resonance Imaging, Volume 6, Issue 3,1988, Pages 281-289

[Chen 2021]
Chen C, Liu Y, Simonetti O. Extraction of cardiac and respiratory motion from Pilot Tone—a patient study. SCMR’s Virtual Scientific Sessions. 2021.

and

Chen C, Liu Y, Simonetti OP, Tong M, Jin N, Bacher M, et al. Cardiac and respiratory motion extraction for MRI using Pilot Tone-a patient study. arXiv:2202.00055

[Falcao 2022]
Falcão MBL, Di Sopra L, Ma L, Bacher M, Yerly J, Speier P, Rutz T, Prša M, Markl M, Stuber M, Roy CW. Pilot tone navigation for respiratory and cardiac motion-resolved free-running 5D flow MRI. Magn Reson Med. 2022 Feb;87(2):718-732.

[Grelling 2022]
Grelling J. An Automated Control System for Beat Pilot Tone in MRI. Thesis 2022. EECS Department, University of California, Berkeley 2022, https://www2.eecs.berkeley.edu/Pubs/TechRpts/2022/EECS-2022-203.html

[Griffith]
Griffiths H, Stewart WR, and Gough W. Magnetic induction tomography: a measuring system for biological tissues. Annals of the New York Academy of Sciences, 873:335–345, 1999.

[Hanson 2007]
Hanson LG, Lund TE, Hanson CG. Encoding of electrophysiology and other signals in MR images. J Magn Reson Imaging 2007, 25(5), 1059-1066

[Hayes 2022]
Hayes C, Huang YT, Rick M, Kroeker R, Bacher M, Pan Y, et al. Multi-center evaluation of the novel Beat Sensor Cardiac triggering technology. ISMRM 2022 London, #4786

[Huang SS 2021]
Huang SS, Boyacioglu R, Bolding R, MacAskill C, Chen Y, Griswold MA. Free-Breathing Abdominal Magnetic Resonance Fingerprinting Using a Pilot Tone Navigator. J Magn Reson Imaging. 2021 Oct;54(4):1138-1151

[Huang YT 2022]
Huang YT, Speier P, Hilbert T, and Kober T. Motion correction using Pilot Tone: a general model-based approach. ISMRM2022, #3169

[Huang YT 2023]
Huang YT, Tan X, Zhang Q, Speier P. Pilot Tone respiratory signal processing with RF interference suppression and validation against image navigator. ISMRM 2023 Toronto, #3014

[Jaeschke 2019]
Jaeschke, Sven & Robson, Matthew & Hess, Aaron. (2019). Scattering matrix imaging pulse design for real‐time respiration and cardiac motion monitoring. Magn Reson Med. 2019; 82: 2169– 2177

[Kudielka 2016]
Kudielka GP. Coil load changes for physiological motion acquisition in cardiac magnetic resonance imaging. Thesis 2016 l'Université de Lorraine, Nancy.
http://docnum.univ-lorraine.fr/public/DDOC_T_2016_0071_KUDIELKA.pdf

[Lin 2023]
Lin K, Sarnari R, Speier P, Hayes C, Davids R, Carr JC, Markl M. Pilot Tone-Triggered MRI for Quantitative Assessment of Cardiac Function, Motion, and Structure. Invest Radiol. 2023 Mar 1;58(3):239-243

[Ludwig 2021]
Ludwig J, Speier P, Seifert F, Schaeffter T, Kolbitsch C. Pilot tone–based motion correction for prospective respiratory compensated cardiac cine MRI. Magn Reson Med. 2021 May;85(5):2403-2416.

[Ludwig 2023]
Ludwig J, Kerkering KM, Speier P, Schaeffter T, Kolbitsch C. Pilot tone-based prospective correction of respiratory motion for free-breathing myocardial T1 mapping. MAGMA. 2023 Feb;36(1):135-150

[Lustig 2021]
Anand S, Lustig M. Beat Pilot Tone: Exploiting Preamplifier Intermodulation of UHF/SHF RF for Improved Motion Sensitivity over Pilot Tone Navigators. ISMRM 2021 online, #0568

[Ma 2017]
Ma L and Soleimani M. Magnetic induction tomography methods and applications: a review. Measurement Science and Technology, Volume 28, Number 7

[Moskalenko]
Moskalenko YE. Utilization of superhigh frequencies in biological investigations. Biophysics (USSR) (English translation).1958;3:619–26. [Only second hand knowledge! I have not been able to find a copy of the original article yet. If you find it, please let me know]

[Navest 2020]
https://github.com/rnavest/noise-navigator

[Neumann 2023]
Neumann T, Ludwig J, Kerkering KM, Speier P, Seifert F, Schaeffter T, and Kolbitsch C. Ultra-wide band radar for prospective respiratory motion correction in the liver. Physics in Medicine & Biology, Volume 68, Number 5, 2023

[Pruitt 2020]
Pruitt A, Speier P, Chen C, Liu Y, Jin Y, Simonett O5, and Ahmad R. Extracting the respiratory signal from Pilot Tone for highly accelerated, respiratory-resolved whole-heart 4D flow imaging. ISMRM 2020 Online, #1331

[Sahonero 2017]
Sahonero G, Calderon H. A Comparison of SOBI, FastICA, JADE and Infomax Algorithms.
Conference: International Multi-conference on Complexity, Informatics and Cybernetics: IMCIC 2017, Orlando, Florida, US.

[Schroeder 2016]
Schroeder L, Wetzl J, Maier A, Rehner R, Fenchel M, Speier P. Two-Dimensional Respiratory-Motion Characterization for Continuous MR Measurements Using Pilot Tone Navigation. ISMRM 2016 Singapore, #3103

[Schroeder 2016B]
Schroeder L, Wetzl J, Maier A, Lauer L, Bollenbeck J, Fenchel M, et al. A Novel Method for Contact-Free Cardiac Synchronization Using the Pilot Tone Navigator. ISMRM 2016 Singapore, #410

[Solomon 2021]
Solomon E, Rigie DS, Vahle T, Paška J, Bollenbeck J, Sodickson DK, Boada FE, Block KT, Chandarana H. Free-breathing radial imaging using a pilot-tone radiofrequency transmitter for detection of respiratory motion. Magn Reson Med. 2021 May;85(5):2672-2685

[Speier 2015]
Speier P, Fenchel M, Rehner R. PT-Nav: a novel respiratory navigation method for continuous acquisitions based on modulation of a pilot tone in the MR-receiver. Magnetic Resonance Materials in Physics, Biology and Medicine. 2015; 28:1–135.

[Speier 2018]
Speier P, Bacher M, Bollenbeck J, Fenchel M, Kober T. Separation And Quantification Of Head Motion Modes By Pilot Tone Measurements. ISMRM 2018 Paris, #4101

[Speier 2022]
Speier P, Huang YT, Hayes C, Kroeker R, Rick M, Schwertfeger M, and Bacher M. Enabling Pilot Tone cardiac triggering for complete cardiac examinations using an RF calibration procedure. ISRMM 2022 London, #1653

[Tarjan]
Tarjan PP, McFee R. Electrodeless measurements of the effective resistivity of the human torso and head by magnetic induction. IEEE Trans Biomed Eng. 1968;15(4):266-78.

[Vahle 2020]
Vahle T, Bacher M, Rigie D, Fenchel M, Speier P, Bollenbeck J, et al. Respiratory Motion Detection and Correction for MR Using the Pilot Tone: Applications for MR and Simultaneous PET/MR Examinations. Invest Radiol. 2020;55(3):153-159.

[Wen 1995]
H. Wen, T.J. Denison, R.S. Balaban. A Low Noise Monitoring Mechanism of the Cardiac and Respiratory Cycles Using Their Influence on Penetrating R.F. Fields. ISMRM 1995, Nice, #307

[Wilkinson 2021]
Wilkinson W, Godinez F, Brackenier Y, Tomi-Tricot R, Cordero-Grande L, Bridgen P, Giles S, Hajnal JV, and Malik SJ. Motion Estimation for Brain Imaging at Ultra-High Field Using Pilot-Tone: Comparison with DISORDER Motion Compensation. ISMRM 2021 Online, #122

[Zhang 2020]
Zhang Q, Zhang YX, Liu Y. A Component Projection Algorithm for eliminating the interference of Pilot Tone Signal. ISMRM 2020 Singapore, #4287

Proc. Intl. Soc. Mag. Reson. Med. 31 (2023)