Motivation

Common approaches for reconstructing images from measured MRI signals usually assume that the signals’ samples are a direct measurement of a correctly encoded k-space, thus only requiring an inverse Fourier transformation for reconstruction. However, residual echo paths can lead to more than only the aimed-at echo which contributes to the signal but is wrongly encoded and has a different contrast. In this case the sum of different k-space locations will be measured, producing imaging artifacts. Typically, such problems are solved by introducing sufficient spoiling to suppress unwanted paths.
In this work, we propose a method to gain insight into the exact encoding of the measured signal by using a simulation based on Phase Distribution Graphs [1] (PDG). This knowledge can then be transferred to a reconstruction of the signal of a real measurement, tailored to the sequence that produced it. This process, titled Automatic Reconstruction, is outlined in figure 1. Since it adapts to any measurement that can be reproduced by the simulation, it lifts restrictions set by a fixed conventional reconstruction algorithm, which is desirable for sequence optimizations. This paves the way to less coherent and more complex sequence strategies, especially involving only partially spoiled magnetization that can still be separated by Automatic Reconstruction.

Materials and Methods

Signal simulations were performed by using PDGs, which is part of the MRzero [2] framework and suitable for simulating arbitrary MRI sequences in 3D. PDGs split magnetization into distributions with known encoding, $$$T_2'$$$ dephasing, phase, and simulated magnetization, to calculate the signal.
The known partition of the measured signal into individual distributions can be used to reconstruct them individually. In this work we use inverse Fourier transformation for this task and sum up the result to obtain the final image. This Automatic Reconstruction therefore does not rely on a single k-space trajectory but uses the known encoding of individual distributions, while reversing the rotation introduced by RF phase cycling. This is equivalent to automatically adjusting the ADC phase to the polarity of the echo.
We also introduce an estimator needed for estimating the signal contribution of individual distributions based on the measured signal. While all other properties of the distributions only depend on the sequence and are therefore known, their individual signals can only be estimated since it depends on the exact physical properties of the measured subject. By relying on the correlation between measured signal and individual signals of the distributions, it is possible to construct an estimator for those signals by analyzing the simulation data. The whole Automatic Reconstruction pipeline is shown in figure 2.
The estimator used in this work assumes that all distributions produce similar signals but with different amplitudes, which is adequate for sequences like bSSFP [3]. It stores the average signal of every distribution divided by the simulated signal to then multiply the measured signal with these complex factors to return signal estimates for individual distributions.

Results

The estimator used in this work produces distribution signals close to the ones obtained by simulating the sequence (fig. 3). While the estimation is not exact, this still results in noticeable improvements compared to conventional reconstruction, which can be seen as a trivial estimator that describes the magnetization consisting of one single distribution.
The improvement of the resulting image can be seen in figure 4. It shows strong ghosting artifacts when using “Default” (inverse Fourier transformation) reconstruction. They are a result of using only the previous pulse to determine the ADC phase, which is insufficient in this sequence. Automatic Reconstruction splits the magnetization into different parts with known phases, reducing the imaging artifacts. The estimator was generated using a different subject to the one it was applied to, demonstrating that it can be transferred to other measurements of the sequence.
As stated above, Automatic Reconstruction is suited well for optimization. As shown in figure 5, it produces a smooth loss landscape by adapting to the sequence. Because conventional reconstruction assumes that the previous pulse is sufficient to determine the phase of the signal, the loss increases faster with increasing randomization, but also depends on how close the assumed phase matches the actual polarization of the signal. This means Automatic Reconstruction not only results in a lower loss, but also in a smoother loss landscape, and is therefore leading to faster optimization convergence.

Discussion

By utilizing the proposed pipeline, it is possible to take advantage of the PDG simulation by returning additional information about the measured signal, which can then be used to automatically reconstruct an image without the need for additional inputs. Further improvements can be made by modifying the estimator and the reconstruction used in this abstract. Nevertheless, they are a good fit for sequences producing signals with unknown polarity, where it is difficult to calculate the ADC rotation needed for reconstruction otherwise.
Additionally, Automatic Reconstruction can remove restrictions when used for an end-to-end sequence optimization like in MRzero. Conventional reconstruction imposes a predefined reconstruction strategy onto the optimization, restricting its degrees of freedoms. In contrast, Automatic Reconstruction is only based on the encoding of the signal itself and can thus adapt to any change.

Acknowledgements

No acknowledgement found.