Steen Moeller1, Sebastian Schmitter1, and Mehmet Akcakaya1,2
1Center for Magnetic Resonance Research, University of Minnesota, Minneapolis, MN, United States, 2Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN, United States
Synopsis
An investigation into the noise and resolution performance
of SLIDER using a series of shifted low-resolution images to obtain a single
high-resolution. The evaluation is performed both theoretical and experimentally
using a FLASH acquisition, to remove experimental limitations from
understanding the merits of the technique.Purpose
Recently, a novel
reconstruction technique has been proposed for diffusion weighted imaging,
termed SLIDER [1], which allows the reconstruction of a single high resolution 3D
dataset from multiple low resolution 3D datasets. The technique shares
similarities with the original multiband technique [2] (not SMS), which
has a sqrt(M) SNR gain for M acquisitions of M slices, and also has parallels to the works [3,4]. In this work we
investigate the performance of SLIDER with respect to resulting SNR and
resolution in a FLASH acquisitions obtained in-vivo and in phantoms.
Methods
A SLIDER acquisition consisting of three 3D low-resolution
FLASH datasets for a FOV of 256x232x90 mm^3, with a resolution of 1x1x3
(ROxPExSL), and each shifted 1mm relative to each other along the
slice-direction was acquired on a phantom and on a human subject.
A matching high resolution acquisition with 1x1x1 (ROxPExSL)
was acquired. For the phantom the high resolution was a 2D multi-slice and for
the in-vivo a 3D acquisition was used. The phantom was head shaped with an
embedded rectilinear grid. Imaging was performed in accordance with the IRB of
the University of Minnesota and was acquired on Siemens Magnetom 7T system
equipped with a nova medical 32 channel head coil.
A 2.56 ms sinc RF pulse with a BWTP=8 was used for all
experiments, which for SLIDER with 3X slice-thickness yields a subslice weigth
of [0.89 1 0.89]. The in-vivo slice orientation was chosen as coronal/sagittal to null signal in the outer slices. The encoding system,
denoted by $$$f=Ax$$$, for resolving the higher resolution signal $$$x$$$ was chosen as a
circulant matrix. The low-resolution SLIDER images was concatenated to a single image prior to reconstruction. Using the forward mapping in SLIDER, a set of low-resolution
images was generated and then reconstructed using a regularized reconstruction.
The obtained simulated results where visually compared with the high resolution
reconstructions from acquired and reconstructed SLIDER data.
Similarly an in-vivo experiment was performed, and the
acquired and reconstructed SLIDER data was compared qualitatively with high
resolution FLASH acquisition of matched duration.
Results
The impact of noise from the encoding matrix $$$A$$$ can for
the $$$k^{th}$$$ element (reconstructed slice) be expressed as
$$
\begin{bmatrix} \left(\begin{array}{c} A^{*}A +\lambda I \end{array}\right)^{-1}
A^{*}A \left(\begin{array}{c} A^{*}A +\lambda I \end{array}\right)^{-1}
\end{bmatrix}_{k,k}
$$
When $$$A$$$ is a circulant matrix, the noise scaling is
identical for all slices and can for each estimated value be expressed as
$$ std(f)=\sigma \sqrt{\frac{1}{N}\sum_{i}\frac{|h_i|^2}{(|h_i|^2+\lambda)^2}}=\sigma
\eta, $$ where $$$h_i $$$ are the singular values of the encoding system $$$
\sigma^2 $$$ the noise variance, $$$N$$$ total number of slices. Noise
amplification is plotted in figure 1A. Using a value of $$$\lambda$$$ which corresponds
to a noise amplification of 1 (one), the simulation for reconstructing a square
profile is plotted in figure 1B, based on an RF slice-profile as shown in figure
1C.
The simulation of a SLIDER encoding reconstruction is shown
in figure 2. The simulated data (Figure 2A) is based on the image in figure 2B.
Reconstructions based on simulated SLIDER data are shown in figure 2C and 2D
for different values of $$$\lambda$$$. A matching view of the same phantom
acquired with a SLIDER technique are shown in figure 3A-D, where the
concatenation of the low-resolution images is displayed in figure 3A, and can
be compared with the directly acquired high resolution image 3B. The
reconstruction for different values of $$$\lambda$$$ are shown in figures 3C
and 3D.
The results from the In-vivo data are shown in figure 4. A
matched slice from the high resolution acquisition is shown in figure 4B, and
the anatomical resolution can be compared with the acquired SLIDER data in 4A.
Reconstructed data are shown in figures 4C-4E for different values of
$$$\lambda$$$.The thermal noise is the same in the low-resolution and
high-resolution acquisitions, and the SNR in the low-resolution images are
larger than in the high resolution, since the signal is averaged. The noise in the SLIDER reconstructed images are the thermal
noise time multiplied with the $$$\eta$$$ from the circulant encoding
matrix.
Discussion
Noise
amplification have been analyzed for the SLIDER technique and it has been
demonstrated how for low values of lambda, there is noise amplification, which
can be reduced with increasing lambda at the cost of through-slice blurring.
These theoretical observations have been validated both in phantom and in-vivo,
and evaluated using a conventional FLASH sequence. The theoretical and experimental observations demonstrated here, shows that if the high resolution acquisition can be performed directly, then
that that will have both improved SNR and resolution compared to SLIDER.
Acknowledgements
P41 EB015894. Kawin Setsompop for discussion on noise properties in SLIDER and Xiaoping Wu for alternate
denoising techniques.References
[1] SLIce Dithered Enhanced Resolution Simultaneous MultiSlice (SLIDER-SMS) for high resolution (700 um) diffusion imaging of the human brain. Kawin Setsompop et al. page 339, ISMRM 2015.
[2] SIMA: Simultaneous Multislice Acquisition of MR Images by
Hadamard-encoded Excitation. S.P. Souza, J. Szumowski, C.L. Dumoulin, D.P. Plewes, G.H. Glover, J. Comput. Assist. Tomogr. 12 (6) pp.
1026-30 (Nov-Dec. 1988).
[3] A Spectral Approach to Analyzing Slice Selection inPlanar Imaging: Optimization for Through-Plane Interpolation. Douglas Noll, MRM 38:151-160 (1997)
[4] Super-resolution reconstruction of diffusion parameters from diffusion-weighted images with different slice orientations. Van Steenkiste G, Jeurissen B, Veraart J, den Dekker AJ, Parizel PM, Poot DHJ, Sijbers J. Magnetic Resonance in Medicine 2015