Denoising / Super-Resolution

This code denoises or super-resolves multi-contrast MR images.

It inverts a generative model of the data with a multi-channel total-variation prior. It handles multiple contrasts with different resolutions and field-of-views. It can also take advantages of multiple repeats of a same contrast.

Dependencies

This code is written in Matlab and depends on the development branch of the SPM12 software, which should be on your Matlab path.

For increased speed, it is advised to recompile SPM with OpenMP activated. This can be done by following these instructions, except that the option USE_OPENMP=1 must be specified. For example, on linux:

cd /home/login/spm12/src
make distclean
make USE_OPENMP=1 && make install
make external-distclean
make external && make external-install

Usage

SPM Batch

If the super-resolution is copied into the toolbox/ folder of SPM, it can be used within the SPM batch system, which can be accessed by clicking the Batch Button in the main window. The super-resolution tool can then be loaded from SPM > Tools > Denoising / Super-Resolution.

The top-level field allows the user to chooose between the super-resolution and denoising modes. Most other options are identical between these two modes, but the super-resolution lets the user specify a few more parameters, such as the target voxel-size and the slice profiles.

Graphical

The tool can also be run using a small graphical interface outside of SPM. Assuming that you have a series of noisy images in nifti format, and that you like graphical interfaces, the most simple usage is:

>> sr_fit;

You will be asked:

• Number of contrasts: the number of different MR contrasts (T1w, T2w, ...)
• Mode (denoising|super-resolution): super-resolution allows MRIs to be upsampled to a finer grid (i.e., smaller voxel size). Note that super-resolution implies denoising.
  • Voxel Size: Target voxel size (only for super-resolution).
  • Thick slice (yes|no): The thick-slice mode can be used for anisotropic acquisitions, with high in-plane and low through-plane resolution (only for super-resolution).
• Regularisation (5E3): Higher = stronger denoising
• Number of iterations (10): Higher = closer to the optimum

You will then be asked to select all input files for each contrast. You can select multiple files (i.e., repeats) for each contrast. Finally, you will be asked to choose an output directory.

The algorithm will then run and write the results on disk. There will be as many denoised/super-resolved images as contrasts.

Command line

If more flexibility is required, sr_fit can be used as a function:

>> [out,in] = sr_fit(dat, opt);

The input dat can be either:

• A cell of cells of nifti filenames. The outer loop corresponds to contrasts and the inner loop corresponds to repeats of a given contrast.
• A 4D numeric or file array. This works in the denoising case only, when all inputs are registered and reslices to the same lattice.
• Empty. In this case, files can be selected through the GUI.

The outputs are:

• out is a structure with fields:
  • dat - a file array containing the denoised images
  • rls - a file array containing the L1 weights
  • mat - the output orientiation matrix
  • dim - the output dimensions
  • lam - the corrected regularisation factor for each contrast).
• in is a cell of cells of structures with fields:
  • dat - a file array containing the observed data
  • mat - the input orientation matrix
  • dim - the input dimensions
  • var - the observation uncertainty (based on the data type)
  • lam - the estimated noise precision
  • mu - the estimated mean tissue intensity (used to corrected the regularisation factors)
• If no output argument is asked (>> r_fit(dat, opt);), an output folder is asked for through the GUI and the output images are writen on disk.

Several options are available, as fields of the opt structure:

Name	Range	Default	Description
mode	'denoise' / 'superres'	'denoise'
log	bool	false	Solve for-log images (makes the prior scale-indepdendent)
itermax	int > 0	10	Maximum number of iterations
tolerance	float > 0	1E-3	Gain threshold for early stopping
reg.mode	0 / 1 / 2	1	Regularisation mode: 0=None/1=L1/2=L2
reg.value	float > 0	5E4	Regularisation factor per channel
reg.smo	float > 0	1E-3	RLS smoothing term
vs	float > 0	NaN	Target voxel size. By default, it is the average input voxel size.
fov	int >= 0	0	Target field of view. If 0, an average orientation matrix is computed from the input matrices. If N>0, the orientation matrix of the N-th input image is used.
coreg.do	bool	true	Start by coregistering all input volumes.
coreg.fwhm	float > 0	[21 14 7]	Series of FWHM used to smooth the joint histogram
threads	int >= 0 / 'matlab' / 'automatic'	'matlab'	Number of threads used by both Matlab and SPM: 'matlab' = Matlab's current settings / 'automatic = Matlab's automatic setting
verbose	int >= 0	1	Verbosity level: 0=quiet / 1=print / 2=plot
out.mem	'map' / 'load'	'map'	Memory map output data (slower but saves RAM)
out.folder	char	'.'	Output folder.
slice.dir	'thickest' / 'all'	'thickest'	Which directions are 'slice-selection' directions?
slice.gap	float >= 0	1/3	Gap between slices in the slice direction(s)
armijo	float >= 0	[2 1]	Series of damping factors used for Gauss-Newton .
solver.fmg	int >= 0	[2 2]	Number of cycles (1) and relaxation iterations (2) used by the multigrid solver .
solver.cg	int >= 0	50	Number of conjugate gradient iterations .
solver.relax	int >= 0	0	Series of relaxation iterations .

References

The use of Multi-Channel Total-Variation as a prior for MR super-resolution is described in:

• MRI Super-Resolution using Multi-Channel Total Variation.
  Mikael Brudfors, Yaël Balbastre, Parashkev Nachev, John Ashburner
  MIUA 2019
  https://arxiv.org/abs/1810.03422

• A Tool for Super-Resolving Multimodal Clinical MRI.
  Mikael Brudfors, Yaël Balbastre, Parashkev Nachev, John Ashburner
  Preprint
  https://arxiv.org/abs/1909.01140

The reweighted least squares scheme used in this implementation is described in :

• Joint Total Variation ESTATICS for Robust Multi-Parameter Mapping.
  Yaël Balbastre, Mikael Brudfors, Michela Azzarito, Christian Lambert, Martina F. Callaghan, John Ashburner
  MICCAI 2020
  https://arxiv.org/abs/2005.14247

License

This software is released under the GNU General Public License version 3 (GPL v3). As a result, you may copy, distribute and modify the software as long as you track changes/dates in source files. Any modifications to or software including (via compiler) GPL-licensed code must also be made available under the GPL along with build & install instructions.

TL;DR: GPL v3