Operators

The MRI reconstruction problem can best be represented by a series of linear operators. In the full reconstruction commands (Reconstruction) these are already combined into pipelines to complete the full transform from non-cartesian data to final image. However, sometimes it is useful to have access to the key steps and hence the operators are also exposed as commands.

Note that all of these operators are defined with the forward, default, direction going from image space towards non-cartesian space. Hence you likely want to specify the --adj option.

• grid

• nufft

• pad

• `prox`_

• sense

grid

riesling grid will carry out only the first step of the NUFFT, i.e. it will grid non-Cartesian k-space to Cartesian (or vice versa) and save the result. This can be useful to check that a dataset has been acquired correctly.

To diagnose trajectory and sample density issues, you can instead use riesling traj.

Usage

riesling grid file.h5 --adj

Input/Output

For the forward operation, file.h5 must contain the dataset cartesian, and the output file-grid.h5 will contain the noncartesian dataset. The adjoint operation must contain noncartesian in the input and will produce cartesian in the output.

Important Options

• --adj

  Apply the adjoint operation, i.e. from non-cartesian to cartesian.

• --sdc=none,pipe,pipenn,file.h5

  Choose the sample density compensation scheme. The default is pipenn. none means no density compensation. pipe is the full Pipe/Zwart/Menon density compensation. pipenn is a fast approximation to pipe. file.h5 uses a pre-computed sample density from the specified file.

nufft

Applies a NUFFT - i.e. combines gridding and an FFT.

Usage

riesling nufft file.h5 --adj

Input/Output

The forward operation expects a dataset channels and outputs a dataset noncartesian. The adjoint operation expects a dataset noncartesian and outputs a dataset channels.

Important Options

• --adj

  Apply the adjoint operation.

• --traj=file.h5

  Use the trajectory from a different file for gridding.

pad

The forward operation pads an image, the adjoint crops an image.

Usage

riesling pad file.h5 X,Y,Z

The second option X,Y,Z is a comma-delimited set of numbers indicating the required output dimensions. The other dimensions of the image dataset (frames and volumes) are not affected.

Output

file-pad.h5 containing the padded/cropped dataset.

Important Options

• --adj

  Apply the adjoint operation (cropping).

• --channels

  Changes the operation to work on 6D channels datasets. The extra dimension (channels) is also not affected.

prox —

Applies a proximal operator, i.e. regularization to an image. Useful to check what the impact of the regularizer during admm will be. See the ADMM documentation for how the regularizers work. Only the straightforward regularizers available in admm are available in prox. For instance, TGV regularization is formalated as two simultaneous optimization problems and so cannot be applied to a standalone image.

Usage

riesling reg file.h5 --llr --patch-size=N --lambda=L

Output

file-prox.h5 containing the regularized image dataset.

sense

Applies SENSE channel combination (adjoint operation) or splitting (forward operation).

Useage

riesling sense file.h5 sense.h5 --adj

Input/Output

Forward operation requires file.h5 containing a dataset channels, outputs file-sense.h5 containing image. Adjoint operation requires the image dataset, outputs channels.

The SENSE maps contained in sense.h5 must match the spatial dimensions of the dataset in file.h5.

Important Options

• -adj

  Apply the adjoint operation (SENSE channel combination)