Linear Operators

Linear Operators#

Sub-package containing Linear operators for MR imaging.

Each operator is derived from torch.nn.Module(). As a consequence, they can be composed to build neural network architectures.

Currently implemented linear operator include:

  • centered n-dimensional FFT and iFFT with masking and low rank subspace projection;

  • n-dimensional NUFFT with embedded low rank subspace projection;

  • coil combination and projection operators.

Coil Sensitivity#

deepmr.linops.SenseOp

Multiply input image by coil sensitivity profile.

deepmr.linops.SenseAdjointOp

Perform coil combination.

FFT#

deepmr.linops.FFTOp

Fast Fourier Transform operator.

deepmr.linops.IFFTOp

Inverse Fast Fourier Transform operator.

deepmr.linops.FFTGramOp

Self-adjoint Sparse Fast Fourier Transform operator.

Non-Uniform FFT (NUFFT)#

deepmr.linops.NUFFTOp

Non-Uniform Fast Fourier Transform operator.

deepmr.linops.NUFFTAdjointOp

Adjoint Non-Uniform Fast Fourier Transform operator.

deepmr.linops.NUFFTGramOp

Self-adjoint Non-Uniform Fast Fourier Transform operator.