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.