Fourier Transform

Sub-package containing Fast Fourier transform routines.

FFT routines include:

• centered n-dimensional FFT and iFFT;

• n-dimensional sparse uniform FFT/iFFT with embedded low rank subspace projection;

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

Centered FFT

deepmr.fft.fft	Centered Fast Fourier Transform.
deepmr.fft.ifft	Centered inverse Fast Fourier Transform.

Sparse FFT

deepmr.fft.sparse_fft	N-dimensional sparse Fast Fourier Transform.
deepmr.fft.sparse_ifft	N-dimensional inverse sparse Fast Fourier Transform.
deepmr.fft.plan_toeplitz_fft	Compute spatio-temporal kernel for fast self-adjoint operation.
deepmr.fft.apply_sparse_fft_selfadj	Apply self-adjoint Fast Fourier Transform via Toeplitz convolution.

Non-Uniform FFT (NUFFT)

deepmr.fft.nufft	N-dimensional Non-Uniform Fast Fourier Transform.
deepmr.fft.nufft_adj	N-dimensional adjoint Non-Uniform Fast Fourier Transform.
deepmr.fft.plan_toeplitz_nufft	Compute spatio-temporal kernel for fast self-adjoint operation.
deepmr.fft.apply_nufft_selfadj	Apply self-adjoint Non-Uniform Fast Fourier Transform via Toeplitz Convolution.