Fourier Transform

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.