Figure 4.
Flowchart of the operator . The implementation of the weighting matrix W−1 and its adjoint W−H applies a diagonal weighting matrix DW−1 and a forward or inverse fast Fourier transform (FFT, iFFT) for each channel. The derivative of the multiplication of the image ρ and the coil sensitivities cj and its adjoint are composed of pointwise multiplication (∗), addition (+), and summation (∑) operations. The combination of the nonuniform Fourier transform and its adjoint ℱHℱ is implemented as a convolution with the point-spread function, consisting of a mask (msk) restricting the oversampled grid to the field of view, application of fast Fourier transform and its inverse, and a pointwise multiplication with the convolution kernel (P). Padding (pad) and cropping (crop) operations are used to reduce computational cost in the overall iterative algorithm.