Figure 4.

Flowchart of the operator $D{\widehat{F}}_{{\widehat{x}}_n}^{H}D{\widehat{F}}_{{\widehat{x}}_n}$. The implementation of the weighting matrix W⁻¹ and its adjoint W^−H applies a diagonal weighting matrix D_W⁻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 c_j and its adjoint are composed of pointwise multiplication (∗), addition (+), and summation (∑) operations. The combination of the nonuniform Fourier transform and its adjoint ℱ^Hℱ 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.