Accelerated Computing in Magnetic Resonance Imaging: Real-Time Imaging Using Nonlinear Inverse Reconstruction

Figure 4

Flowchart of the operator . The implementation of the weighting matrix and its adjoint applies a diagonal weighting matrix and a forward or inverse fast Fourier transform (FFT, iFFT) for each channel. The derivative of the multiplication of the image and the coil sensitivities and its adjoint are composed of pointwise multiplication , addition (+), and summation () operations. The combination of the nonuniform Fourier transform and its adjoint 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.