Figure 3.

Intermediate images in the proposed reconstruction method. Images in the first row are reconstructed using zero-filling and exhibit coherent aliasing artifacts due to the regular undersampling by parallel imaging. Images in the second row are reconstructed using parallel imaging calibrated for a regularly-undersampled pattern. These images do not have coherent aliasing (parallel imaging) artifacts, although images I_t and Ĩ_t exhibit expected spatial blurring and incoherent artifacts due to the IVD undersampling. However, these artifacts can be suppressed in the constrained reconstruction in the next step (bottom equation). Note that although images shown here are coil-combined (for demonstration purpose), the multiplicative constrained reconstruction is applied in a coil-by-coil basis (see Discussion). Also notice that the compensation for non-linear gradient effects is not applied to the intermediate images shown here; instead it is only applied to the image Î_t after the constrained reconstruction and coil combination.