The influence of granularities in the background suppressed phase of susceptibility‐weighted images (SWI) and susceptibility‐weighted angiogram (SWAN) becomes significant when the susceptibility based contrast is enhanced by exponential weighting of the high‐pass filtered phase. Furthermore, the effect of noise due to the inherently low signal‐to‐noise ratio resulting from high‐resolution SWI/SWAN acquisition, can be minimized by application of edge‐preserved denoising of the channel phase images without loss of venous structural details. Simultaneous reduction of granularity effects with edge‐preserved denoising is achieved using the proposed granularity controlled adaptive edge‐preserved regularization (GRADER). In this approach, the edge‐preserving cost is minimized with respect to the desired channel phase image and an unknown scale parameter that adaptively tunes the high‐pass filter. The algorithm is implemented using quasi‐Newton type iterations, with the scale parameter updated using a search procedure in each alternating minimization step. The iterations are stopped once the scale parameter converges to a steady state value. Extension of GRADER to parallel MRI (pMRI) by processing the real and imaginary components of complex channel images (IR‐GRADER) results in enhanced susceptibility‐related contrast‐to‐noise ratio of the magnitude SWI, leading to improved visualization of superficial veins and deep gray matter structures.