A high-resolution (HR) MRI capable of resolving the detail of bony structures at sub-millimeter resolution is desired. A short MR acquisition results in under-sampled k-space data below the Nyquist rate, leading to artifacts and high noise. We developed an HR reconstruction method regularized by a complex deep-learning prior (RECD). We achieved high-resolution MR (0.6x0.6x0.8mm3) with a one-minute acquisition time. Using images reconstructed from a 5-minute MR scan as the gold standard, we compared the peak signal to noise ratio (PSNR) and similarity index (SSIM) for 1-min RECD and 1-min compressed sensing (CS) reconstructed images. RECD outperformed CS.