Auto-regularized Gradients of Adaptive Interpolation for MRI Super-Resolution

In this paper, a method for adaptive pure interpolation (PI) of magnetic resonance imaging (MRI) in the frequency domain, with gradient auto-regularization, is proposed. The input image is transformed into the frequency domain and convolved with the Fourier transform (FT) of a 2D sampling array (interpolation kernel) of initial LxM size. The inverse Fourier transform (IFT) is applied to the output coefficients and the edges are detected and counted. To get a denser kernel the sampling array is interpolated in the frequency domain and convolved again with the transform coefficients of the original MRI image of low resolution and transformed back into the spatial domain. The process is repeated until a maximum count of edges is reached in the output image, indicating that a local optimum magnification factor has been attained. Finally, the edges are sharpened by using an auto-regularization method. Our procedure is deterministic and independent of external information of large databases of other MRI images for obtain the high resolution output image. The proposed system improves the bi-cubic interpolation method by a mean of 3dB in peak of signal-to-noise ratio (PSNR) and until 6 dB in the best case. The structural similarity index measure (SSIM) is improved over bicubic interpolation with a mean of 0.04 and until 0.08 in the best case. It is a significant result respect to novel algorithms reported in the state of the art