Second-Order Regression-Based MR Image Upsampling

Algorithm 1

Regression-based MR image upsampling.

Input: Low-resolution image

Output: High-resolution image

Initialize: Obtain a denoised version of by using a denoising method, up-scale in the slice-

      selection direction using bicubic interpolation, denote the outcome as .

Mapping function estimation:

() For each image of in the slice-selection direction, generate its smoothed version and

   interpolated version , respectively.

() Partition and into image patches in raster-scan order, so as to construct the LR-HR

   training set ; partition into image patches to construct the LR test patch set .

() For each , estimate the derivatives of the mapping function using Eqs. (6)–(10).

HR image estimate:

() For each patch , search its most similar patch in the LR-HR training set.

() Estimate ’s corresponding HR patch using Eq. (3).

() Generate the HR image by merging all s.

() Correct by enforcing the consistency between and .