Future work

A further application is sharp image zooming using gradient-based interpolation. From the original $N\times N$ gray-scale image we want to generate an $(s\cdot N)\times (s\cdot N)$ zoomed image. Using traditional resampling methods, the following problems arise:

• linear interpolation would result in blurred edges
• nearest neighbor interpolation would cause staircase artifacts

Therefore the goal is to obtain smooth and sharp edges inside a cell, where the interpolation is performed. The basic idea behind the gradient based interpolation is, that the original image is interpolated in each cell on an $s\times s$ subgrid. At the corner pixels the gradients are estimated from the original pixels (central differences or linear regression). The gradients at the subgrid points are calculated from the gradients of the four corner pixels using bilinear interpolation. The FFT method is performed on the entire $(s\cdot N)\times (s\cdot N)$ image (the gradients are known for each pixel and the intermediate pixel values can be defined as a constant (e.g. the average of the four corner voxels). In the FFT method relatively high S and G parameters are used. The penalty function is defined like in the 2D dedithering case [4].