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3. A Simple Nonlinear Prediction
In this section, we replace the filter and the interpolator in the previous section by a nonlinear one. These are introduced by Florencio and Schafer [2]. However, they used closed-loop pyramid while we stick to the same structure (open-loop pyramid). Again, the quantizer are fixed with the same step-sizes as the previous section.
Filter

In this section, we don't use any filter. The higher-level image in the Gaussian pyramid is just a subsampled version of the lower-level image.
Interpolator

The interpolator works as follows. We have a lower-resolution image represented by the white pixels in the above figure. We want to interpolate all the pixels shown. There are four categories:

White pixels: Let y2i,2j = xi,j

Red pixels: Consider the one in the middle. Let y2i,2j+1 be the weighted median of xi-1,j, xi-1,j+1, xi,j, xi,j+1, xi+1,j, xi+1,j+1 with weight 1,1,3,3,1,1 respectively.

Blue pixels: For y2i+1,2j, compute the weighted median similar to the red pixels but on the symmetric side.

Green pixels: Let y2i+1,2j+1 be the median of xi,j, xi+1,j, xi,j+1, xi+1,j+1.

where x represents the higher-level image pixel and y represents the interpolated pixels.

The reconstructed image is shown below.
Reconstructed Lena Using Nonlinear Interpolator
Reconstructed image using nonlinear prediction
We can see some improvement over the linear prediction. Edges are preserved and blurring effect is reduced. The PSNR and the bit-rate are shown in the table below comparing to the linear Gaussian filter and interpolator.
PSNR (dB)
bit-rate (bit/pixel)
Burt/Adelson
32.77
0.8278
Subsampling and weighted median interpolator
34.00
0.6544
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