Improving the quality of a blocky image

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Does anyone have any idea how I could go about converting jacko's
method using Photoshop into a format I could perform using Matlab?:

Some idea but don't know how exact this is

1) scale to twice size x and y, with the interpolated value depending
on the weighted sums of the four by four grid of pixels surrounding it
(i think this is bicubic).
2) quantize each pixel to 1 bit black or white and diffuse the
risidual error of the quantization into surrounding pixels at 1/12 for
a corner and 1/6 for a side. then see if any pixels changed their
final 1 bit quantization and repeat risidual diffusion. look up floyd
steinberg for the absolute best on this. This process diffuses the
block boundries which have been smoothed into each other but the image
looks VERY pixelated. but the noise is all above 4 pixels in
frequency, well most of it.
3) then blur it by bleeding pixels into each other, via a low pass
filter set to use only closest neighbours (i think thats what happens)
this is done twice as a third time has not much percievable
improvement (not any).
4) all the noise is in the high frequencies and so a weighted SNR
would benefit my methods.

hope this helped.

Sorry to industrial one for making this a fourth post in a row, but I
should point out that if floyd-steinberg dithering is used to
preprocess an image to reduce the colour plane, then maybe a walsh
transform would suite the process better than a DCT.

just a thought.

cheers

And my final word on the matter is that I guess the phase of the walsh
functions at high frequencies (in the oversample range particularly)
do not matter as much as single pixel errors in location are less
objectionable than multi pixel mis location errors of the lower
frequencies. Also the huffmann overhead of variable length symbols is
avoided. A slight noise bleed is tolerable.

Maybe constraining dithering to horizontal scan lines helps with the
amount of oversampling needed, but maybe it doesn't. Work with 1 bit
DACs suggests a 4 * oversample is sufficient.

cheers.

p.s. I say no more.