Very interesting. I will be digging into this one. The first thing that popped out at me:
> We can decompose a given image into the three color channels red, green and blue. Each channel can be represented as a (m × n)‑matrix with values ranging from 0 to 255. We will now compress the matrix A representing one of the channels.
I wonder if the author considered converting to YCbCr colorspace first. The luminance component (Y) is substantially more important to the human visual system than the Cb/Cr components. Some subsampling of the chrominance components would probably work well in these schemes.
This leaped out at me too. Doing lossy compression on RGB is not setting yourself up for success. Of course, then you'd need two sliders in the UI; one for how much to compress the Y and one for the CbCr.
SVD also works on complex matrices. I imagine there's value in compressing the subsampled Cb/Cr channels as real/imaginary components in a complex matrix.
The representation by SVD would work almost identically. SVD is one of those absolutely magical, amazing algorithms that power a ton of things we do every day.
Especially if YCbCr is a linear transform of the RGB. (I'm not sure if it is, but it's likely to be close). If it is, it's essentially just making eigenvectors from a matrix with a different set of bases.
> We can decompose a given image into the three color channels red, green and blue. Each channel can be represented as a (m × n)‑matrix with values ranging from 0 to 255. We will now compress the matrix A representing one of the channels.
I wonder if the author considered converting to YCbCr colorspace first. The luminance component (Y) is substantially more important to the human visual system than the Cb/Cr components. Some subsampling of the chrominance components would probably work well in these schemes.