Formula for NR vs image resizing

Started 2 months ago | Discussions thread
hjulenissen
Senior MemberPosts: 1,593
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Re: Formula for NR vs image resizing
In reply to Joofa, 2 months ago

Joofa wrote:

Hi,

It has been a while since I wrote the above. Reading the above it seems like I said that the quoted numbers in (1)-(4) are for a 1-D downsampling using a window of 4. So in this case, for a constant signal, the expected improvement is 6db and not 3db.

Furthermore, for a constant signal, the best NR is obtained using averaging filter (which gives 6db in this case) so it is better than sinc and lanczos. The latter filters are better than averaging for preserving signal (image) detail, when doing downsampling. However, a constant signal has no detail, just that we don't know the exact value of that constant, that we want to recover. It becomes an estimation problem at this stage. It is important to realize that these numbers are only valid for L2 approximation (estimation). Other methods, such as L1, etc., give some other values. Selection of a metric (say L2) is very important, however, most discussion don't even mention it since the underlying assumption is implicitly L2.

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Surely, any amount of SNR improvement can be dialed in by moving the filter cutoff frequency towards zero? Of course, this will also affect any desired signal in the affected frequency range.

Which brings me to my point in the earlier discussions. Downsampling can be seen as a lowpass filter followed by sample dropping. The latter won't affect noise significantly, so we might as well just discuss how lowpass filters affects "image quality".

I guess that some Wiener-derived filter is going to maximize squared error or some other simple metric. Who knows what filter is perceptually ideal for a given image, but I think that nonlinear, signal-adaptive filtering is a lot more interesting.

-h

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