# Image Oversampling Technique - Pushing the boundaries of digital imaging ( Nokia Lumia 1020 smartphone )

## Image Oversampling Technique - Pushing the boundaries of digital imaging ( Nokia Lumia 1020 smartphone )

Please take a look at a very interesting White Paper related to Image Oversampling Technique:

Pushing the boundaries of digital imaging ( Nokia Lumia 1020 smartphone )

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'Like' : This advertizement article is a good introduction for anyone interested in image quality.

The article suggests reducing the 40-Mpix image into a smaller size image (Oversampling, or  "super-resolution" in the article), using a rectangular window algorithm,                         Output(x,y) =  sum{ tx=1:M , ty= 1:M }  { Input( M*x+tx, M*y +ty) }

In my personal experience, better images are obtained with the 'Gaussian' window, or  the simpler 'OneCos' window,

Output(x,y)  =  sum{ tx= 1:2M, ty= 1:2M}  { Input(M*x+tx, M*y+ty) * W(tx) * W(ty) }          where  2*W(t) = 1 - cos( pai*(2*t-1)/2*M ).

In my experience, I have not found  any significant improvement using Gaussian reduction  W= exp( -2t*t/M/M ) over the OneCos algorithm. This is probably due to noises in the image. Theoretically, the Gaussian window should have a small advantage.

Photons are discrete quantities. Electrons and charge-carriers happen discretely, never 0.6 of a carrier. This causes a quantum-mechanics noise, termed 'Poisson's photons noise'. It states that If the expected number of photons is N0, you will measure all kinds of results, distributed around N0 with a Poisson's distribution, with a standard deviation of sqrt(N). With high-quality  CCD detectors, and pixels 11X11 microns large, this quantum noise is S/N > 1/300.

The Nokia imager boasts pixels 1.1 X 1.1 microns large. I estimate its noise figure to be much worse,  S/N ~~ 1/30 or worse (40 Mpix image).

Errata: Should be S/N < 1/300  ( on the third line from the bottom)/

>>...In my personal experience, better images are obtained with the 'Gaussian' window...

It would be nice to see test images to prove that statement. Modern algorithms for increasing image resolution do some magic and some Sony cameras have it for more than one year already. Even very simple FFT-based algorithm does a pretty good job when increasing resolution of an image up to 4x or 8x.

>>...The Nokia imager boasts pixels 1.1 X 1.1 microns large. I estimate its noise figure to be much worse...

As soon as www.dpreview.com will add test images at different ISOs with their standard test scene I will let you know.

>>...Even very simple FFT-based algorithm does a pretty good job when increasing resolution of an image up to 4x or 8x...

Here is example:

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An FFT filter and a sliding smoothing windows are equivalent ways of performing the same mathematical transformation. It is two ways of computing the same thing. The local sliding-window allows one to change the filter locally, because middle-of-the-image has much higher resolution then side-of-the-image.

(FFT)   (a)  f(qx,qy)=FFT( I(x,y) )  ;  (b)   bf (qx,qy) = G(qx,qy)*f(qx,qy) ;  (c)  FI_new = IFFT( bf(qx,qy) )

( Real_space)     RI_new( x,y)  =   {sum{tx,ty} }  { RG(tx,ty)*I(x+tx, y+ty) }

==> As long as  G(qx,qy) = FFT( RG ) ,  RI_new(x,y) = FI_new( x,y)

Your example shows an amazing performance in expanding an image. The image on the right has at least 8 times more pixels then the source on the left.  I have seen such feats before only where the exact reduction formula was known, either in mathematical simulations or reduced images. In real-life situations, the lens MTF changes over the field of view, turbulence smears the image or deforms it, and non-ideal optics complicates everything further. I have never seen a real-life raw image (as out of the camera) expanded with such a performance.

But all that is beside the point. I was talking about the best way to REDUCE (compact) the image.

>>...But all that is beside the point. I was talking about the best way to REDUCE (compact) the image.

Thank you for all your comments and I found them very interesting.

Speaking about Nokia Lumia 1020 smartphone I consider that device as one of the Most Innovative Gadget of 2013 year.

>>...As soon as www.dpreview.com will add test images at different ISOs with their standard test scene I will let you know.

It usually takes some time and here is another update about the device and its capabilities:

Web-article: First impressions and photos from Nokia's 41MP Lumia 1020