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What is the best way to resize an image without any loss in quality? I have a wallpaper that is 1280x960 and I want to make a few copies of it at different resolutions. What's the best way todo this?
If you want to print it, you have to change the resolution. This will reduce the size when printed, assuming that you now have 72dpi and go to 150->300.
To change the size of the image on any monitor (I do suppose you're reffering to screen resolution), you have to make the bitmap smaller, meaning that PS will have to discard/kill [slick] /eliminate certain pixels, so that you lose information and quality.
Best way to do this is:
1/ do it in several steps
2/ always take random (though still smaller) numbers that have no connection (half, one third,...) to the original so PS cannot simply dicard, say one out of two pixels, but has to recalculate.
Because of the loss of information, your image will be a bit blurry and lack a tad of dynamic range. So Unsharp mask it a bit, and give it a gentle curves treatment to enhance the quality.
Remember that you van open a duplicate, so you can see and compare. Keep in mind that if PS shows something at less than 100%, you don't see all its pixels, so it will also have a blurry quality over it.
In fact, this is something I remarked. When you use Gaussian Blur, you lose dynamics.
try it out yourselves: Open a new doc, press D for black and white Default colours and drag a gradient. Open Levels and check that the full range is there.
Now posterize in say some 24 steps, and apply a Gaussian Blur of say 10 pixels to show clearly what I mean. Now reopen your levels, and look at the place of the sliders vs the histogram: the histogram has shrunk, meaning that your image lost dynamics and you have to enhance a bit.
Resizing 
Linear Mode
