Image resizing

[DestinyIsCallin]

How can I resize an image with the following measurements:
Pixel dimensions:
Width: 792 pixels
Height: 528 pixels
Document Size:
Width: 11 inches
Height: 7.333 inches
Resolution: 72 pixels/inch

...to an image of:
Pixel dimensions:
Width: 1500 pixels
Height: 1000 pixels
Document Size:
Width: 20.833 inches
Height: 13.889 inches
Resolution: 72 pixels/inch

without losing quality? Or is there any way to "clear" up the image after resizing?

[RTW1]

You can not resize without a loss of quality, the question is will it be noticeable? That depends on how good the original is.
Use the Bicubic smoother, setting to resize in Photoshop for the best results. Try the despeckle filter found in the filters listed under noise, to clear up some jpeg problems, after using that filter you will nead to re-sharpen just a little.

[jnerf]

You could record a script, that programs one of the function keys
to enlarge a jpg at 10% increments, when clicked
this way you can view it at 100%, while clicking
to arrive where you think the size is suitable, before it gets too pixelated.

[Mike Bailey]

When enlarging an image you are not necessarily loosing quality. You are making the existing pixels larger.

If I want to enlarge an image by 200%. To begin I will enlarge the image to perhaps 400%, then I retouch the image, blur, smudge, filter, layer, ect..., its much easier to remove defects at this resolution. Then reduce down to the final image size.

I use a program called Photo zoom pro to enlarge images. It does a fair job of averaging surounding pixels.

Attached is an example enlargement. The original image is straight out of my little Canon power shot, fairly high res, The only editing was the use of photoshops Dust and scratches filter on the enlargment. I reduced all images for the forum, hopefully you get the idea.