I have an old photo of my brother which is 29KB and resolution is 461 × 491.
I need to print it in a regular image size.
Is there a way to increase its size/resolution? either by iphone app or desktop software (but not Photoshop)
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Short answer: Oh, boy...
The way exists, of course. However, the quality most probably will be very low because the difference in dimensions are too big.
I assume that "print it in a regular image size" from your question talks about an image somewhere around 6 MPixels, which is rather conservative. Perhaps other would say 8 Mpixels.
Anyway your image is 0.22 MPixels. Waaaay too small. There is way too much information which is missing and even the best interpolation algorithms (aka. resampling kernels) cannot "guess" such a big amount of data to fill it up.
Also, what makes the things worse is that different kernels give different results, depending on what kind of image you have.
If you take this path you can download a free image manager like XnView MP or FastStone Viewer and try there different kernels/methods:
(XnView MP Resize/Resample dialog above)
There are also other algorithms which claim somewhat better results (for ex. Alien Skin Blow Up) but these are not free products (usually these are paid plugins for Photoshop) and, anyway, they claim good resize till "just" @300% in best case which is far away in your case.
Beside above, another thing which you can do is to do the upscale in steps: scale to 200% using the Kernel/Method 1, after this Sharpen if needed, after this scale to 200% using the Kernel 2 etc. Do it step by step and look and how the intermediate steep looks in your eyes. Apply the appropriate filter/scaling algorithm in order to keep the picture 'on track'.
Also, 29KB file size for an image spells to me "JPEG" which is a lossy compression which can have artifacts, complicating the things even more.
OTOH, I didn't saw the picture but if this is a computer art or any other form of imagery which can be traced then there exists another approach: intelligent tracing and resampling - but there you need to be a geek to find/write the program. In this case, tough, the results are quite impressive. Go here and hover the mouse over the blue algorithm names to see the comparison.
In fact this kind of problem is rather art & craft than straightforward. And most probably the result will not hold up to (your) print quality standards.
The act of adding pixels to make the image larger (without adding extra information (this is an important point)) is a basic function of any image processor. There are any number of applications that can do this, however NO image processors can add information to your image, at least not automatically. They can use the information that is already there to have a guess at what might have been there when the photo was taken, but this is not at all perfect and has it's limitations.
You gain very little by enlarging the size of the photo because 461x491 is the entirety of the information that you have to work with. Enlarging the photo can sometimes be useful as it can be used to disguise the edges of the pixels.
Assuming 200 ppi (pixels per inch) as acceptable quality for a regular sized (assuming long edge is 6") print, you would need an image that is 1127x1200 pixels.
Here I have scaled a larger image to 1127x1200, then taken a crop fro the middle, scaled the image to 461x491, taken an equivalent crop and then scaled the image back to 1127x1200 and again taken an equivalent crop. We can see that the original image is sharp and defined, whereas the image that has been scaled back to it's original size after being scaled down is a lot less sharp. This demonstrates that the image has lost a lot of the original information. However we can see that the use of an interpolation method has meant the image may be in a better state for printing (depending on your needs), with less defined edges to the pixels. BUT the scaled images are nowhere near as detailed as the original. I used GIMP for this, which is a free and powerful image editing program.
Original 1127x1200 crop Rescaled 1127x1200 crop using cubic interpolation
Scaled 461x491 crop
Rescaled 1127x1200 crop using no interpolation
You can print a 461 by 491 image at whatever size you want, but it isn't going to have any more detail than it has right now. You can't invent detail, you can create new pixels that will make a smooth shading to make it seem less pixely, but it will then just seem more blurry. Unfortunately, at that low of resolution, you really are not going to be able to do much at any reasonable kind of quality level.