Purple is a hard color to capture using a camera. White balance, lighting, brand/model of camera, nothing will help. Purple ends up looking like blue in pictures.
So this requires editing the image to get purple right. Cannot just immediately upload a picture if it is purple you are interested in!
Most times just need an easy fix. Use the Hue color editing tool, change the hue for the blue color by moving it towards the red/purple side.
Using Gimp:
1. (Optional) Select the region to be affected. Using the rough selection free-select hand tool is good enough. Just need to exclude other bluish (or bluish-white) areas of the picture. In many cases, this may not be necessary at all, just apply the hue change to the entire picture and it may be good enough.
2. Use the Colors -> Hue-Saturation command. Select the blue primary color to adjust. Move the Hue slider rightwards, as much as needed.
For this example, a +30 change to Blue Hue was applied.
Now the Balloon Princess has the dress in the color she wants - purple!
Additional info:
The Color Purple and the Digital Camera shows how to use the HSL tool to fix problem colors such as purple, magenta, or dark pink.
Purple, the fake color? shows the hues in the standard color wheel and the spectral-frequency based colors, and explains purple color in detail.
color problem with D2x discussion for this "why is purple blue" problem.