This can be done manually by simply creating an orange layer on top of a white layer and reducing the opacity of the orange layer until it produces the same RGB value as the PNG image, but this is a pretty tedious process, and I'd only recommend that if you only have a handful of pixels you need to calculate the alpha channel for.
A better way of doing it is to open the image in Photoshop, then go to
Channel Mixer... and select the "Black & White Infrared (RGB)" preset. This will turn the image into B&W, with the orange parts black. Now copy the new B&W image and paste it into a new channel.
At this point, you would normally just load the selection from the channel to create the "V" layer. However, your image has been lossily compressed using indexed colors. So if you look closely, you'll notice that the previously orange area is actually a very dark gray with a grid pattern from the dithering, and the outer edges of the V actually look darker than the rest of the BG area.
To fix this, with the new channel active, go to
Replace Color..., click on the damaged background region, and put in the following settings:
- [x] Localized Color Clusters
- Fuzziness 10
- Lightness -100
Now the new channel should look nice and clean, with the background area completely black and the "V" region completely white, with nice clean antialiasing. Now you can load selection from the channel and create a new fill layer with it. Then you can apply a gradient fill to the original PNG layer or create it in a new layer.
Alternatively, with really simple geometric shapes like this, you could just recreate it in Illustrator using vector shapes. This is usually my preferred method, since it makes the image more flexible.