It's funny; I have a theory as to how the image might have been formed naturally through long proximity to a prototype that was originally made from rock bearing sizable amounts of naturally-occurring radioactive materials. Both sides of the authentic/inauthentic crowd have given me grief over it. Both want it to be one thing or the other, and both seem to have a great deal of emotion invested in their respective beliefs.
We now know exactly what the image is composed of. It is a caramel like substance that is the result of a melanoidin reaction. The Shroud fibers are coated with a very fine coating (less than 1/100 the thickness of a human hair) of starch fractions (sugars) deposited on the fibers by the washing of the flax in Soapwort before it was woven into a cloth. This coating exists on both image and non-image areas. However, where there is image, the starch fractions have been chemically changed to a caramel like substance: a melanoidin.
Melanoidins are brown, high molecular weight heterogeneous polymers that are formed when sugars and amino acids combine through a Maillard reaction. Normally melanoidins are created in Maillard reactions with high temperatures in a low-water condition, such as cooking. It is what turns baked goods brown.
High heat cannot be the modality on the Shroud because the temperature required would have converted some of the starches existing INSIDE the Flax itself. The Shroud melanoidins had to have been created with a low-temperature reaction.
One possible, and observed, method of creating low temperature melanoidins, such as are seen on the Shroud although it does not result in such high-resolution images, is the interaction of the starch fractions and certain gases, Putrecine and Cadaverine, that exude from a recently dead body. There are still real problems with the outgassing theory... the images on the Shroud are vertically collimated, both upwards and downwards... something gases just do not do.
Your theory of low level radioactivity, although not seen to produce melanoidins, may be a possible other modality of changing the Starch fractions to the caramel like substance of the image.