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.
Most of it is based on the Byzantine account of the origin of the Mandylion, which was supposedly discovered bricked-up in a wall of the city of Edessa, along with a "tile" bearing an exact duplicate of the image on the cloth. (A second history gives us both the tile and cloth, but depicts a much more fanciful account of their discovery.) The belief has always been that in the first century, the survivors of Abgar V sealed the image in the city's walls to protect it from his pagan successors, and that it stood there, undisturbed, for 500 years or so, until its discovery. So far as the tile was concerned, the belief was that the cloth image had miraculously transferred itself to the tile.
I'm not prepared to think that a soft image on cloth could produce an image on a piece of stone, but it's easier to think that the reverse might have been the case, particularly if the stone prototype contained significant amounts of radioactive elements, such as uranium and thorium. Given 400 or 500 years of undisturbed proximity, the relief image on the stone might well have "cooked" itself onto the cloth.
The most likely scenario is that Abgar V or someone else commissioned the statuary in remembrance of Jesus. The legend claims that Abgar had the cloth image placed above the city gates to be venerated by those entering the city. But a cloth image, exposed to the elements would quickly have deteriorated. It's more likely that the actual image was in stone, and this was the image that Abgar's successors bricked up into the walls to keep it from the sight of Abgar's pagan successors. This wouldn't have been necessary with a cloth image, which could simply have been folded up and removed.
The cloth itself, which ended up bearing a copy of the prototype, was probably intended as a drapery or covering for the statuary.
At least that's how I perceive it, and I'm not at all trying to push the notion that this is exactly how it would have happened. But I think there needs to be more of an attempt to explain the Shroud of Turin image as something other than either a miracle or a forgery.