Image Degradation due to Interacting Adjacent Hot Pixels

Hot Pixels are cosmic ray induced digital imaging sensor defects that accumulate as the camera ages at rates that are highly dependent on pixel size. We previously developed an empirical formula projecting hot pixel defect density (defects/year/mm2) growth rates via a power law, with the inverse of the pixel size raised to the power of $\sim $3, multiplied by the square root of the ISO (gain). We show in this paper that this increasing defect rate results in a higher probability that two defects will occur within a 5x5 pixel square. Under these conditions, the color demosaicing and JPEG image compression algorithms required for picture creation greatly amplify the impact of these two defective pixels, spreading damage to a 16x16 pixel area and creating significant color changes resulting in a very noticeable image degradation. We develop an analytical generalized birthday problem formula in order to estimate the number of hot pixels needed to achieve a given probability of having two defective pixels within a 5x5 square. For a 20 Mpixel DSLR camera, only 128 hot pixels generate a 4.5% probability of such interacting defective pixels, or 1 in 22 cameras. For 4 micron pixels this would occur in 1.4 years at ISO 6400, and in 3.2 years at ISO 3200.