Addition and multiplication of images

Many image processing operations use the addition (or subtraction) of several images, or multiplication (or division), i.e. addition (or subtraction) performed on the logarithm of gray levels. Examples include: offset correction (subtraction) or gain correction (division), recursive filtering (addition), DSA modes (division), double-energy (division), etc.

Consider the addition of two similar images (taken under the same conditions and with the same dose, but not the same image twice!): , the average gray level per pixel, and σ, the noise standard deviation, are identical in both images. If added together, the mean gray levels add up, as do the noise variances σ ² . Noise √σ and SNR (SNR = /√σ) are thus multiplied by √2, a perfectly logical result: image legibility has been improved. If, on the other hand, we...