Integral logarithmic transforms (LT's) are defined for both one- and two-dimensional input functions. These have the desirable properties of linearity and invariance to scale change of the input. One of the two-dimensional LT's is additionally invariant to rotation. The LT's are conveniently inverted by simple differentiation. Also, they are amenable to optical analog implementation by using incoherent light and simple collimating lenses. As an application, the problem of noise suppression of an arbitrarily scaled image, by using Wiener filtering, is considered. Use of the LT of the image data as a preprocessing step permits the creation of a single Wiener filter optimized for use at all scales of magnification. Finally, application to a problem of character recognition and matched filtering is proposed.