Image detection noise is a fundamental limitation in picture processing, whether analog or digital. This noise is characteristically signal-dependent and this signal-dependence introduces significant problems in the design of appropriate noise-suppression techniques. This paper outlines some recent results obtained by the authors in the optimum suppression of two types of signal-dependent image noise: film-grain noise and photoelectron shot noise. The work in grain noise suppression involves deriving the minimum-mean-square error Wiener filter for a new form of signal-dependent noise model suggested in earlier work by T. S. Huang. Implementation of these filters by either coherent optical or digital processing techniques is possible. Digital computer simulations of grain noise suppression using two particular cases of this additive, "signal-modulated" noise model were performed. They demonstrate the potential advantages of noise suppression filters which make use of a priori knowledge of the signal-dependent nature of the grain noise. The results of work on linear, unbiased restoration of images recorded in the presence of photoelectron noise are summarized. Additional work in both of these areas is suggested, with a particular need existing for correlating the properties of various models proposed for grain noise with experimental data obtained on emulsions using scanning microdensitome ters.