Resolution Enhancement Using EM Algorithm

The EM (expectation-maximization) algorithm is a broadly applicable method for calculating maximum likelihood estimates given incomplete data [1]. EM algorithms have received considerable attention due to their computation feasibility in tomographic image reconstruction [2~4], symbol detection [5] and parameter estimation [6]. However, it is less recognized that EM algorithms can be equally applicable to image enhancement applications encountered in scanning, reproduction and rendering processes. No past techniques surveyed can incorporate the potentially complex nature of various image formation processes into a simple probability density array as EM procedure does. In this paper, a resolution enhancement method utilizing EM procedure is proposed. By dynamically giving a priori probability distribution suited for a specific application environment currently considered, the proposed method provides a general framework for rendering good image quality at the designated resolution for a large class of image formation process. In the EM algorithm, a postulated, unobservable “complete data set” is employed to facilitate the process of maximizing the likelihood function of the measured data. The actual calculation consists of a sequence of alternating expectation steps (the E-step, in which the conditional expectation of a new likelihood function defined on the complete data set is derived) and maximization steps (the M-step, where a set of new estimates is obtained by maximizing the conditional expectation formulated in the E-step). This iterative process has the desirable properties of maximizing the likelihood function defined on the measured data monotonically, and converging to a global maximum at a unique point [7]. A schematic representation of the application of the EM algorithm to resolution enhancement encountered in the scanning process is showed in Figure 1. A fluorescent light source pulled by a tracking mechanism from top to bottom emits light on the surface of the scanned hardcopy. The intensity of the light reflected is then detected by an array of light sensors. However, the intensity registered by any specific sensor is affected not only by the area bounded by scanner resolution, but also neighboring areas due to the diffusion of light. The proposed method utilizing EM procedure can be used to compensate the above effect, restore the original density, or increase resolution if desired.