We introduce a new approach to optimal image scaling called Res-
olution Synthesis (RS). In RS, the pixel being interpolated is £rst
classi£ed in the context of a window of neighboring pixels; and
then the corresponding high-resolution pixels are obtained by £l-
tering with coef£cients that depend upon the classi£cation. RS is
based on a stochastic model explicitly re¤ecting the fact that pix-
els falls into different classes such as edges of different orientation
and smooth textures. We present a simple derivation to show that
RS generates the minimum mean-squared error (MMSE) estimate
of the high-resolution image, given the low-resolution image. The
parameters that specify the stochastic model must be estimated be-
forehand in a training procedure that we have formulated as an
instance of the well-known expectation-maximization (EM) algo-
rithm. We demonstrate that the model parameters generated during
the training may be used to obtain superior results even for input
images that were not used during the training.
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