Javier Portilla, Jan. 26, 2001
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We present a model for natural images with application to noise
removal. The image is represented by a set of subbands in an
overcomplete wavelet.  Each subband is modeled as the pointwise
product of a Gaussian random field and a positive random field (the
multiplier field, MF), which determines its local variance at every
location.  We use a Gaussian scale mixture as a local model for
clusters of neighbor coefficients.  Assuming additive Gaussian noise
of known covariance, and a log-normal distribution for the MFs, we
MAP-estimate the multiplier locally.  Conditioned on its MF, each
subband is estimated through local Wiener filtering.  Unlike related
models, 1) we motivate empirically our choice for the density of the
MFs; 2) we use full covariance matrices of signal and noise in the
estimation, and 3) we include inter-scale connections in the model.
These features allow us to outperform in a MSE sense all previous
methods.  It also can be connected with the normalization models of
Eero and Odelia.