Bayesian Image and Video Enhancement Using a Non-Gaussian Prior - Nonlinear Signal and Image Processing: Theory, Methods and Applications - page 311

9.4 Simulations

Bayesian MAP estimation is the enhancement technique of choice in the simu-
lations, because of its versatility in showing the difference between linear and
nonlinear solutions. For each image and video observation model of interest
in Section 9.2, the corresponding Bayesian MAP estimation problem is first
derived. Image magnification, low bit rate block-DCT postprocessing, and su-
perresolution video enhancement all have constraints that must be satisfied,
resulting in constrained optimization problems that can be solved using the
gradient projection algorithm. 1 , 8 Empirical simulation studies involving both
linear (Gauss-Markov) and nonlinear (Huber-Markov) Bayesian estimates
are presented. In the simulations, the Gauss-Markov random field model is
implemented by a quadratic edge penalty function with T H

→∞

, whereas
the Huber-Markov random field model uses the convex but nonquadratic
Huber edge penalty function with T H

= .

5. The 1-m IKONOS satellite pic-
ture shown in Figure 9.2 is used throughout all of the simulations, so that each
enhanced image can be compared visually to the same original information.
Furthermore, only gray scale (8-bit) data are used in the experiments, so that
color/multispectral processing does not obfuscate the enhancement results
obtained by applying the algorithms to a single visible band. Finally, a quan-
titative image quality measure such as peak signal-to-noise ratio (PSNR) will
not be used to compare the estimates, because the only truly effective evalu-
ation of an image enhancement scheme is a qualitative visual comparison of
the results. Unfortunately, qualitative interpretations also happen to be quite
subjective, but the true efficacy of any image processing technique lies in the
eye of the beholder, and this should not be swayed by potentially flawed
quantitative assessment measures.

1

9.4.1 Region-of-Interest Image Magnification

Assuming a Huber-Markov random field model for piecewise smooth image
data, the high-resolution image estimate can be computed from a digital image
still as the following Bayesian MAP estimate:

4

T H d n ,m x

x = arg min

x

1 ρ

. (9.38)

∈X

n

m =

This solution is constrained to the set of images

X ={ x : y = Hx } , (9.39)

such that all candidate high-resolution solutions must retain r r block-

wise averages that are identical to the original, low-resolution image y .

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