Bayesian Image and Video Enhancement Using a Non-Gaussian Prior - Nonlinear Signal and Image Processing: Theory, Methods and Applications - page 296

FIGURE 9.1
Superimposed low-resolution and high-resolution pixel grids, related by the downsampling/
upsampling factor r . The shaded low-resolution pixel contains 16 square high-resolution pixels,
for an upsampling factor of r = 4 in both the horizontal and vertical directions. For the high- to

low-resolution mapping y = Hx defined in this chapter, each low-resolution pixel value is set

equal to the average of the r r square high-resolution pixels contained within its boundary.

This serves to model the integration of light over each sensor's physical area.

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The remotely sensed image of a farm near St. Thomas, North Dakota, is shown
in Figure 9.2, captured by the IKONOS satellite with a 1-m ground sampling
distance (GSD). As the acquired imagery is successively downsampled, an ap-
pearance of “blockiness” results because high-frequency structures become
more and more aliased. Interpolation or reconstruction techniques are used to
recover the original (generally unknown) data from its undersampled, lower-
resolution observations. Several popular techniques exist for the interpolation
of digital still images. These include one-shot methods such as bilinear and
cubic B-spline interpolation, as well as incrementally more accurate itera-
tive techniques such as deterministic Tikhonov regularization and stochastic
Bayesian maximum a posteriori (MAP) estimation. 1
Block-based coding is pervasive in commercial image and video compres-
sion algorithms. The Joint Photographic Experts Group (JPEG) standard, 2
which applies the discrete cosine transform (DCT) to 8 8 pixel blocks

throughout an image, achieves compression ratios on the order of 20:1 through
the quantization of high-frequency DCT coefficients with very little loss of
visual quality. Because the human visual system does not perceive high-
frequency information as readily as low-frequency content, lowpass filter-
ing of the 8

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8 frequency squares through the quantization of DCT coef-
ficients is quite effective at reducing the data volume without severely de-
grading the visual information. For the most part, an arbitrary single-band
image coded with a bit rate as low as 0.5 bits per pixel (bpp) generally does
not appear to have highly noticeable distortion. Figure 9.3 presents the 1-m
IKONOS satellite image compressed at successively lower bit rates, in which
the image content tends to be degraded. As the bit rate decreases, the result-
ing coded image loses more and more high-frequency content. Specifically, for

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