383
d ,d = area of specified "unit area" of dimension d in azimuth
Qa T oa
and dor in range.
el = Capacity relvant to "unit area".
La» Lp = number of looks in respectively azimuth and range
direction relevant to d4 and dr:
Loa». Lor * number of looks in respectively azimuth and range
direction relevant to dg4 and dor:
Yas Yp 7 look overlap in respectively azimuth and range
direction.
The results of (19) are depicted -in figure 1b for the condition L,. = 1,
Loa = 4,,Ya = Yr = 1/3, La = 4Lr and the total number of looks L = La
Lr = 4Lpefor p = 0.7 and r
variance image).
3 (high variance image) and r = 9 (low
Figures la and 1b show that the information content per unit area is low
for relatively low number of looks. Taking the typical case of the Seasat
or ERS-1 radar sensor, when the range and azimuth resolution of the
processed data is approximately 25m, it is evident that for a typical
correlation coefficient of 0.7, the information content is only 0.2 - 0.35
bits per resolution square area with four look processing. Note that this
is only about 50% of the information per unit area provided by an optica!
sensor using 8 bit pixel quantization with a spatial resolution of 80x80m
(like Landsat III). In other words the ratio between the information
content per 8 bit sample of an optical and a radar sensor is at least 15
to 1.
4. RADIOMETRIC RESOLUTION
Rate distortion theory learns that for an information source with variance
c, transmitting through a communication channel with C bits/sample
capacity, the minimum mean square error of the reconstructed signal is
given by:
D(C) m (20)
Applying (17) to each of the channels with the transform coefficient
Z(n,2) as information source, the channel capacity is, using (15) and
{125}:
C(n,2) > 3 1092| —z— (21)
2 qM
where: o (n,2) » c Sn B.
The minimum error per channel is then upperbounded by:
c?(n , 4) o*
p (22)
a, 8) sac.
D(n,2) = 7
ag