and spectral domains. Take video camera images for example. 
Correlations between neighboring frames are strong. Hence, 
images of this kind are able to be compressed with a thousand 
times compression rate. However, satellite image time series 
reflect changes in landscapes which results in a rather weak 
correlation in time domain. And for high-resolution 
panchromatic images, the redundancy mainly resides in spatial 
domain. 
A number of statistical analyses reveal that the grayscales of a 
certain remote sensing image possess the property of the first 
order Markov process, whose covariance may be abstracted as 
(Lin and Zhang, 2006; Hu, 1979) 
1 p p M ae pol 
# ! a 
Czó? 4 1 
p p 1 (1) 
p! 1 
where 6? = variance of signal 
p -autocorrelation coefficient of neighboring pixels 
According to the information theory, the mutual information, 
given two neighboring pixels 7 and (#+1), of their gray values is 
calculated by the following formula (Lin and Zhang, 2006; Tao 
and Tao, 2004): 
I(,t+1)=-In(1- p) Q) 
Hence, the information amount of a rectangular image with L, 
in length and L, in width is 
  
Bal rl x uf es +In(1- p) (3) 
n 
where Ó,,,- standard deviation of noise-disturbed signal 
0, = standard deviation of noise 
In other words, the average information amount of each pixel is 
reduced by In(1 — p) nats, i.e., log, (1 — p)/log, e bits, due to 
the correlation of neighboring pixels. Table 1 lists several auto- 
correlation coefficients and their corresponding reduced 
information amounts, i.e., mutual information. 
  
Auto-correlation coefficients | 0.9 0.8 0.7 0.6 
Mutual information -23 | -1.6 -1.2 -0.9 
  
  
  
  
  
  
  
  
Table 1. Several auto-correlation coefficients and their 
corresponding reduced information amounts (unit: bits) 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
   
The auto-correlations residing in spatial domain of remote 
sensing images, shown in Table 1, reflect data redundancy 
which would be reduced by data compression. 
2.2 Differential Encoding 
The steps of the differential encoding are as follows: 
l. Substitute the difference of gray values pertaining to 
two neighboring rows (or columns), i.e., the ith (/ 2 2) 
and the (i-1)th, for the gray values of Row(or Column) 
i. Thatis, g; 2X; Xj; ,. 
2. Substitute the e difference of gray values pertaining to 
two neighboring columns (or rows), ie., the jth 
( j Z 2) and the (j-1)th, for the gray values of Column 
(or Row) j. That is, gj 7X,—-X.-L 
3. Huffman encoding would be applied to compress the 
obtained difference image ( g; ). 
The three steps are together called bidirectional differential 
encoding. A mutually exclusive execution of Step 1 and 2, 
together with Step 3, may be treated as a uni-directional 
differential encoding algorithm. 
2.3 District Forecast Differential Coding 
From the perspective of information theory, the information 
amount provided by a remote sensing image is not only lying 
on the transit capacity of information during the imaging 
process (Tao and Tao, 2004), but resting with the land objects, 
i.e., the uncertain degrees of landscapes. 
Given a landscape with » possible states, the probabilities of 
which are respectively B, i 2 1,2...,n , the uncertain degree of 
it may be characterized by entropy 
n n 
1 
H= > pilog——=-> pilogp; (4) 
il i i=l 
If a landscape, e.g., built-up areas, is of great uncertainty 
calculated by Formula (4), the information amount of the 
remote sensing image which imaging the landscape will be 
large. Otherwise, a landscape exemplified by seawater would be 
of less uncertainty, whose information amount contained in the 
remotely sensed image could be much smaller compared to the 
built-up areas even if the spatial resolution of the image is 
higher. Therefore, the image covering built-up areas would 
have less redundancy and a higher compression rate than the 
image of seawater even if the images are of the same resolution. 
As a kind of entropy coding method, the encoding efficiency of 
Huffman coding, to a great extent, lies on how accurate the 
prediction on probability distribution of data is. Hence, if we 
are capable of carrying out the histogram statistics of the 
historic images according to the preconcerted satellite orbit, and 
further utilize the statistics to implement district forecast 
differential encoding, the compression rates will be further 
improved.