1Cp)1 2Cp)2 3Cp)3 4Cpd4 
1(p>2 2Cp)3 3Cp)4 4Cpd0 
1(p>3 2Cp)4 3Cpd0 , 
1€p4 2(p»0 
4 0 
and S) SCIO A. 
J=1 
In which, the sub-composition form ( 1(p)1 2(p)2 
3(p)3 4(p)4 ) represents probability distribution 
subspace of first class enhanced results,which can 
fully reflect the grade of actualities signals 
hidden in original image. ( 1(p)2 2(p)3 3(p)4 
4(p)0O ),...and so on respectively represents vari-: 
ous probability distribution subspaces responding 
to those enhanced results reduced to a lower class 
orderly,in which , enhanced result responding to 
( 1(p)O ) is low class. 
3. THE CALCULATION OF ENTROPY H(a) 
AND INFORMATION LEVEL IL. 
Entropy H(@ ) is a indeterminateness measure of 
random experiment a. If a has n mutually 
incompatible results having respective probability 
Pi, then according to the entropy definition, the 
entropy value whose unit is bit can be obtained by 
following formula: 
n 
H(a)=-Z Pi: log Pi, ZPizl. (1) 
i=1 
Where,the logarithm base number is 2,in results of 
equal pobability (Pi distribution is uniform), the 
indeterminateness is maximum, its value is logn; 
when some one Pi equals 1 (Pi distribution is 
highly concentrated) , the decisivity is maximum, 
its entropy H(a)z0. 
Placing composite probabilities I(p)j into formula 
(1) respectively, can obtain the combined entropy 
H(Y,X) of experiment Y and X. 
In respect to the actualities signal Y at input 
end, its probability distribution composition form 
can be written by its grade I as follows: 
1 2 3 4 
PyCl> PyC2d PyC3) PyC4) 
Py(I) are probabilities corresponding to mutually 
incompatible results I (I-1, 2, 3, 4),which can be 
obtained by composite probabilities I(p)J: 
Py(1)=1(p)1+1(p)2+1(p)3+1(p)4+1(p)0 
Py(2)=2(p)2+2(p)3+2(p)4+2(p)0 (2) 
Py(3)=3(p)3+3(p)4+3(p)0 
Py(4)=4(p)4+4(p)0 
To place Py(I) into formula (1) respectively, the 
a-priori indeterminateness of experiment Y, or 
entropy H(y), can be obtained. 
In respect to the gain signal X transformed by a 
certain function at output end, the following 
probability composition form can bè written 
by grade J as follows: 
1 2 3 4 0 
Px(1) PxC2) Px(3) Px(4) Px(D) 
Probabilities Px(J) can be obtained by following a 
set of formulas: 
Px(1)=1(p)1 
Px(2)=1(p)2+2(P)2 
Px(3)=1(p)3+2(p)3+3(p)3 (3) 
Px(4)=1(p)4+2(p)4+3(p)4+4(p)4 
Px(0)=1(p)0+2(p)0+3(p)0+4(p)0 
64 
To place Px(J) into formula (1),can obtain entropy 
H(X) of experiment X . 
Under conditions of understanding random 
experiment X at output end, the posterior 
indeterminateness of experiment Y, or conditional 
entropy H(Y/X), can be obtained. the indeterminat- 
eness H(Y,X) combined by random experiment Y with 
X, should be sum of X experiment one H(X) and Y 
experiment posterior one H(Y/X), thus: 
H(Y/X) zH(Y,X) -H(X) 
The transform from H(Y) to H(Y/X) explains that 
the Y signals indeterminateness is reduced as a 
result of function transform, from the information 
theory definition, this absolute reduced content 
is just information content (I)concerned with such 
signals Y which are contained by signals X,thus: 
(I)zH(Y)-H(Y/X) zH(X) -H(Y) -H(Y/X) 
Function Information Level IL, or probability of 
its obtaining information in the Y signals a-prior 
indeterminateness, oan be obtained by following 
formula: 
IL=(1)/H(Y)=[H(X)+H(Y)-H(Y/X)] “H(Y) (4) 
IL reflects total enhancement benefit of function, 
and will not vary with different information 
source , thus it represents function reliability, 
should be used as a reliable basis for evaluating 
enhancement effect. 
4, ANALYSIS OF THE IL CALCULATION FORMULA. 
With respect to the IL calculation formulas (1)--- 
(4) , whose theoretical base is reliable. From 
analysis of formula (4) , H(Y) represents a-prior 
indeterminateness, which does not relate to 
funcfion transforming, any function having higher 
IL value must embody that its H(Y, X) wants small 
and H(X) wants large. those I(P)J concentrating in 
any range of probability space all can send H(Y,X) 
becoming small, but H(X)can not necessarily become 
large. the composition of formula (3) has limited 
concentrative ranges of I(P)J destribution, only 
such I(P)J distribution concentrating in ( 1(p)l 
2(p)2 3(p)3 4(p)4 )and ( 1(p)2 2(p)3 3(p)4 4(p)O ) 
subspaces mostly oan send Px(J) distribution 
trending toward uniformization and cause H(X) to 
become large. It may be seen , that any function 
having higher IL value can actually or 
approximately reflect the attainable enhanced 
grade of signal Y hidden in original image. 
5.THE CALCULATION PATTERN FOR FIRM STATISTICS 
I(P)J distribution is concentrated in probability 
space for the function self enhancement feature. 
When the statistical number N ( or probability 
denominator) reach a certain number,even if adding 
some I(C)J results into N,the I(P)J total distrib- 
ution range can not be changed for this reason, in 
the mean time I(P)J change rate is small,IL calcu- 
lation places oneself in the firm state. Theoreti- 
cally N should be infinite, when the N is finite, 
reducing signal dividual grade or applying 
Feedback Dynamic Recognition Pattern can attain 
the purpose of firm statistics. 
This pattern is to add statistic number N 
progressively and quantitatively , to observe the 
dynamical variation range of calculated IL value 
for each time, if and when the calculated values 
oscillate in smaller dynamic range time after 
time, the 
consider 
Through 
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IL% 
30 
  
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