1. EL Kourd kaouther

2. Plan of WorkPlan of Work
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3. 3
IntroductionIntroduction
In statistics, nonlinear regression is a form of
regression analysis in which observational data are modeled
by a function which is a nonlinear combination of the model
parameters and depends on one or more independent
variables. The data are fitted by a method of successive
approximations.
Some nonlinear regression problems can be moved to a linear
domain by a suitable transformation of the model
formulation.

4. 4
For example, consider the nonlinear regression
problem:
With parameters C, and error e. If we take the
logarithm of both sides, this becomes.
Y: vector(normal image) ; F:vector(pathologic image); c:parameter ;e:
error
Y= F*c+e
Where: Y=lny

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The problem of this work is:
Defined the least square ?What is the estimate ?
What are the statistical techniques applied ?
What is the difference between Fisher(f) and Student(t)
for linear & non linear model to extract the lesion?

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Expression of linear model
Minimise the error (Q) by using the difference beween Y &
Y estimate.
least square methode

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Student test:
To compeer between two samples means independant

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Equation of fisher sneidicor f-test
where: α=0, 01
R²: Correlation parameter

9. Conception & result
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ALGORITHM
It must convert the image using MRI software (Dicom, Mrirco, SPM ...) to a further form
(jpg.png, nii, img, hdr ... ... ..) to allow working with matlab.
•Recognition of a sample image by the demand for doctor
•Analysis of the sample: This step is composed by the following:
-Data analysis: the composition protocol.
-Application of the method of least square
-Application of the method F-test and T-linear test
-Application of the method F-test and T-test non-linear
•Comparison between F-test and T-linear test
•Comparison between F-test and T-test non-linear .
•The results obtained and information technology the most accurate.

11. .Data analysis (Protocol)
This protocol is for a patient aged 46 years , sulfur
headache with vomiting and syncope in a jet-resistant or
treatment.
The patient is made by an MRI scan with injection of
contrast.
The machine uses radiation is of type "SIEMENS" with
a field B = 1.5 tesla.
The sequences performed in T1 and T2.
The result shows:
Presence –tumor 74*53*60 sat frontal-parietal trio's
structure: scattered calcifications, cystic and fleshy
necrosis.
Irregular-device.
-Presence of a cyst-like extra-brain producing a mass
effect on the cortex. Fig
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Surface 36*36
ttest non linear(exponentiel)
10 20 30
10
20
30
ttest linear
10 20 30
10
20
30
ftest non linear(exponentiel)
10 20 30
10
20
30
ftest linear
10 20 30
10
20
30
0 10 20 30 40
0
0.005
0.01
0.015
0 10 20 30 40
-2.5
-2
-1.5
-1
-0.5
0
x 10
-3
0 10 20 30 40
0.34
0.345
0.35
0.355
0.36
0.365
0 10 20 30 40
0.36
0.365
0.37
0.375
tes, r:tnlin

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Surface 56*56
ttest non linear(exponentiel)
10 20 30 40 50
10
20
30
40
50
ttest linear
10 20 30 40 50
10
20
30
40
50
ftest non linear(exponentiel)
10 20 30 40 50
10
20
30
40
50
ftest linear
10 20 30 40 50
10
20
30
40
50
0 20 40 60
0
2
4
6
8
x 10
-3
0 20 40 60
-8
-6
-4
-2
0
x 10
-3
0 20 40 60
0.564
0.565
0.566
0.567
0.568
0.569
0 20 40 60
0.565
0.566
0.567
0.568
0.569
0.57
tes, r:tnlin

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ttest non linear(exponentiel)
20 40 60 80
20
40
60
80
ttest linear
20 40 60 80
20
40
60
80
ftest non linear(exponentiel)
20 40 60 80
20
40
60
80
ftest linear
20 40 60 80
20
40
60
80
96*96
0 50 100
0
0.2
0.4
0.6
0.8
1
x 10
-3
0 50 100
-3
-2
-1
0
1
2
x 10
-4
0 50 100
0.76
0.78
0.8
0.82
0.84
0.86
0 50 100
0.8
0.82
0.84
0.86
0.88
0.9
tes, r:tnlin

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Surface 120*120
ttest non linear(exponentiel)
20 40 60 80 100 120
20
40
60
80
100
120
ttest linear
20 40 60 80 100 120
20
40
60
80
100
120
ftest non linear(exponentiel)
20 40 60 80 100 120
20
40
60
80
100
120
ftest linear
20 40 60 80 100 120
20
40
60
80
100
120
0 50 100 150
-6
-4
-2
0
x 10
-3
0 50 100 150
0
1
2
3
4
x 10
-3
0 50 100 150
1.22
1.225
1.23
1.235
0 50 100 150
1.22
1.225
1.23
1.235
tes, r:tnlin

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General Conclusion
According to these executions, we can notice that:
Fisher-nonlinear is more accurate than other techniques for small areas.
-From theory of reference; that student is used for middle & small samples; and fisher is used
for any problem need to precise the measure of physic-chemic kind . from our work we can
see the following result:
- The results for F-test(fisher) linear and nonlinear (exponential) are with same result.
-F-test accuracy lost response for a sample greater than 69.
There isn't response if the values of t (student) or f (fisher) with negative sign.​​
Does non-linear test is completely different to the linear t-test, and can perform the lesion area
for small and medium surface against the other t-test is only liable for large surface.
-Although we did not use directly the test using the hypothesis, but we have obtained results
consistent with the picture.
:

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