Bayesian Maximum Entropy Based Algorithm for Digital X-ray Mammogram Processing
Abstract
:1. Introduction
2. Methods
2.1. Inverse problems
2.2. Bayesian image modeling
2.3. Image entropy
2.4. Bayesian image restoration
Likelihood
Prior probability
Posterior probability
2.5. Regularization of the inverse problem
2.6. Derivation of the potential function
- Conservation of the total number of photons in the measured image, g, and the model image f:
- Linear transform between the model space and the data space:
- The errors , are normally distributed with zero mean, , and variances :where Ω denotes the expected value of the statistical goodness-of-fit .
2.7. Multidimensional optimization
3. Results and Discussion
3.1. Physics of X-ray imaging
X-ray beam energy (keV) | Central recorded photons | Total recorded photons |
18 | 15,660 ± 125 | 18,390 ± 135 |
20 | 59,130 ± 240 | 70,900 ± 270 |
22 | 184,070 ± 430 | 226,290 ± 475 |
24 | 337,400 ± 580 | 424,340 ± 650 |
26 | 531,130 ± 730 | 683,330 ± 825 |
28 | 738,230 ± 860 | 976,540 ± 990 |
30 | 890,710 ± 940 | 1,204,780 ± 1100 |
Columns | (0) | (1) | ..... | (xsize-2) | (xsize-1) |
Rows | |||||
(0) | 0 | 1 | ..... | xsize-2 | xsize-1 |
(1) | xsize | xsize+1 | ..... | 2*xsize-2 | 2*xsize-1 |
(2) | 2*xsize | 2*xsize+1 | ..... | 3*xsize-2 | 3*xsize-1 |
: | ..... | ..... | ..... | ..... | ...... |
(ysize-2) | (ysize-2)*xsize | (ysize-2)*xsize+1 | ..... | (ysize-1)*xsize-2 | (ysize-1)*xsize-1 |
(ysize-1) | (ysize-1)*xsize | (ysize-1)*xsize+1 | ..... | ysize*xsize-2 | ysize*xsize-1 |
0.0030 | 0.0050 | 0.0070 | 0.0050 | 0.0030 |
(k-2*xsize-2) | (k-2*xsize-1) | (k-2*xsize) | (k-2*xsize+1) | (k-2*xsize+2) |
0.0050 | 0.0120 | 0.0160 | 0.0120 | 0.0050 |
(k-xsize-2) | (k-xsize-1) | (k-xsize) | (k-xsize+1) | (k-xsize+2) |
0.0070 | 0.0160 | 0.7950 | 0.0160 | 0.0070 |
(k-2) | (k-1) | (k) | (k+1) | (k+2) |
0.0050 | 0.0120 | 0.0160 | 0.0120 | 0.0050 |
(k+xsize-2) | (k+xsize-1) | (k+xsize) | (k+xsize+1) | (k+xsize+2) |
0.0030 | 0.0050 | 0.0070 | 0.0050 | 0.0030 |
(k+2*xsize-2) | (k+2*xsize-1) | (k+2*xsize) | (k+2*xsize+1) | (k+2*xsize+2) |
3.2. X-ray image quality assessment
3.3. Improvement of digital and digitized mammograms
4. Conclusion
Acknowledgements
References and Notes
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Mutihac, R. Bayesian Maximum Entropy Based Algorithm for Digital X-ray Mammogram Processing. Algorithms 2009, 2, 850-878. https://doi.org/10.3390/a2020850
Mutihac R. Bayesian Maximum Entropy Based Algorithm for Digital X-ray Mammogram Processing. Algorithms. 2009; 2(2):850-878. https://doi.org/10.3390/a2020850
Chicago/Turabian StyleMutihac, Radu. 2009. "Bayesian Maximum Entropy Based Algorithm for Digital X-ray Mammogram Processing" Algorithms 2, no. 2: 850-878. https://doi.org/10.3390/a2020850