Parameter Optimization for Local Polynomial Approximation based Intersection Confidence Interval Filter Using Genetic Algorithm: An Application for Brain MRI Image De-Noising
Abstract
:1. Introduction
2. Rician Distributed Noise and MR Signals De-Noising
2.1. Rician Noise Mathematical Model
2.2. MR Images De-noising
3. Methodology
3.1. Image De-Noising using LPA-ICI
- Step 1:
- Set Γ = and s=1,…,E.
- Step 2:
- Calculates the estimates , the adaptive window size and the estimates for . (Calculate for different scales the estimates and compare them)
- Step 3:
- Repeat steps 1 and 2 for all .
- Step 4:
- Find and select the estimates corresponding to as the final ones. (Find the adaptive scale which is the largest where the estimate does not vary significantly from the estimates corresponding to the smaller scales).
3.2. Optimal Selection of Parameters using Genetic Algorithm
- Step 1:
- (Begin) Generate random population of chromosomes. (Suitable solutions for the problem)
- Step 2:
- (Evaluate population-Fitness) In the population, evaluate the fitness of each chromosome.
- Step 3:
- (New population) Create a new population. (By repeating the following steps until the new population is complete)
- (a)
- Selection: From a population, select two parent chromosomes according to their fitness. (Better fitness, provides bigger chance to be selected to be the parent).
- (b)
- Crossover: With a crossover probability, cross over the parents to form new offspring (children). If no crossover was performed, offspring is the exact copy of parents.
- (c)
- Mutation: With a mutation probability, mutate new offspring at each locus.
- (d)
- Accepting: Place new offspring in the new population.
- Step 4:
- (Replace) Use new generated population for a further algorithm run.
- Step 5:
- (Test) If the end condition is satisfied, stop, and return the best solution in current population.
- Step 6:
- (Loop) Go to step 2.
4. The Proposed LPA-GA System
- Step 1.
- The original MRI-brain image is added with Rician noise with various values of “s” ranging from 0.1 to 0.6 to produce the corrupted images.
- Step 2.
- The genetic algorithm is used to optimize the input parameters of LPA-ICI.
- Step 3.
- The input parameters include the Gamma ICI parameter Γ, sharpness parameter, number of directions = 4 or 8, and fusion parameter which is classical or piecewise.
- Step 4.
- The upper and lower bounds of the input parameters are set as [−1 to 10] for the Gamma ICI parameter, [0–5] for sharpness parameter, [[4 or 8] for direction parameter, [[1 or 2] for fusion parameter.
- Step 5.
- The fitness function uses the LPA-ICI with optimized parameters given by the GA to produce the restored image.
- Step 6.
- The genetic algorithm is used to maximize the fitness function (by multiplying the result by −1). The number of generations is set to 100 by default.
- Step 7.
- The genetic algorithm stopped around 50 generations for all noise ratios. Where, convergence occurred around 25 generations.
- Step 8.
- The optimized parameters generated by the genetic algorithm are then given to the LPA-ICI filter to de-noise the corrupted image.
- Step 9.
- The fitness function (FF), calculates PSNR+100*MSSIM between the original image and the restored image. Where, the LPA-ICI with parameters selected by GA is used to produce the restored image.
5. Result and Discussion
5.1. Comparing the results of LPA-ICI-GA versus LPA-ICI Algorithm
5.2. Proposed System Performance Analysis
- Signal-to-noise ratio (SNR): is defined as the ratio of the power of the original image values and the power of noise values. It is given by:
- The improvement in signal to noise ratio (ISNR) between the original and restored images is given by:
- The peak signal to noise ratio (PSNR) between the original and restored images is given by [68]:
- The mean squared error (MSE): measures the average of the squares of the “errors”, known as the difference between the original image and the restored image. It is given by,
- The mean absolute error (MAE): is the average of the absolute errors between the original image and the restored image. It is given by:
- The maximum absolute difference (MAD) is given by:
- The SSIM index measure between two windows and of the original and restored images is given by:
- The mean structural similarity (MSSIM) index is given by:
S | ISNR | SNR | PSNR | MSE | RMSE | MAE | MAX | MSSIM |
---|---|---|---|---|---|---|---|---|
0.1 | 1.55 | 12.2267 | 19.5451 | 722.0499 | 26.871 | 23.7222 | 95.379 | 0.44208 |
0.2 | 1.6386 | 6.31 | 13.6284 | 2819.9239 | 53.103 | 46.5034 | 190.9031 | 0.31629 |
0.3 | 1.6375 | 2.8197 | 10.1381 | 6299.0275 | 79.3664 | 69.6002 | 245.642 | 0.22051 |
0.4 | 1.612 | 0.31846 | 7.6369 | 11204.5665 | 105.8516 | 93.8354 | 367.7877 | 0.15175 |
0.5 | 1.5691 | -1.6638 | 5.6546 | 17685.5917 | 132.9872 | 119.8152 | 463.6092 | 0.10741 |
0.6 | 1.5325 | -3.3066 | 4.0118 | 25816.7765 | 160.676 | 147.2261 | 559.6435 | 0.084966 |
0.7 | 1.4968 | -4.718 | 2.6004 | 35730.901 | 89.0262 | 175.6339 | 655.8092 | 0.070399 |
- Sharpness parameter range = [−1, from 0 till 10];
- Γ range = [from 0 till 5];
- Directional resolution range = [[4 or 8];
- Fusing range = [[1 or 2], where Fusing = 1 for classical estimation, and equal 2 for piecewise estimation.
- Step 1.
- According to the noise variance level, the ICI parameter optimal values are changeable. This proves the importance of the GA to obtain the optimized values for these parameters. Also, these parameter values are changeable with any change in the image concerned.
- Step 2.
- The ICI tuned parameters (optimized), are different than the fixed values used in LPA-ICI. Also, as the noise variance increase and equal 0.6 both fusing and the directional resolution switches their values, to be able to overcome the high noise level.
- Step 3.
S | SharpParam | Γ | Directional Resolution | Fusing |
---|---|---|---|---|
0.1 | −0.4495 | 0.4984 | 8 | 2 |
0.2 | −0.7464 | 0.7165 | 8 | 2 |
0.3 | 0.0126 | 0.6696 | 8 | 2 |
0.4 | −0.1287 | 0.5449 | 8 | 2 |
0.5 | −0.0556 | 0.5540 | 8 | 2 |
0.6 | −0.2439 | 0.5234 | 8 | 2 |
0.7 | −0.8946 | 2.3293 | 4 | 1 |
S | ISNR | SNR | PSNR | MSE | RMSE | MAE | MAX | MSSIM | Fitness Function = PSNR+100*MSSIM |
---|---|---|---|---|---|---|---|---|---|
0.1 | 1.5982 | 12.275 | 19.5934 | 714.0724 | 26.7221 | 23.4761 | 95.379 | 0.44871 | 64.4645 |
0.2 | 1.6994 | 6.3708 | 13.6892 | 2780.722 | 52.7325 | 45.9734 | 190.9031 | 0.32608 | 46.2971 |
0.3 | 1.8495 | 3.0317 | 10.3501 | 5998.932 | 77.4528 | 68.2574 | 211.127 | 0.24197 | 34.5472 |
0.4 | 1.822 | 0.52845 | 7.8469 | 10,675.67 | 103.3231 | 91.4624 | 238.5945 | 0.18155 | 26.0015 |
0.5 | 1.7566 | −1.4763 | 5.8421 | 1,6938.2 | 130.1469 | 116.3874 | 297.4721 | 0.13606 | 19.4483 |
0.6 | 1.6849 | −3.1542 | 4.1642 | 2,4926.53 | 157.8814 | 143.7663 | 312.2485 | 0.10795 | 14.9587 |
0.7 | 1.4848 | −4.73 | 2.5884 | 3,5829.55 | 189.2869 | 176.1798 | 363.922 | 0.085832 | 11.1716 |
5.3. Proposed System Convergence Graphs
S. No. | Authors | Year | De-Noising Technique | Comments/Notes |
---|---|---|---|---|
1 | Bao et al. [15] | 2003 | Adaptive wavelet thresholding | To, this method multiplied the adjacent wavelet sub bands, then applied threshold to the multi-scale products to differentiate edge structures in an improved approach from noise and amplify the significant features. Results of MRI images proved that this method achieved high mean-to-standard-deviation ratio (MSR) and contrast to noise ratio (CNR). |
2 | Wang et al. [18] | 2006 | Wavelet and the total variation minimization methods | An effective automatic stopping time criterion extensively. |
3 | Manjon et al. [19] | 2009 | Novel filter averaging similar patches around the image using a robust multicomponent similarity measure filter, then local Principal Component Analysis decomposition as a post-processing for more noise removal. | This method showed a consistent improvement in the results when the number of images increases in contrast with the erratic behavior of the basic version. |
4 | Jaya et al. [23] | 2009 | Median filter, the weighted median and the adaptive filter. | The results proved that weighted median filter was outperforming the other filters with peak signal to noise ratio PSNR = 0.924. |
5 | Rajeesh et al. [20] | 2010 | Curvelet shrinkages were superior than using the wavelet method. | The reconstructed MRI data have high Signal to Noise Ratio (SNR) compared to the curvelet and wavelet domain denoising approaches. |
6 | Erturk et al. [22] | 2013 | Spectral subtraction method. | The results showed enhanced signal to noise ratio (SNR) up to 40% in the MRI reconstructed signal |
7 | Proposed system | 2015 | Local polynomial approximation with intersection confidence interval based genetic algorithm filter. (LPA-ICI-GA) | The results proved that using GA optimization to support the LPA-ICI outperform the classic LPA-ICI. For variance of 0.1, the PSNR using the proposed method is 19.5934 dB, while that obtained by the LPA-ICI was 19.5451. Comparing with respect to the MSE at the same variance value, it was obtained that the LPA-ICI-GA compared to the LPA-ICI achieved 714.0724 and 722.0499; respectively. That established that the proposed method gained les MSE compared to the classical LPA-ICI approach. |
6. Conclusions and Future work
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Dey, N.; Ashour, A.S.; Beagum, S.; Pistola, D.S.; Gospodinov, M.; Gospodinova, Е.P.; Tavares, J.M.R.S. Parameter Optimization for Local Polynomial Approximation based Intersection Confidence Interval Filter Using Genetic Algorithm: An Application for Brain MRI Image De-Noising. J. Imaging 2015, 1, 60-84. https://doi.org/10.3390/jimaging1010060
Dey N, Ashour AS, Beagum S, Pistola DS, Gospodinov M, Gospodinova ЕP, Tavares JMRS. Parameter Optimization for Local Polynomial Approximation based Intersection Confidence Interval Filter Using Genetic Algorithm: An Application for Brain MRI Image De-Noising. Journal of Imaging. 2015; 1(1):60-84. https://doi.org/10.3390/jimaging1010060
Chicago/Turabian StyleDey, Nilanjan, Amira S. Ashour, Samsad Beagum, Dimitra Sifaki Pistola, Mitko Gospodinov, Еvgeniya Peneva Gospodinova, and João Manuel R. S. Tavares. 2015. "Parameter Optimization for Local Polynomial Approximation based Intersection Confidence Interval Filter Using Genetic Algorithm: An Application for Brain MRI Image De-Noising" Journal of Imaging 1, no. 1: 60-84. https://doi.org/10.3390/jimaging1010060