Denoising of Medical Images Using Multiwavelet Transforms and Various Thresholding Techniques

Abdullah Al Jumah, Mohammed Gulam Ahamad, Syed Amjad Ali

Department of Computer Engineering, College of Computer Engineering & Science, Salman bin Abdulaziz University, Al-Kharj, Saudi Arabia.
Department of Electronics & Communication Engineering, Lords Institute of Engineering & Technology, Hyderabad, India.

DOI: 10.4236/jsip.2013.41003                

Abstract

The problem of estimating an image corrupted by additive white Gaussian noise has been of interest for practical reasons. Non-linear denoising methods based on wavelets, have become popular but Multiwavelets outperform wavelets in image denoising. Multiwavelets are wavelets with several scaling and wavelet functions, offer simultaneously Orthogonality, Symmetry, Short support and Vanishing moments, which is not possible with ordinary (scalar) wavelets. These properties make Multiwavelets promising for image processing applications, such as image denoising. The aim of this paper is to apply various non-linear thresholding techniques such as hard, soft, universal, modified universal, fixed and multivariate thresholding in Multiwavelet transform domain such as Discrete Multiwavelet Transform, Symmetric Asymmetric (SA4), Chui Lian (CL), and Bi-Hermite (Bih52S) for different Multiwavelets at different levels, to denoise an image and determine the best one out of it. The performance of denoising algorithms and various thresholding are measured using quantitative performance measures such as, Mean Square Error (MSE), and Root Mean Square Error (RMSE), Signal-to-Noise Ratio (SNR), Peak Signal-to-Noise Ratio (PSNR). It is found that CL Multiwavelet transform in combination with modified universal thresholding has given best results.

Keywords

Multiwavelets; Noise; Thresholding; Additive White Gaussian Noise; Signal-to-Noise Ratio; Discrete Multiwavelet Transforms; Chui Lian; Symmetric Asymmetric Multiwavelet Transform; Bi-Hermite Multiwavelet Transform; Modified Universal Thresholding

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	G. Strang and V. Strela, “Short Wavelets and Matrix Dilation Equations,” IEEE Transactions on Signal Processing, Vol. 43, No. 1, 1995, pp. 108-115. doi:10.1109/78.365291
[2]	G. Strang and V. Strela, “Orthogonal Multiwavelets with Vanishing Moments,” Journal of Optical Engineering, Vol. 33, No. 7, 1994, pp. 2104-2107. doi:10.1117/12.172247
[3]	V. Strela, P. N. Heller, G. Strang, P. Topiwala and C. Heil, “The Application of Multiwavelet Filterbanks to Image Processing,” IEEE Transactions on Image Processing, Vol. 8, No. 4, 1999, pp. 548-563.
[4]	V. Strela, and A. T. Walden, “Signal and Image Denoising via Wavelet Thresholding: Orthogonal and Biorthogonal, Scalar and Multiple Wavelet Transforms,” Statistic Section Technical Report TR-98-01, Department of Mathematics, Imperial College, London, 1998.
[5]	B. R. Johnson, “Multiwavelet Moments and Projection Prefilters,” IEEE Transactions on Signal Processing, Vol. 48, No. 11, 2000, pp. 3100-3108.
[6]	C. K. Chui and J. A. Lian, “A Study of Orthogonal Multiwavelets,” Applied Numerical Mathematics, Vol. 20, No. 3, 1996, pp. 273-298. doi:10.1016/0168-9274(95)00111-5
[7]	D. P. Hardin and D. W. Roach, “Multiwavelet Prefilters-I: Orthogonal Prefilters Preserving Approximation Order P ≤ 2,” IEEE Transactions on Circuits and Systems-II: Analog and Digital Signal Processing, Vol. 45, No. 8, 1998, pp. 1106-1112.
[8]	T. R. Downie and B. W. Silverman, “The Discrete Multiple Wavelet Transform and Thresholding Methods,” IEEE Transactions on Signal Processing, Vol. 46, No. 9, 1998, pp. 2558-2561.
[9]	J. Y. Tham, L. X. Shen, S. L. Lee and H. H. Tan, “A General Approach for Analysis and Application of Discrete Multiwavelet Transforms,” IEEE Transactions on Signal Processing, Vol. 48, No. 2, 2000, pp. 457-464.
[10]	K. Attakitmongcol, D. P. Hardin and D. M. Wilkes, “Multiwavelet Prefilters-Part II: Optimal Orthogonal Prefilters,” IEEE Transactions of Image Processing, Vol. 10, No. 10, 2001, pp. 1476-1487.
[11]	G. Andria, F. Attivissimo, G. Cavone, M. Spadavecchia and T. Magli, “Denoising Filter to Improve the Quality of CT Images,” Proceedings of IEEE Conference on Instrumentation and Measurement Technology, 5-7 May 2009, pp. 947-950.
[12]	L. X. Shen, H. H. Tan and J. Y. Tham, “Some Properties of Symmetric-Antisymmetric Orthonormal Multiwavelets,” IEEE Transactions on Signal Processing, Vol. 48, No. 7, 2000, pp. 2161-2163.
[13]	V. Strela and A. T. Walden, “Orthogonal and Biorthogonal Multiwavelets for Signal Denoising and Image Compression,” Proceedings of SPIE, Vol. 3391, 1998, pp. 96-107. doi:10.1117/12.304924
[14]	X. G. Xia, J. Geronimo, D. Hardin and B. Suter, “On Computations of Multiwavelets Transforms,” Proceedings of SPIE, San Diego, July 1995.
[15]	X.-G. Xia, J. Geronimo, D. Hardin and B. Suter, “Design of Prefilters for Descrete Multiwavelets Transforms,” IEEE Transactions on Signal Processing, Vol. 44, No. 1, 1996, pp. 25-35. doi:10.1109/78.482009
[16]	E. Bala and A. Ertuzun, “A Multivariate Thresholding Technique for Image Denoising Using Multiwavelets,” EURASIP Journal on Applied Signal Processing, Hindawi Publishing Corporation, Cairo, 2005, pp. 1205-1211.
[17]	T.-C. Hsung, D. P.-K. Lun and K. C. Ho, “Optimizing the Multiwavelet Shrinkage Denoising,” IEEE Transactions on Signal Processing, Vol. 53, No. 1, 2005, pp. 240-251.