Document Type : Research Articles

Authors

Department of Electrical Engineering,Control Group,Tafresh University

Abstract

This paper aimed to formulate image noise reduction as an optimization problem and denoise the target image using matrix low rank approximation. Considering the fact that the smaller pieces of an image are more similar (more dependent) in natural images; therefore, it is more logical to use low rank approximation on smaller pieces of the image. In the proposed method, the image corrupted with AWGN (Additive White Gaussian Noise) is locally denoised, and the optimization problem of low rank approximation is solved on all fixed-size patches (Windows with pixels needing to be processed). This method can be implemented in parallelly for practical purposes, because it can simultaneously handle different image patches. This is one of the advantages of this method. In all noise reduction methods, the two factors, namely the amount of the noise removed from the image and the preservation of the edges (vital details), are very important. In the proposed method, all the new ideas including the use of TI image (Training Image) and SVD adaptive basis, iterability of the algorithm and patch labeling have all been proved efficient in producing sharper images, good edge preservation and acceptable speed compared to the state-of-the-art denoising methods.

Keywords

[1] Zhang, X., et al., Compression artifact reduction by
overlapped-block transform coefficient estimation with block
similarity. IEEE transactions on image processing, 2013.
22(12): p. 4613-4626.

[2] Khan, A., et al., Image de-noising using noise ratio
estimation, K-means clustering and non-local means-based
estimator. Computers & Electrical Engineering, 2016. 54: p.
370-381.

[3] Takeda, H., S. Farsiu, and P. Milanfar, Kernel regression for
image processing and reconstruction. IEEE Transactions on
image processing, 2007. 16(2): p. 349-366.

[4] Fan, L., et al., Nonlocal image denoising using edge-based
similarity metric and adaptive parameter selection. Science
China Information Sciences, 2018. 61(4): p. 049101.

[5] Zhang, X., et al., Gradient-based Wiener filter for image
denoising. Computers & Electrical Engineering, 2013. 39(3):
p. 934-944.

[6] Shanthi, S.A., C.H. Sulochana, and T. Latha, Image
denoising in hybrid wavelet and quincunx diamond filter
bank domain based on Gaussian scale mixture model.
Computers & Electrical Engineering, 2015. 46: p. 384-393.

[7] Chen, M., et al. An OCT image denoising method based on
fractional integral. in Optical Coherence Tomography and
Coherence Domain Optical Methods in Biomedicine XXII.
2018. International Society for Optics and Photonics.
[8] shamsi, a., Reconfigurable CT QDSM with mismatch
shaping dedicated to multi-mode low-IF receivers.
International Journal of Industrial Electronics, Control and
Optimization, 2019. 2(3): p. 257-264.

[9] Smirnov, M.W. and D.A. Silverstein, Noise reduction using
sequential use of multiple noise models. 2019, Google
Patents.

[10] Huang, Z., et al., Progressive dual-domain filter for
enhancing and denoising optical remote-sensing images.
IEEE Geoscience and Remote Sensing Letters, 2018. 15(5):
p. 759-763.

[11] Gavaskar, R.G. and K.N. Chaudhury, Fast adaptive bilateral
filtering. IEEE Transactions on Image Processing, 2018.
28(2): p. 779-790.

[12] Guo, Q., et al., An efficient SVD-based method for image
denoising. IEEE transactions on Circuits and Systems for
Video Technology, 2015. 26(5): p. 868-880.

[13] Aharon, M., M. Elad, and A. Bruckstein, K-SVD: An
algorithm for designing overcomplete dictionaries for sparse
representation. IEEE Transactions on signal processing,
2006. 54(11): p. 4311-4322.

[14] Elad, M. and M. Aharon, Image denoising via sparse and
redundant representations over learned dictionaries. IEEE
Transactions on Image processing, 2006. 15(12): p.
3736-3745.

[15] Mallat, S. and G. Yu, Super-resolution with sparse mixing
estimators. IEEE transactions on image processing, 2010.
19(11): p. 2889-2900.

[16] Jiang, L., X. Feng, and H. Yin, Structure and texture image
inpainting using sparse representations and an iterative
curvelet thresholding approach. International Journal of
Wavelets, Multiresolution and Information Processing, 2008.
6(05): p. 691-705.

[17] Kalantari, S. and M.J. Abdollahifard, Optimization-based
multiple-point geostatistics: A sparse way. Computers &
geosciences, 2016. 95: p. 85-98.

[18] Pizurica, A. and W. Philips, Estimating the probability of
the presence of a signal of interest in multiresolution
single-and multiband image denoising. IEEE Transactions on
image processing, 2006. 15(3): p. 654-665.

[19] Zhang, J., et al., Image restoration using joint statistical
modeling in a space-transform domain. IEEE Transactions
on Circuits and Systems for Video Technology, 2014. 24(6):
p. 915-928.

[20] Jiang, J., L. Zhang, and J. Yang, Mixed noise removal by
weighted encoding with sparse nonlocal regularization. IEEE
transactions on image processing, 2014. 23(6): p. 2651-2662.

[21] Dabov, K., et al., Image denoising by sparse 3-D
transform-domain collaborative filtering. IEEE Transactions
on image processing, 2007. 16(8): p. 2080-2095.

[22] Dabov, K., et al., Image denoising with shape-adaptive
principal component analysis. Department of Signal
Processing, Tampere University of Technology, France,
2009.

[23] He, Y., et al., Adaptive denoising by singular value
decomposition. IEEE Signal Processing Letters, 2011. 18(4):
p. 215-218.

[24] Dong, W., G. Shi, and X. Li, Nonlocal image restoration
with bilateral variance estimation: a low-rank approach.
IEEE transactions on image processing, 2012. 22(2): p.
700-711.

[25] Mallat, S., A Wavelet Tour of Signal Processing: The
Sparse Way (Academic, Burlington, MA). 2008.
[26] Starck, J.-L., E.J. Candès, and D.L. Donoho, The curvelet
transform for image denoising. IEEE Transactions on image
processing, 2002. 11(6): p. 670-684.

[27] Mallat, S. and G. Peyré, A review of bandlet methods for
geometrical image representation. Numerical Algorithms,
2007. 44(3): p. 205-234.

[28] Do, M.N. and M. Vetterli, The contourlet transform: an
efficient directional multiresolution image representation.
IEEE Transactions on image processing, 2005. 14(12): p.
2091-2106.

[29] Walter, G.G. and X. Shen, Convergence and Summability of
Fourier Series, in Wavelets and Other Orthogonal Systems.
2018, CRC Press. p. 93-110.

[30] Eckart, C. and G. Young, The approximation of one matrix
by another of lower rank. Psychometrika, 1936. 1(3): p.
211-218.