Abstract
This paper presents an efficient image denoising method that adaptively combines the features of wavelets, wave atoms and curvelets. Wavelet shrinkage is used to denoise the smooth regions in the image while wave atoms are employed to denoise the textures, and the edges will take advantage of curvelet denoising. The received noisy image is firstly decomposed into a homogenous (smooth/cartoon) part and a textural part. The cartoon part of the noisy image is denoised using wavelet transform, and the texture part of the noisy image is denoised using wave atoms. The two denoised images are then fused adaptively. For adaptive fusion, different weights are chosen from the variance map of the denoised texture image. Further improvement in denoising results is achieved by denoising the edges through curvelet transform. The information about edge location is gathered from the variance map of denoised cartoon image. The denoised image results in perfect presentation of the smooth regions and efficient preservation of textures and edges in the image.
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Gonzalez R.C., Woods R.E.: Digital Image Processing. 2nd edn. Pearson Education, Singapore (2002)
Starck J.L., Candes E.J., Donoho D.L.: The curvelet transform for image denoising. In: IEEE Trans. Image Process. 11(6), 670–684 (2002)
Donoho D.: Wedgelets: nearly minimax estimation of edges. Ann. Stat. 27(3), 859–897 (1999)
Le Pennec E., Mallat S.: Sparse geometrical image approximation with bandlets. In: IEEE Trans. Image Process. 14(4), 423–438 (2005)
Demanet L., Ying L.: Wave atoms and sparsity of oscillatory patterns. Appl. Comput. Harmon. Anal. 23(3), 368–387 (2007)
Swami, P.D., Jain, A., Singhai, J.: A multilevel Shrinkage approach for curvelet denoising. In: Proceeding of International Conference on Information and Multimedia Technology, pp. 268–272, Jeju Island, Korea (Dec. 16–18, 2009)
Pizurica A., Philips W.: Estimating the probability of the presence of a signal of interest in multiresolution single- and multiband image denoising. In: IEEE Trans. Image Process. 15(3), 654–665 (2006)
Chang S.G., Yu B., Vetterli M.: Spatially adaptive wavelet thresholding with context modeling for image denoising. In: IEEE Trans. Image Process. 9(9), 1522–1531 (2000)
Tessens L., Pizurica A., Alecu A., Munteanu A., Philip W.: Context adaptive image denoising through modeling of curvelet domain statistics. J. Electron. Imaging 17(3), 033021-1–033021-17 (2008)
Liu J., Moulin P.: Information-theoretic analysis of interscale and intrascale dependencies between image wavelet coefficients. In: IEEE Trans. Image Process. 10(11), 1647–1658 (2001)
Nasri M., Pour H.N.: Image denoising in the wavelet domain using a new adaptive thresholding function. Elsevier J. Neurocomput. 72, 1012–1025 (2009)
Bhutada G.G., Anand R.S, Saxena S.C.: PSO-based learning of sub-band adaptive thresholding function for image denoising. Signal Image Video Process. 6(1), 1–7 (2012)
Elad M., Aharon M.: Image denoising via sparse and redundant representations over learned dictionaries. In: IEEE Trans. Image Process. 15(12), 3736–3745 (2006)
Elad M., Figueiredo M.A.T., Ma Y.: On the role of sparse and redundant representation in image processing. In: IEEE Proc. Special Issue Appl. Sparse Represent. Compress. Sens. 98(6), 972–982 (2010)
Po D.D.Y., Do M.N.: Directional multiscale modeling of images using the contourlet transform. In: IEEE Trans. Image Process. 15(6), 1610–1620 (2006)
Liu, W., Shui, P., Cheng, Y.: Residue-based fusion of denoised images by different filter banks. In: Proceeding of Industrial Electronics and Applications, 2009, pp. 2420–2423
Miller M., Kingsbury N.: Image denoising using derotated complex wavelet coefficients. In: IEEE Trans. Image Process. 17(9), 1500–1511 (2008)
Durand S., Froment J.: Reconstruction of wavelet coefficients using total variation minimization. SIAM J. Sci. Comput. 24, 1754–1767 (2003)
Ma J., Plonka G.: Computing with curvelets: from image processing to turbulent flows. In: IEEE J. Comput. Sci. Eng. 11(2), 72–80 (2009)
Plonka G., Ma J.: Nonlinear regularized reaction-diffusion filters for denoising of images with textures. In: IEEE Trans. Image Process. 17(8), 1283–1293 (2008)
Starck J.L., Donoho D.L., Candes E.: Very high quality image restoration by combining wavelets and curvelets. Proc. SPIE Conf. Signal Image Process. Wavelets: Appl. Signal Image Process. IX 4478, 9–19 (2001)
Weibin, Z., Wenjuan, Z.: A variational model combining curvelet Shrinkage and nonlinear anisotropic diffusion for image denoising. In: Proceeding of IEEE Information Assurance and Security, pp. 497–500, (Aug. 18–20, 2009)
Li, H., Wang, S., Deng, C.: New image denoising method based wavelet and curvelet transform. In: Proceeding of IEEE Conference ICIE, WASE vol. 1, pp. 136–139 (July 10–11, 2009)
Bhutada G.G., Anand R.S., Saxena S.C.: Edge preserved image enhancement using adaptive fusion of images denoised by wavelet and curvelet transform. Digit. Signal Process. 21, 118–129 (2011)
Swami P.D., Jain A.: Segmentation based combined wavelet-curvelet approach for image denoising. Int. J. Inf. Eng. 2(1), 32–37 (2012)
Vese L.A., Osher S.J.: Image denoising and decomposition with total variation minimization and oscillatory functions. J. Math. Imaging Vis. 20, 7–18 (2004)
Mumford D., Shah J.: Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math. 42(5), 577–685 (1989)
Starck J.L., Elad M., Donoho D.L.: Image decomposition via the combination of sparse representation and a variational approach. In: IEEE Trans. Image Process. 14(10), 1570–1582 (2005)
Buades A., Le T.M., Morel J.M., Vese L.: Fast cartoon+texture image filters. In: IEEE Trans. Image Process. 19(8), 1978–1986 (2010)
Shen, J.: Piecewise H −1 + H 0 + H 1 images and the Mumford–Shah–Sobolev model for segmented image decomposition. Appl. Math. Res. Exp. (4), 143–167 (2005)
Pratt W.K.: Digital Image Processing. 3rd edn. Wiley, New York (2006)
Wang Z., Bovik A.C.: Universal image quality index. In: IEEE Signal Process. Lett. 9(3), 81–84 (2002)
Wang Z., Bovik A.C., Sheikh H.R., Simoncelli E.P.: Image quality assessment from error visibility to structural similarity. In: IEEE Trans. Image Process. 13(4), 600–612 (2004)
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Swami, P.D., Jain, A. Image denoising by supervised adaptive fusion of decomposed images restored using wave atom, curvelet and wavelet transform. SIViP 8, 443–459 (2014). https://doi.org/10.1007/s11760-012-0343-z
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DOI: https://doi.org/10.1007/s11760-012-0343-z