Abstract
This paper addresses the recovery of original images from multiple copies corrupted with the noises, which can be represented sparsely in some dictionary. Sparse representation has been proven to have strong ability to denoise. However, it performs suboptimally when the noise is sparse in some dictionary. A novel joint sparse representation (JSR)-based image denoising method is proposed. The images can be recovered well from multiple noisy copies. All copies share a common component—the image, while each individual measurement contains an innovation component—the noise. Our method can separate the common and innovation components, and reconstruct the images with the sparse coefficients and the dictionaries. Experiment results show that the performance of the proposed method is better than that of other methods in terms of the metric and the visual quality.



Similar content being viewed by others
References
Lu, X., Sakaino, H.: A spatial adaptive filter for smoothing of non-Gaussian texture noise. In: IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Taipei, Taiwan, pp. 841–844 (2009)
Faghih, F., Smith, M.: Combining spatial and scale-space techniques for edge detection to provide a spatially adaptive wavelet-based noise filtering algorithm. IEEE Trans. Image Process. 11(9), 1062–1071 (2002)
Sun, L., Zhang, C., Hu, M.: Interferogram phase noise suppressing using nonlinear partial differential equation. In: International Conference on Radar, Shanghai, China, pp. 1–4 (2006)
You, Y.L., Kaveh, M.: Fourth-order partial differential equations for noise removal. IEEE Trans. Image Process. 9(10), 1723–1730 (2000)
Nath, V.K., Hazarika, D., Mahanta, A.: Video noise reduction in 3-D mixed transform domain using its efficient wavelet structure. In: Annual IEEE India Conference (INDICON), Ahmedabad, India, pp. 1–4 (2009)
Su, W., Zhou, Y.: Wavelet transform threshold noise reduction methods in the oil pipeline leakage monitoring and positioning system. In: International Conference on Measuring Technology and Mechatronics Automation (ICMTMA), Changsha, China, pp. 1091–1094 (2010)
Jiao, C., Wang, D., Lu, H., Zhang, Z., Jerome, Z.: Multiscale noise reduction on low-dose CT sinogram by stationary wavelet transform. In: IEEE Nuclear Science Symposium Conference Record, Dresden, Germany, pp. 5339–5344 (2008)
Grace Chang, S., Yu, B., Vetterli, M.: Wavelet thresholding for multiple noisy image copies. IEEE Trans. Image Process. 9(9), 1631–1635 (2000)
Luisier, F., Blu, T., Unser, M.: SURE-LET for orthonormal wavelet-domain video denoising. IEEE Trans. Circuits Syst. Video Technol. 20(6), 913–919 (2010)
Banerjee, S.: Low-power content-based video acquisition for super-resolution enhancement. IEEE Trans. Multimed. 11(3), 455–464 (2009)
Donoho, D.L., Elad, M., Temlyakov, V.N.: Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Trans. Inf. Theory 52(1), 6–18 (2006)
Carrillo, R.E., Barner, K.E., Aysal, T.C.: Robust sampling and reconstruction methods for sparse signals in the presence of impulsive noise. IEEE J. Sel. Top. Signal Process. 4(2), 392–408 (2010)
Fuchs, J.J.: A frame construction and a universal distortion bound for sparse representations. IEEE Trans. Inf. Theory 51(10), 3601–3608 (2005)
Wakin, M., Duarte, M., Sarvotham, S., Baron, D., Baraniuk, R.: Recovery of jointly sparse signals from few random projections. In: Proceedings of the Workshop on Neural Information Processing Systems (NIPS), Vancouver, Canada, pp. 1435–1442 (2005)
Chen, S.S., Donoho, D.L., Saunders, M.A.: Atomic decomposition by basis pursuit. SIAM Rev. 43(1), 129–159 (2001)
Bronstein, A.M., Bronstein, M.M., Zibulevsky, M.: On separation of semitransparent dynamic images from static background. Lect. Notes Comput. Sci. 3889, 934–940 (2006)
Duarte, M., Sarvotham, S., Baron, D., Wakin, M., Baraniuk, R.: Distributed compressed sensing of jointly sparse signals. In: Asilomar Conf. Signals, Systems and Computers, Pacific Grove, November 2005
Pati, Y.C., Rezaiifar, R., Krishnaprasad, P.S.: Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition. In: 1993 Conference Record of the Twenty-Seventh Asilomar Conference on Signals, Systems and Computers, Pacific Grove, pp. 40–44 (1993)
Aharon, M., Elad, M., Bruckstein, A.: K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation. IEEE Trans. Signal Process. 54(11), 4311–4322 (2006)
Elad, M., Aharon, M.: Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. Image Process. 15(15), 3736–3745 (2006)
Yin, L., Yang, R., Gabbouj, M., et al.: Weighted median filters: A tutorial. IEEE Trans. Circuits Syst. 43(3), 157–192 (1996)
Popovici, A., Dan, P.: Cellular automata in image processing. In: Proceedings of AMS, pp. 1–6 (2000)
Ji, Z., Liao, H., Zhang, X., Wu, Q.H.: Simple and efficient soft morphological filter in periodic noise reduction. In: TENCON 2006. 2006 IEEE Region 10 Conference, pp. 1–4 (2006)
Starck, J.-L., Elad, M., Donoho, D.: Image decomposition via the combination of sparse representations and variational approach. IEEE Trans. Image Process. 14(10), 1570–1582 (2005)
CAVIAR Test Case Scenarios: http://groups.inf.ed.ac.uk/vision/CAVIAR/CAVIARDATA1/
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yu, N., Qiu, T. & Ren, F. Denoising for Multiple Image Copies through Joint Sparse Representation. J Math Imaging Vis 45, 46–54 (2013). https://doi.org/10.1007/s10851-012-0343-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10851-012-0343-1