A Multivariate Thresholding Technique for Image Denoising Using Multiwavelets
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A Multivariate Thresholding Technique for Image Denoising Using Multiwavelets Erdem Bala Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19716, USA Email: [email protected]
¨ un ¨ Ays¸in Ertuz Electrical and Electronics Engineering Department, Bo˘gazic¸i University, 34342 Bebek, Istanbul, Turkey Email: [email protected] Received 20 January 2004; Revised 21 November 2004; Recommended for Publication by Kiyoharu Aizawa Multiwavelets, wavelets with several scaling functions, offer simultaneous orthogonality, symmetry, and short support, which is not possible with ordinary (scalar) wavelets. These properties make multiwavelets promising for signal processing applications, such as image denoising. The common approach for image denoising is to get the multiwavelet decomposition of a noisy image and apply a common threshold to each coefficient separately. This approach does not generally give sufficient performance. In this paper, we propose a multivariate thresholding technique for image denoising with multiwavelets. The proposed technique is based on the idea of restoring the spatial dependence of the pixels of the noisy image that has undergone a multiwavelet decomposition. Coefficients with high correlation are regarded as elements of a vector and are subject to a common thresholding operation. Simulations with several multiwavelets illustrate that the proposed technique results in a better performance. Keywords and phrases: multiwavelets, image denoising, multivariate thresholding.
1.
INTRODUCTION
Multiwavelets are a relatively new addition to the wavelet theory, and have received considerable attention since their introduction [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]. Contrary to ordinary wavelets, multiwavelets offer simultaneous orthogonality, symmetry, and short support. Similar to performing wavelet decomposition with filters, multiwavelet decomposition can be realized with filterbanks. The filter coefficients in this case are, however, matrices instead of scalars. Therefore, two or more input streams to the multiwavelet filterbank are required to perform the decomposition. Several methods have been developed for obtaining multiple input streams from a given single input stream [2, 3, 4, 15, 16, 17]. One of the widely used applications of wavelet decomposition is the removal of additive white Gaussian noise from noisy signals [18, 19]. The discrimination between the actual signal and noise is achieved by choosing an orthogonal basis, which efficiently approximates the signal with few nonzero coefficients. A signal enhancement can then be obtained by discarding components below a predetermined threshold value. Although the performance of multiwavelets has been evaluated for image compression and coding (see, e.g., [20] and the references therein), less work about denoising applications of multiwavelets exists [21, 22, 23]. Most of the
existing work concentrates on denoising of one-dimensional signals. A detailed discussion of multiwavelets and their applications to signal and imag
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