A Wavelet Multiscale De-Noising Algorithm Based on Radon Transform
Xueling Zhu, Xiaofeng Yang, Qinwu Zhou, Liya Wang, Fulai Yuan, Zhengzhong Bi · InTech eBooks · 2012
Specifically, multiscale methods, based on wavelet transforms, have widely been applied for noise reduction in medical images.Among the wavelet-based noise reduction techniques, nonlinear thresholding is simple yet very effective.Healy et al. [6] were the first to apply wavelet techniques, based on soft thresholding, for filtering MR images.Nowak [7] squared the magnitude MR image and used a wavelet-based Wiener-filter-like filtering method.Donoho [8] showed a universal threshold of asymptotically optimal in the minimax sense, but it is well-known that the universal threshold over-smoothes images.Pan et al. [9] presented a hard threshold with a nonorthogonal wavelet expansion.At the same time the correlation between wavelet coefficients in several scales has also been employed to filter.Paul et al.[10] presented a multiscale thresholding scheme that incorporated the merits of interscale dependencies into the thresholding technique for filtering, and then applied thresholding to the multiscale products instead of the wavelet coefficients.The interscale correlation information is exploited by Pizurica et al. [11] to classify the wavelet coefficients.Xu et al. [12] developed a spatially selective filtering technique by iteratively selecting edge pixels in the multiscale products.Zhang et al. [13] used Radon transform and an adaptive median filter based on Walsh list in the Laplacian pyramid domain to denoise medical image.These methods are effective for noise suppression.However, there are some significant problems such as blurring, losing of detail texture, the changing of edge points, and generating artificial smear.In this paper we present a medical image filtering method based on the Radon and wavelet transforms.We perform Radon transform for input images to get sinograms.Then we apply 1D non-orthogonal wavelets transform along s in sinograms, and use threshold-based methods to filter it.Dissimilar to the traditional threshold schemes that apply the same threshold to the wavelet coefficients at every scale, the proposed method can get robust and adaptive noise threshold at every scale.We can take advantage of the interscale dependency information between wavelet scales to evaluate original noise variance.Finally we apply the inverse Radon transform algorithm to reconstruct the original images.Our method has been validated using MR images.The detailed steps of our method and its evaluative results are reported in the following sections.