Research On Novel Denoising Algorithm For MR Images Based On Structural Similarity

Magnetic resonance imaging (MRI) is a non-invasive high-resolution multi-parameter imaging modality that is widely used in current clinical diagnosis and scientific research because of its ability to reveal the 3D internal structures of objects. However, images are inevitably affected by noise due to the limitation of MRI mechanism and subject. The noise may blur image details, reduce the signal-noise-ratio (SNR) and influence the clinical diagnosis and the followig analysis tasks. Thus, how to reduce noise and increase the SNR in magnetic resonance (MR) images has become an important subject in the MR image processing field.The MR image quality can be improved by averaging multiple repeatedly acquired images. However, this approach significantly increases data acquisition time and cost. Moreover, this approach will increase the possibility of subject motion during the long imaging process and result in image artifacts, thus is not feasible in practical applications. Another method is to denoise MR images by post-processing techniques. This method does not increase the acquisition time, thus obtains wide attention in recent decades and is widely used in clinical diagnosis and treatment. Various algorithms were developed for denoising MR images. Among these denoising algorithms, nonlocal means (NLM) and block matching and 3D filtering (BM3D) are the two classic ones, both of which expliots the image structural similarity for denoising. Specifically, Buades et al. have proposed NLM algorithm in 2005. The basic idea of the NLM algorithm is that images generally have structural similarity, that is, the same structure will be repeated multiple times in image such as image edge. We will exploit the redundant information of image for denoising. For any target pixel to be denoised, we find the patches similar to the target patch in a fixed searching window and average these pixels with similar patches for denoising. BM3D is another great breakthrough on the basis of the NLM and is proposed by Dabov et al. in 2007. This method exploits the structural similarity between patches and image sparsity for image denoising. It can produce a denoised result with higher quality and accuracy and is regarded as the state-of-the-art algorithm in the filed of image denoising. Recently, Rajwade et al. proposed a denoising method based on higher-order singular value decomposition (HOSVD). The HOSVD denoising algorithm is similar to the BM3D, both of which exploit the structural similarity among patches and image sparsity for denoising image. The difference is that the bases used in the BM3D method is the fixed bases such as discrete cosine transform (DCT) and wavelet bases which are not adaptable to the image content. However, the HOSVD bases are learned from image and thus more adaptable to the image content and may achieve a more sparse and better representation. This paper mainly studied the HOSVD-based denoising algorithm and NLM denoising algorithm, and did three main work around these two algorithms as follows:(1) This paper proposed a 3D MR denoising algorithm by using higher-order singular value decomposition.Rajwade et al. proposed patch-based HOSVD denoising method and wiener filter-augmented HOSVD (HOSVD-W) method for denoising natural images with white Gaussian noise. The HOSVD-based method has not been previously considered for MR denoising, although it presents promising properties. We firstly extended and applied the HOSVD-W to denoise 3D MR data. For better denoising performance, we also proposed to augment a standard HOSVD stage by using the recursive regularization in the second stage (HOSVD-R) for denoising 3D MR data.The HOSVD-R denoising algorithm includes two stages HOSVD denoising. The first stage is a standard patch-based HOSVD, which clusters similar 3D patches into a 4-order tensor, performs the HOSVD transform of such a 4-order tensor to obtain its representation by the HOSVD bases and coefficients, manipulates these coefficients by hard thresholding, inverts the HOSVD transform to obtain the estimates of these similar 3D patches and performs hypotheses averaging at each pixel to produce the final filtered image. The second stage is another patch-based HOSVD by using the recursive regularization. Specifically, this stage fisrtly obtains the combined image by adding filtered noise back to the denoised image and then perform the HOSVD denoising of this combined image. The filtered noise by using any denoising algorithms will contains some structure information and the feedback of filtered noise in the second stage maintains a two-step regularization effect to encourage the solution toward a better result. This method considers the conventional 3D MR image with Rician noise. The HOSVD-based method is designed for data that are contaminated by additive Gaussian noise independent of the signal and cannot be directly applied to denoise MR magnitude images with Rician noise. To obtain the image with standard deviation independent of signal and the unbiased estimate of the filtered data, we adopted forward variance-stabilizing transformation (VST) and inverse VST before and after filtering. The performance of the HOSVD-W and HOSVD-R algorithms are compared against two state-of-the-art MR denoising algorithms. Experimental results over synthetic and real data demonstrate that the proposed HOSVD-R outperforms other compared denoising algorithms.(2) This paper proposed a diffusion-weighted image denoising algorithm by using higher-order singular value decomposition.Diffusion-weighted imaging (DWI) is a novel MRI technique which is developed in the mid 1990s and is able to achieve the noninvasive and in vivo mapping of the diffusion process of molecules in biological tissues. Thus, DWI has important clinical value. For example, DWI can be used in diagnosing early strokes and can display abnormal signal which is not displayed in conventional MRI. Other brain tissue lesion can be also observed in diffusion-weighted (DW) image. However, the DW image usually suffers from noise and these noises are generally more serious than those of conventional MR image especially in the high-spatial-resolution or high-b-value imaging. The noise in the DW image will seriously affect clinical diagnosis, blur the image details and then influence the subsequent quantitative analysis.The HOSVD-based algorithm is a very simple, structural similarity-based and sparsity-based denoising method. This method can learn different adaptive basis from different similar patch group and better represent image content. Different from other singular value decomposition-based nonlocal denoising method, HOSVD does not require unfolding the higher dimensional array into matrix,thus dees not destroy the topological structures and can exploit relevant and redundant information among higher dimensional array for better denoising. Compared with the conventional MR images, DW images not only have the structural similarity across the spatial domain but also are highly correlated along different diffusion directions. Thus, the HOSVD denoising algorithm is more suitable for DW data as its relevant information is more abundant and can more sparsely represent DW image content. However, the basis learned from image is more sensitive to noise,and this phenomenon is more obvious in DW images with serious noise. In our preliminary experiments, we find that the patch-based HOSVD algorithm can preserve well the rapid-changing details while reduce the noise in DW images, but may introduce some stripe-like artifacts in the homogeneous regions. We hypothesis that these stripe artifacts are aroused by noise-deteriorated HOSVD bases learned from similar noise patterns in grouped patches when denoising DW images in the presence of severe noise. To improve the denoising image quality and reduce stripe artifacts, we introduce a global HOSVD prefiltering stage to produce the guidance image to guide the patch-based local HOSVD. The global HOSVD denoising stage can improve the performance of the patch-based HOSVD denoising stage in the following two aspects, (a) To improve the accuracy of searching similar cuboids, we calculate the photometric distance on the prefiltered images to measure the dissimilarity between two cuboids, (b) Compared with original noisy image, the noise is significantly reduced in the prefiltered image, thus we can utilize the HOSVD bases learned from similar cuboid group in the prefiltered image to transform the corresponding similar cuboid group in the original noisy image and then mitigate the stripe artifacts in the final denoised image.In order to distinguish from the global HOSVD, we call the patch-based HOSVD denoising as local HOSVD denoising. To validate the effect of introducing the global HOSVD perfiltering stage to the local HOSVD method, we compared the proposed GL-HOSVD method with several HOSVD-based methods. Our method considers the DW images with Rician and noncentral-chi distributed noise. Similarly, in order to obtain a image with independent noise variance and the unbiased estimate of the filtered image, we adopted VST and inverse VST before and after filtering. Simulated results illustrate that introducing global HOSVD stage into local HOSVD denoising can improve the image quality and reduce stripe artifact. In addition, we compare our proposed method with two other state-of-the-art DW image denoising algorithms. The experimental result demonstrates that our proposed method can better restore image details while reduce noise and produce a more accurate fractional anisotropy (FA) mapping.(3) This paper proposed a NLM-based algorithm for denoising MR imagesThe NLM algorithm exploits the structural similarity among patches for denoising and exhibits capability to preserve details and supress noise as well. However, this algorithm may lead to the blurring or loss of small high-contrast particle details contained in MR images. As these small high-contrast particles may be clinically relevant, the loss of these particles may lead to missed and delayed diagnosis and is generally unacceptable. As far as I know, the blurring of high-contrast particles in NLM-based denoising algorithms has not been addressed in previous studies, including MR image denoising. Through extensive experiments, we find that the blurring of sharp particles in NLM-based algorithms is related to the weighting strategy of the central pixel. To avoid overweighting of the central pixel from very high self-similarity, Buades et al. suggested that the weight of the central pixel was assigned the maximum weight of the non-central pixels in the search window and this strategy was adopted in subsequent NLM-based denoising algorithms. However, when the intensity of the central pixel is significantly different from those of all other pixels in the search window, the aforementioned central pixel weighting strategy causes the reduced contribution of the central pixel to the weighted average output. Thus, small high-contrast particles are unavoidably blurred or filtered out in the denoised MR images. To retain the small high-contrast particle details in the MR images, we propose a novel weight method using combined patch and pixel (RNLM-CPP) similarity. That is to say, only those noncentral pixels with high patch and pixel similarity simultaneously are assigned large weights in the search window. The central pixel is assigned the maximum weight of noncentral pixels in the search window only when the central pixel is similar to that pixel with maximum weight. Otherwise,the central pixel will be assigned higher weight to increase the contribution of the central pixel to the filtered result. This method addresses MR images with Rician noise and adopted Rician NLM (RNLM) model which is proposed by Wiest-Daessle et al. to obtain the unbias estimate of filtered MR images. The performance of the RNLM-CPP algorithm is evaluated and compared with original RNLM filter and the simulation and real experiment results demonstrate that our proposed method could well preserve particles and reduce noise as well.