A novel method for removing Rician noise from MRI based on variational mode decomposition
Introduction
Magnetic resonance imaging (MRI) is a noninvasive medical imaging technique, which provides the functional behavior and structural features of human tissues and internal organs. MRI is mainly used for determining the pathological or physiological abnormalities present in the internal human body [1]. During the acquisition and transmission, MRI got corrupted by noise. The most common noise found in MRI is thermal noise, which is due to the thermal agitation of electrons from the machines or objects to be imaged. Noise can tremendously reduce the delicate structural features present in MRI that contributes to important medical information for accurate clinical diagnosis [2]. Noise in image limits its further processing such as visual evaluation, computer-aided analysis, registration, segmentation of relevant features, classification, etc. [3]. The MRI has a trade-off between the image spatial resolution and signal to noise ratio (SNR), hence the acquired MRI can be categorized into two: (1) high-resolution low SNR image; (2) low-resolution high SNR image. The human eye can effectively differentiate the delicate structure even from the noisy image [4], [5]. However, it is ineffective in the case of the noisy image with low SNR or low-resolution because it degrades the structural characteristics. The correct diagnosis requires high-resolution, high SNR images. The SNR of MRI can be improved by its repeated acquisition and averaging, which is an acquisition based noise reduction method. However, it requires more acquisition time due to certain factors such as patient discomfort or physiological constraints. Hence, post-acquisition image denoising methods are preferred [5].
Image and the noise are statistically modeled based on the scanner coil architecture, which is of two types, single-coil, and multi-coil [6], [7]. In single-coil architecture, the complex magnetic resonance (MR) data is Gaussian modeled and corrupted by uncorrelated Gaussian noise with uniform variance and zero mean. Hence the magnitude image follows a Rician distribution with same variance for the entire image, which means the single variance value characterizes the whole dataset, called homogeneous Rician distribution or stationary Rician distribution. In the multi-coil acquisition system, the image follows either Rician distribution or non-central chi (nc-) distribution if no up-sampling in -space [8], [9]. For effective image enhancement, it is necessary to devise a post-acquisition image denoising method that can efficiently remove the Rician noise characteristics from MRI. The proposed work developed a post-acquisition image denoising method for Rician distribution in MRI.
Variational mode decomposition (VMD) is an efficient decomposition technique that sparsely decomposes the image into its principal components or modes based on frequency [10], [11]. The algorithm rendered optimal reconstruction of the original image from the ensembles of modes. VMD can effectively capture all the precise frequency variations present in the image into its respective modes. The novelty of the proposed work is the effective utilization of properties of the VMD algorithm in capturing the high-frequency noise characteristics from the noisy MRI. The MRI enhancement over Rician noise is achieved by discarding the high-frequency components obtained by decomposition and the denoised image is reconstructed by combining the low-frequency components. However, the resultant image may contain noise details that degrade the structural details of MRI. Hence, the proposed work performed a total variation (TV) smoothing in the second stage of VMD enhancement [12].
The paper is organized as follows: Section 2 probes the review of related work. Section 3 presents the characteristics of Rician noise. Section 4 discusses the theory and the proposed method. Section 5 presents experimental analysis. Section 6 concludes the article.
Section snippets
Review of related work
Several outstanding denoising algorithms have been developed for MRI. Henkelman [13] estimated the magnitude of the MRI from the noisy image for the first time. He introduced a correction scheme, which is based on intensity to rectify the overestimation of the amplitude of the image due to noise. Numerous post-acquisition filtering techniques have been devised. McVeigh et al. [14] proposed spatial and temporal filters for removing Gaussian noise from MRI. The spatial filter reduces the
Characteristics of Rician noise
The complex MR raw data in -space indicates the Fourier transform representation of the volume of tissue. The noise in -space has Gaussian distribution with same variance and zero mean in the real and imaginary parts. The inverse Fourier transformation reconstructs the complex MR images and its Gaussian noise characteristics remain unchanged due to the Fourier transform properties such as orthogonality and linearity [48]. In single-coil MRI system, MR complex image is transformed into
Proposed VMD based MRI denoising
The proposed method performed in two stages:
- 1.
To extract the Rician noise, the noise-corrupted MRI is decomposed into different frequency components using VMD. Identify and eliminate the high-frequency components contain Rician characteristics. The denoised image is reconstructed from low-frequency components.
- 2.
The remnant noise details from the first stage is removed using the TV regularization method based on non-convex optimization.
Performance Comparison
To emphasize the significance of the proposed work, the algorithm is compared with other denoising methods. The proposed two-stage algorithm is compared with (1) the first stage of the proposed method (VMD), where denoising is performed using VMD only, (2) TV image denoising based on non-convex optimization [12], [52], (3) Rician denoising using LMMSE method [35] and (4) Bilateral filter (BF) [60]. The experiments use the default setting of all parameters for all the comparing algorithms and
Conclusions
The proposed method exploited the properties of VMD for eliminating the Rician noise from MRI. In the two-stage denoising algorithm, the first stage is used to extract the Rician noise from the decomposed modes and the denoised image is reconstructed from the lower modes. In the second stage, the remnant noise details from the first stage are regularized using total variation method based on non-convex optimization. The performance of the proposed algorithm is compared with other denoising
Acknowledgment
The authors would like to acknowledge Dr. Jebin Ibrahim, Radiologist for providing anonymous clinical MRI data and would like to thank both Dr. Jebin Ibrahim and Dr. Dipak Patil, Neurologist for spending their valuable time to perform the subjective evaluation.
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