Magnetic Resonance Imaging (MRI) is a non-invasive imaging modality that generates tissue contrast by exciting hydrogen nuclei in a strong magnetic field and spatially encoding the resulting signals using radio-frequency pulses and gradient fields. MRI image contrast mainly depends on longitudinal relaxation (T1), transverse relaxation (T2) and proton density (PD), and is also influenced by repetition time (TR) and echo time (TE). To meet different clinical diagnostic needs, structural MRI contrasts such as T1-weighted (T1w), T2-weighted (T2w) and PD-weighted (PDw) imaging are commonly used. Across these modalities, MRI is susceptible to these noises, which are primarily caused by the thermoelectric potential generated by the object within the receiving coil during signal acquisition and transmission [1]. These noises such as Gaussian and Rician noise degrade image quality, especially blurring details and structures, affecting contrast and reducing SNR. The noise finally negatively impacts its accuracy in medical diagnosis. Consequently, the ability to effectively and adaptively remove noise from MRI images while preserving details and critical structural information becomes a crucial step to disease diagnosis [2].

Numerous denoising algorithms are successfully implemented, including mathematical models-based methods and deep learning-based methods. Mathematical models-based methods have wide practicability. Gaussian filter [3] is one of the most popular filtering methods for denoising, but it often leads to image edge blurring due to the lower weights assigned to pixels farther from the center [4]. Compared with the Gaussian filter, the Bilateral filter considers both spatial distance and grayscale intensity differences, thereby effectively preserving edge information while denoising. However, this approach may be inadequate in complex noise scenes and potentially result in over-smoothing in some cases [5]. The Non-Local Means (NLM) algorithm is an effective denoising method with advantages in processing textured and natural images [6]. But the method is computationally complex and may fail to completely remove noise with edge sharpening artifacts in certain cases. Regularization methods like the nonlinear total variation (TV) [7] and a fast projection algorithm for TV regularization [8] can effectively remove noise while preserving edges, but the method is highly dependent on the noise model and may lead to over-smoothing. Moreover, matrix decomposition methods such as Robust Principal Component Analysis (RPCA) decompose an image matrix into a low-rank matrix and a sparse matrix by minimizing the nuclear norm and L1-norm of the matrix [9]. This method separates noise from the signal while preserving structural information. However, it suffers from high computational complexity, loss or blurring details when handling large-scale data. Considering MRI image reconstruction problem is reformulated as a high-order low-rank tensor and sparse tensor recovery task. An improved Robust Tensor Principal Component Analysis (iRTPCA) method introduces a novel tensor nuclear norm (TNN) to enhance denoising performance [10]. Despite its effectiveness in noise removal, iRTPCA also has high computational complexity and may lead to over-smoothing for edges and details. In addition, a novel MRI denoising method based on global self-similarity (PNLM-PCA) is proposed. This method uses a particle swarm optimization algorithm to determine the optimal parameters for the PCA component relaxing the original constraints. By traversing voxel signal intensities instead of spatial locations, the PRI-NLM component is adjusted. This adjustment reduces redundant calculations and expands the search range. However, this method still faces issues with edge preservation [11]. As image structures and details become increasingly complex, the limitations of mathematical models-based algorithms in removing noise become evident. This encourages researchers to explore deep learning methods for more effective denoising solutions. Denoising Convolutional Neural Network (DnCNN) model utilizes a residual learning strategy to predict the difference between a noisy image and its potentially clear image [12]. However, this method exhibits limited adaptability to non-Gaussian noise and may result in the loss of texture information. Based on this, the Dense Attention DnCNN model is proposed. This method effectively improves image denoising performance by incorporating the attention mechanism into the DnCNN model. However, it has challenges in parameter tuning and increases the complexity of model [13]. A three-dimensional MRI denoising method based on a Residual Encoder-Decoder Wasserstein Gener- ative Adversarial Network (RED-WGAN) improves denoising performance by integrating perceptual similarity loss with MSE and adversarial loss, but this method may generate artifacts and has high computational complexity [14]. An image denoising method based on a deep residual dense network (RDUNet), leverages densely connected con- volutional layers to reuse feature maps. It also uses both local and global residual learning to mitigate the vanishing gradient problem and accelerate the training process [15]. Though RDUNet demonstrates its strong noise removal capabilities, it may result in the loss of image textures and edges during the denoising process. A self-supervised denoising method based on generative diffusion models DDM2, uses a three-stage framework that combines statistical noise modeling with conditional diffusion sampling. Without relying on clean labels, it significantly improves the denoising performance of diffusion MRI images. However, the method suffers from relatively slow inference speed and may generate pseudo-structures under extreme conditions [16].

Though mathematical models-based methods achieve notable success, they still show some limitations such as over-smoothing, edge and texture loss, high computational complexity and strong dependence on noise models. Deep learning denoising methods leverage the powerful modeling capabilities of neural networks to improve performance. However, they require sufficient sample data and have some challenges in addressing non-Gaussian noise, complex textures and detail preservation. Therefore, further advancements are needed to achieve effective denoising while preserving more image details and structural information. MRI images are prone to noise interference during the imaging process and different types of noise impact image clarity, edge structures, and detailed information [17]. Therefore, a comprehensive understanding of noise structure and characteristics is crucial to achieving optimal denoising results.

Gaussian noise primarily originates from the thermal motion of electrons in the electronic components of the imaging system, such as radio-frequency coils and pre-amplifiers [18]. In MRI, it causes random fluctuations in pixel values, resulting in a grainy appearance. When the noise level is high, the details are blurred by the noise and result in a low SNR. Gaussian noise has a significant impact on low-intensity regions of an image, potentially masking subtle tissue contrasts and impacting clinical diagnosis.

Rician noise typically occurs in signal regions and its distribution is asymmetric, especially evident in regions with low SNR. Its probability distribution follows a Rician distribution, which converges to a Rayleigh distribution at low SNR. In such cases, when the noise exhibits a significant bias, it will result in signal loss and low contrast [19].

In addition to the noise types discussed above, MRI also includes noise from various sources such as physiological processes, eddy currents, random variations, artifacts caused by magnetization between adjacent tissues, rigid body motion, non-rigid motion and other sources [20]. Unlike other types of noise, Gaussian and Rician noise uniformly affect the entire image, which significantly impedes visual interpretation and decreases the precision of medical diagnosis [21]. Consequently, we focus on analyzing the effects of Gaussian noise and Rician noise to better propose denoising methods.

In this study, we consider the characteristics of Gaussian noise and Rician noise and propose an innovative model that combines Nonlinear Mapping Network (NLMap) with an Attention Mechanism-based Adaptive Total Variation Regularization (ATVR). The framework is primarily designed for T1w MRI denoising, we additionally evaluate its generalization performance on T2w and PDw images. The main contributions are as follows:(1)

An enhanced fusion of NLMap and ATVR: NLMap captures complex nonlinear structures and ATVR adjusts smoothing intensity over regions to preserve edge details. This is achieved through integrating the method into the network training process, which simultaneously optimizes the process to circumvent the over-smoothing issue inherent to the traditional TV method. The method achieves an effective balance between noise removal and detail preservation which can be well applied in MRI denoising.

(2)

Joint loss function design: This paper integrates MSE loss, perceptual loss and ATVR loss to optimize image quality at the pixel level, feature level and spatial structure level. By optimizing the weights of perceptual loss and ATVR loss using Bayesian optimization, the model balances multi-level errors and maintains pixel-level consistency. Compared with traditional methods, our method shows significant improvement in preserving more local details.

(3)

Parameters Optimization: A Bayesian optimization framework is utilized to efficiently search the hyperparameter space using a Gaussian process, enabling the automatic selection of the optimal combination of hidden units, learning rate, training iterations and loss weights. Compared with traditional manual tuning or grid search methods, this approach achieves an optimal balance between denoising performance and image detail preservation. It also improves both model performance and tuning efficiency.

(4)

Adaptability to small sample data: Different from other deep learning-based methods, NLMap-ATVR can even be applied using small sample data. Since there is limited data available in real applicaiton, our approach is highly meaningful.

This paper is further organized as follows: Section 2 describes the proposed method. Section 3 describes simulation and experimental validation and section 4 includes the discussion of the study. The conclusion is included in section 5.