Enhancing diffusion-weighted prostate MRI through self-supervised denoising and evaluation

Abstract

Diffusion-weighted imaging (DWI) is a magnetic resonance imaging (MRI) technique that provides information about the Brownian motion of water molecules within biological tissues. DWI plays a crucial role in stroke imaging and oncology, but its diagnostic value can be compromised by the inherently low signal-to-noise ratio (SNR). Conventional supervised deep learning-based denoising techniques encounter challenges in this domain as they necessitate noise-free target images for training. This work presents a novel approach for denoising and evaluating DWI scans in a self-supervised manner, eliminating the need for ground-truth data. By leveraging an adapted version of Stein's unbiased risk estimator (SURE) and exploiting a phase-corrected combination of repeated acquisitions, we outperform both state-of-the-art self-supervised denoising methods and conventional non-learning-based approaches. Additionally, we demonstrate the applicability of our proposed approach in accelerating DWI scans by acquiring fewer image repetitions. To evaluate denoising performance, we introduce a self-supervised methodology that relies on analyzing the characteristics of the residual signal removed by the denoising approaches.

Fig. 1

Representative averaged diffusion-weighted prostate images from the fastMRI data set for both b-values b50 and b1000 in the x, y, and z-directions are presented along with their corresponding trace images.

Fig. 2

The proposed denoising pipeline using only image data. We start from the tri-directional image repetitions for two distinct b-values, b50 and b1000. During the preprocessing phase, we generate an averaged image for each direction x,y, and z by employing complex averaging alongside phase correction for both b-values. Corresponding noise maps are further computed for the b1000 images. The averaged images for b50 and b1000 are then concatenated along the channel dimension into a joint input for the denoising network DnCNN, where the b50 images serve as guidance. The noise maps are employed in the calculation of the SURE loss, facilitating the optimization of network parameters.

Fig. 3

The impact of different processing techniques on the fastMRI b1000 data. The first image shows a single repetition (magnitude image) exhibiting low SNR. Then, we show three different ways of computing the trace image: using the conventional magnitude averaging, complex averaging and complex averaging in combination with a phase correction (PC). For comparison, all trace images are displayed within the same intensity range. The last image shows a noise map, indicating the noise level with pixel accuracy derived directly from the image repetitions.

Fig. 4

The proposed pipeline using a dedicated noise prescan as additional input. The denoising process initiates with phase correction applied to all image repetitions, followed by generating averaged images for each of the four diffusion directions. These averaged images serve as input for the U-Net denoising network, which is trained through a self-supervised approach utilizing an extended SURE method tailored for spatially variant Gaussian noise. The SURE method incorporates a noise map that represents the pixel-wise noise standard deviation. This map is derived from a dedicated noise adjustment scan conducted during scanner calibration, taking into consideration the g-factor map, bias field, and scaling factors to accommodate phase correction and the effects of averaging.

Fig. 5

The first column shows a 0.55 T image from a single repetition for both b-values, b50, and b800. Notably, the b800 repetition demonstrates particularly low SNR. In the second through fifth columns, averaged images for the four distinct diffusion directions are displayed. These images are derived from two repetitions for b50 and 15 repetitions for b800 (instead of the routinely acquired four and 22 repetitions, respectively), serving as the input to the network. Furthermore, corresponding noise maps are presented, detailing the standard deviation of noise for each pixel. The noise maps were derived from a dedicated noise prescan.

Fig. 6

Comparison of different denoising methods using the full number of repetitions included in the fastMRI data set acquired at 3 T. The top row exhibits the b1000 images and the corresponding region of interest (ROI) displayed in the second row. In the third row, the residual noise, i.e., the difference between the noisy and denoised images, is presented. The last row depicts the pixel intensities of the noisy input and the respective denoising result along the lines presented in the second row. Our SURE-based approach excels in effectively removing noise from the image while preserving image sharpness. In the pixel intensity plot, it is clear that the denoised pixel intensities exhibit peaks aligned with those of the noisy pixel intensities, albeit with a noticeably smoother curve.

Fig. 7

The quantitative evaluation of denoising for fastMRI b1000 images encompasses two aspects: (1) the variance of the corrected residual (optimal value: close to 1.0, represented by the green line), and (2) the Gaussian log-likelihood of the corrected residual. Notably, the SURE method achieves a variance close to 1.0 and the highest Gaussian log-likelihood, signifying that the noise removed by SURE aligns closely with the physical noise model.

Fig. 8

The impact of including the low b-value fastMRI data (3 T). The figure displays denoised b1000 images generated by each method, showing results without the incorporation of b50 data (first row) and with its incorporation (second row). In the third row, the difference between the images when b50 data is included and when it is omitted is presented. While incorporating b50 data considerably impacts the denoising performance of the MPPCA-based method, the difference images indicate a subtle edge enhancement effect for the learning-based methods.

Fig. 9

Comparison of different denoising methods using 50% of the available image repetitions included in the fastMRI data set (3 T). The upper row displays both the b1000 images and their corresponding ROI, which is presented in the second row. FRC denotes the trace image using the full repetition count (12) per diffusion direction, while the network input was derived from six repetitions per diffusion direction. The third row shows the residual noise, which displays the difference between the noisy and denoised images. The final row depicts the pixel intensities of both the noisy input and the corresponding denoising results, along the lines presented in the second row.

Fig. 10

Visual assessment for both b50 and b800 0.55 T images. The first row exhibits the noisy/denoised trace images, with the repetition count per diffusion direction indicated in brackets. The second row displays the difference (i.e., residual) images with respect to the input, all displayed within the same intensity range. The image recovered from the full repetition count (FRC) exhibits considerable alterations of image content, potentially attributed to motion. Conversely, the SURE result showcases efficient noise reduction without any apparent loss of image content.

Fig. 11

Quantitative assessment for both b-values (b50 and b800) of the 0.55 T in-house data set includes (1) the variance of the corrected residual (ideal value: close to 1.0, denoted by the green line) and (2) the Gaussian log-likelihood of the corrected residual. Remarkably, SURE attains a variance close to 1.0 and the highest Gaussian log-likelihood, indicating that the noise eliminated by SURE closely adheres to the physical noise model.

Fig. 12

Quantitative assessment of the SURE-based model on the b800 0.55 T in-house data set for a varying number of image repetitions (5, 10, and 15). Left: the variance of the corrected residual (ideal value: close to 1.0, denoted by the green line). Right: the Gaussian log-likelihood of the corrected residual. As the number of image repetitions increases, the variance decreases slightly, while the Gaussian log-likelihood shows a slight increase.

Fig. 13

Representative b800 0.55 T image slices including 5, 10, and 15 repetitions per diffusion direction. The model, trained exclusively on higher field data using our proposed SURE-based methodology, successfully delivers effective denoising results across all tested variations.