Speckle reduction remains a critical issue for ultrasound image processing and analysis. The nonlocal means (NLM) filter has recently attached much attention due to its competitive despeckling performance. However, the existing NLM methods usually determine the similarity between two patches by directly utilizing the gray-level information of the noisy image, which renders it difficult to represent the structural similarity of ultrasound images effectively. To address this problem, the NLM method based on the simple deep learning baseline named PCANet is proposed by introducing the intrinsic features of image patches extracted by this network rather than the pixel intensities into the pixel similarity computation. In this approach, the improved two-stage PCANet is proposed by using Parametric Rectified Linear Unit (PReLU) activation function instead of the binary hashing and block histograms in the original PCANet. This model is firstly trained on the ultrasound database to learn the convolution kernels. Then, the trained PCANet is utilized to extract the intrinsic features from the image patches in the pre-denoised version of the noisy image to be despeckled. These obtained features are concatenated together to determine the structural similarity between image patches in the NLM method, based on which the weighted mean of all pixels in a search window is computed to produce the final despeckled image. Extensive experiments have been conducted on a variety of images to demonstrate the superiority of the proposed method over several well-known despeckling algorithm and the PCANet based NLM method using ReLU function and sigmoid function. Visual inspection indicates that the proposed method outperforms the compared methods in reducing speckle noise and preserving image details. The quantitative comparisons show that among all the evaluated methods, our method produces the best structural similarity index metrics (SSIM) values for the synthetic image, as well as the highest equivalent number of looks (ENL) value for the simulated image and the clinical ultrasound images.

Magnetic resonance (MR) images are often corrupted by Rician noise which degrades the accuracy of image-based diagnosis tasks. The nonlocal means (NLM) method is a representative filter in denoising MR images due to its competitive denoising performance. However, the existing NLM methods usually exploit the gray-level information or hand-crafted features to evaluate the similarity between image patches, which is disadvantageous for preserving the image details while smoothing out noise. In this paper, an improved nonlocal means method is proposed for removing Rician noise in MR images by using the refined similarity measures. The proposed method firstly extracts the intrinsic features from the pre-denoised image using a shallow convolutional neural network named Laplacian eigenmaps network (LEPNet). Then, the extracted features are used for computing the similarity in the NLM method to produce the denoised image. Finally, the method noise of the denoised image is utilized to further improve the denoising performance. Specifically, the LEPNet model is composed of two cascaded convolutional layers and a nonlinear output layer, in which the Laplacian eigenmaps are employed to learn the filter bank in the convolutional layers and the Leaky Rectified Linear Unit activation function is used in the final output layer to output the nonlinear features. Due to the advantage of LEPNet in recovering the geometric structure of the manifold in the low-dimension space, the features extracted by this network can facilitate characterizing the self-similarity better than the existing NLM methods. Experiments have been performed on the BrainWeb phantom and the real images. Experimental results demonstrate that among several compared denoising methods, the proposed method can provide more effective noise removal and better details preservation in terms of human vision and such objective indexes as peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM).