A multi-stage algorithm for image denoising based on PCA and adaptive TV-regularization

In this paper, we present an image denoising algorithm comprising three stages. In the first stage, Principal Component Analysis (PCA) is used to suppress the noise. PCA is applied to image blocks to characterize localized features and rare image patches. In the second stage, we use the Gaussian curvature to develop an adaptive total-variation-based (TV) denoising model to effectively remove visual artifacts and noise residual generated by the first stage. Finally, the denoised image is sharpened in order to enhance the contrast of the denoising result. Experimental results on natural images and computed tomography (CT) images demonstrated that the proposed algorithm yields denoising results better than competing algorithms in terms of both qualitative and quantitative aspects.

Denoising of Tourist Street Scene Image Based on ROF Model of Second-Order Partial Differential Equation

The noise pollution in tourist street view images is caused by various reasons. A major challenge that researchers have been facing is to find a way to effectively remove noise. Although in the past few decades people have proposed many methods of denoising tourist street scene images, the research on denoising technology of tourist street scene images is still not outdated. There is no doubt that it has become a basic and important research topic in the field of digital image processing. The evolutionary diffusion method based on partial differential equations is helpful to improve the quality of noisy tourist street scene images. This method can process tourist street scene images according to people’s expected diffusion behavior. The adaptive total variation model proposed in this paper is improved on the basis of the total variation model and the Gaussian thermal diffusion model. We analyze the classic variational PDE-based denoising model and get a unified variational PDE energy functional model. We also give a detailed analysis of the diffusion performance of the total variational model and then propose an adaptive total variational diffusion model. By improving the diffusion coefficient and introducing a curvature operator that can distinguish details such as edges, it can effectively denoise the tourist street scene image, and it also has a good effect on avoiding the step effect. Through the improvement of the ROF model, the loyalty term and regular term of the model are parameterized, the adaptive total variation denoising model of this paper is established, and a detailed analysis is carried out. The experimental results show that compared with some traditional denoising models, the model in this paper can effectively suppress the step effect in the denoising process, while protecting the texture details of the edge area of the tourist street scene image. In addition, the model in this paper is superior to traditional denoising models in terms of denoising performance and texture structure protection.

Ensemble Adaptive Total Variation Graph Regularized NMF for Single-cell RNA-Seq Data Analysis

Background: Single-cell RNA sequencing techniques have emerged as effective approaches for finding the heterogeneity between cells and discovering the differentiation stage. Adaptive total variation graph regularized nonnegative matrix factorization (ATV-NMF) has been proposed to capture the inner geometric structure and determine whether to retain feature details or denoise, which is suitable for analyzing single-cell data. However, the rank of matrix factorization significantly affects clustering performance greatly, and it is still challenging to determine the optimal rank. Objective: To solve the problem, in this paper, we propose an ensemble clustering method ANMF-CE to integrate several base clustering results corresponding to different parameter rank values. Method: First, we use the ATV-NMF algorithm to obtain clustering results with different dimension reduction ranks. Second, the consensus function based on connected-triple-based similarity is applied to obtain the similarity matrix. Finally, the spectral clustering method is used to find the final optimal partition. Results: Clustering results on six single-cell sequencing datasets show that our method is more advanced than the individual ATV-NMF method and other comparison methods, which can illustrate that our method is effective in finding the heterogeneity in single-cell datasets. Moreover, the identification of gene markers also achieves accurate results. Conclusion: In summary, our method is effective for analyzing single-cell RNA sequencing datasets.

Image Deconvolution with Hybrid Reweighted Adaptive Total Variation (HRATV) for Optoacoustic Tomography

Optoacoustic tomography (OAT) is a hybrid biomedical imaging modality that usually employs a transducer array to detect laser-generated ultrasonic signals. The reconstructed image suffers low contrast and degraded resolution due to the limited bandwidth and the spatial directivity of the transducer element. Here, we introduce a modified image deconvolution method with a hybrid reweighted adaptive total variation tailored to improve the image quality of OAT. The effectiveness and the parameter dependency of the proposed method are verified on standard test images. The performance of the proposed method in OAT is then characterized on both simulated phantoms and in vivo mice experiments, which demonstrates that the modified deconvolution algorithm is able to restore the sharp edges and fine details in OAT simultaneously. The signal-to-noise ratios (SNRs) of the target structures in mouse liver and brain were improved by 4.90 and 12.69 dB, respectively. We also investigated the feasibility of using Fourier ring correlation (FRC) as an indicator of the image quality to monitor the deconvolution progress in OAT. Based on the experimental results, a practical guide for image deconvolution in OAT was summarized. We anticipate that the proposed method will be a promising post-processing tool to enhance the visualization of micro-structures in OAT.