Edge-Preserving Median Filter and Weighted Coding with Sparse Nonlocal Regularization for Low-Dose CT Image Denoising Algorithm

The impulse noise in CT image was removed based on edge-preserving median filter algorithm. The sparse nonlocal regularization algorithm weighted coding was used to remove the impulse noise and Gaussian noise in the mixed noise, and the peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) were calculated to evaluate the quality of the denoised CT image. It was found that in nine different proportions of Gaussian noise and salt-and-pepper noise in Shepp-Logan image and CT image processing, the PSNR and SSIM values of the proposed denoising algorithm based on edge-preserving median filter (EP median filter) and weighted encoding with sparse nonlocal regularization (WESNR) were significantly higher than those of using EP median filter and WESNR alone. It was shown that the weighted coding algorithm based on edge-preserving median filtering and sparse nonlocal regularization had potential application value in low-dose CT image denoising.

Medical Image Denoising Algorithm Based on Sparse Nonlocal Regularized Weighted Coding and Low Rank Constraint

Medical image information may be polluted by noise in the process of generation and transmission, which will seriously hinder the follow-up image processing and medical diagnosis. In medical images, there is a typical mixed noise composed of additive white Gaussian noise (AWGN) and impulse noise. In the conventional denoising methods, impulse noise is first removed, followed by the elimination of white Gaussian noise (WGN). However, it is difficult to separate the two kinds of noises completely in practical application. The existing denoising algorithm of weight coding based on sparse nonlocal regularization, which can simultaneously remove AWGN and impulse noise, is plagued by the problems of incomplete noise removal and serious loss of details. The denoising algorithm based on sparse representation and low rank constraint can preserve image details better. Thus, a medical image denoising algorithm based on sparse nonlocal regularization weighted coding and low rank constraint is proposed. The denoising effect of the proposed method and the original algorithm on computed tomography (CT) image and magnetic resonance (MR) image are compared. It is revealed that, under different σ and ρ values, the PSNR and FSIM values of CT and MRI images are evidently superior to those of traditional algorithms, suggesting that the algorithm proposed in this work has better denoising effects on medical images than traditional denoising algorithms.

Variational Fusion of Hyperspectral Data by Non-Local Filtering

The fusion of multisensor data has attracted a lot of attention in computer vision, particularly among the remote sensing community. Hyperspectral image fusion consists in merging the spectral information of a hyperspectral image with the geometry of a multispectral one in order to infer an image with high spatial and spectral resolutions. In this paper, we propose a variational fusion model with a nonlocal regularization term that encodes patch-based filtering conditioned to the geometry of the multispectral data. We further incorporate a radiometric constraint that injects the high frequencies of the scene into the fused product with a band per band modulation according to the energy levels of the multispectral and hyperspectral images. The proposed approach proved robust to noise and aliasing. The experimental results demonstrate the performance of our method with respect to the state-of-the-art techniques on data acquired by commercial hyperspectral cameras and Earth observation satellites.

Nonlocal regularization of an anisotropic critical state model for sand

Many advanced constitutive models which can capture the strain-softening and state-dependent dilatancy response of sand have been developed. These models can give good prediction of the single soil element behaviour under various loading conditions. But the solution will be highly mesh-dependent when they are used in real boundary value problems due to the strain-softening. They can give mesh-dependent strain localization pattern and bearing capacity of foundations on sand. Nonlocal regularization of an anisotropic critical state sand model is presented. The evolution of void ratio which has a significant influence on strain-softening is assumed to depend on the volumetric strain increment of both the local and neighbouring integration points. The regularization method has been implemented using the explicit stress integration method. The nonlocal model has been used in simulating both drained plane strain compression and the response of a strip footing on dry sand. In plane strain compression, mesh-independent results for the force–displacement relationship and shear band thickness can be obtained when the mesh size is smaller than the internal length. The force–displacement relationship of strip footings predicted by the nonlocal model is much less mesh-sensitive than the local model prediction. The strain localization under the strip footing predicted by the nonlocal model is mesh independent. The regularization method is thus proper for application in practical geotechnical engineering problems.

Inverse Halftoning Based on Weighted Nuclear Norm Minimization

The inverse halftoning technology refers to restore a continuous-tone image from a halftone image with only bi-level pixes. However, recovering the continuous images from their halftoned ones is normally ill-posed, which making the inverse halftoning algorithm very challenging. In this paper, we propose an optimization model with two alternate projections (TAP) for image inverse halftoning under the weighted nuclear norm minimization (WNNM) framework. The main contributions are two-folds. First, the WNNM nonlocal regularization term is established, which offers a powerful mechanism of nonlocal self-similarity to ensure a more reliable estimation. Second, the alternate minimization projections are formulated for solving the image inverse halftoning, which reconstructs the continuous-tone image without destroying the image details and structures. The experiment results shown that the proposed method outperformed the state of the arts in terms of both objective measurements and subjective visual performance.

Hybrid High-Order and Fractional-Order Total Variation with Nonlocal Regularization for Compressive Sensing Image Reconstruction

Total variation often yields staircase artifacts in the smooth region of the image reconstruction. This paper proposes a hybrid high-order and fractional-order total variation with nonlocal regularization algorithm. The nonlocal means regularization is introduced to describe image structural prior information. By selecting appropriate weights in the fractional-order and high-order total variation coefficients, the proposed algorithm makes the fractional-order and the high-order total variation complement each other on image reconstruction. It can solve the problem of non-smooth in smooth areas when fractional-order total variation can enhance image edges and textures. In addition, it also addresses high-order total variation alleviates the staircase artifact produced by traditional total variation, still smooth the details of the image and the effect is not ideal. Meanwhile, the proposed algorithm suppresses painting-like effects caused by nonlocal means regularization. The Lagrange multiplier method and the alternating direction multipliers method are used to solve the regularization problem. By comparing with several state-of-the-art reconstruction algorithms, the proposed algorithm is more efficient. It does not only yield higher peak-signal-to-noise ratio (PSNR) and structural similarity (SSIM) but also retain abundant details and textures efficiently. When the measurement rate is 0.1, the gains of PSNR and SSIM are up to 1.896 dB and 0.048 dB respectively compared with total variation with nonlocal regularization (TV-NLR).

Adaptive Weighted High Frequency Iterative Algorithm for Fractional-Order Total Variation with Nonlocal Regularization for Image Reconstruction

We propose an adaptive weighted high frequency iterative algorithm for a fractional-order total variation (FrTV) approach with nonlocal regularization to alleviate image deterioration and to eliminate staircase artifacts, which result from the total variation (TV) method. The high frequency gradients are reweighted in iterations adaptively when we decompose the image into high and low frequency components using the pre-processing technique. The nonlocal regularization is introduced into our method based on nonlocal means (NLM) filtering, which contains prior image structural information to suppress staircase artifacts. An alternating direction multiplier method (ADMM) is used to solve the problem combining reweighted FrTV and nonlocal regularization. Experimental results show that both the peak signal-to-noise ratios (PSNR) and structural similarity index (SSIM) of reconstructed images are higher than those achieved by the other four methods at various sampling ratios less than 25%. At 5% sampling ratios, the gains of PSNR and SSIM are up to 1.63 dB and 0.0114 from ten images compared with reweighted total variation with nuclear norm regularization (RTV-NNR). The improved approach preserves more texture details and has better visual effects, especially at low sampling ratios, at the cost of taking more time.