Maximum entropy method for imaging through turbid medium

In medical applications, computed tomography (CT) is widely used to evaluate various sample characteristics. However, image quality of CT reconstruction can be degraded due to artifacts. To propose and test a truncated total variation (truncation TV) model to solve the problem of large penalties for the total variation (TV) model. In this study, a truncated TV image denoising model in the fractional B-spline wavelet domain is developed to obtain the best solution. The method is validated by the analysis of CT reconstructed images of actual biological Pigeons samples. For this purpose, several indices including the peak signal-to-noise ratio (PSNR), structural similarity index (SSIM) and mean square error (MSE) are used to evaluate the quality of images. Comparing to the conventional truncated TV model that yields 22.55, 0.688 and 361.17 in PSNR, SSIM and MSE, respectively, using the proposed fractional B-spline-truncated TV model, the computed values of these evaluation indices change to 24.24, 0.898 and 244.98, respectively, indicating substantial reduction of image noise with higher PSNR and SSIM, and lower MSE. Study results demonstrate that compared with many classic image denoising methods, the new denoising algorithm proposed in this study can more effectively suppresses the reconstructed CT image artifacts while maintaining the detailed image structure.

The problem for image restoration is usually reduced to a constraint optimization problem. Different choice of optimization operator leads to various restoration models, e.g. least squares model and original total variation (TV) model. The TV model and its modified version can efficiently preserve the edge of the restored image well, but there exist obvious staircases in smooth area of the restored image. To reduce those staircases, we propose a new modified TV model, by adding a constraint term for smooth area protection as a penalty function. The numerical experiment shows our model can not only preserve the edge as well as TV model, but also efficiently reduce the staircase appearing in the smooth areas. Furthermore, It is shown that the restored image by our model has higher signal-to-noise ratio, less mean square error and better visual effect than those by the least squares model and by the TV models.

Several methods based on Total Variation (TV) have been proposed for Hyperspectral Image (HSI) denoising. However, the TV terms of these methods just use various l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norms and penalize image gradient magnitudes, having a negative influence on the preprocessing of HSI denoising and further HSI classification task. In this paper, a novel l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> Total Variation (l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV) is first introduced and analyzed for the HSI noise removal framework to preserve more information for classification. We propose a novel Tensor low-rank constraint and l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> Total Variation (TLR-l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV) model in this paper. l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV directly controls the number of non-zero gradients and focuses on recovering the sharp image edges. The spectral-spatial information among all bands is exploited uniformly for removing mixed noise, which facilitates the subsequent classification after denoising. Including the Weighted Sum of Weighted Nuclear Norm (WSWNN) and the Weighted Sum of Weighted Tensor Nuclear Norm (WSWTNN), we propose two TLR-l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV-based algorithms, namely WSWNN-l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV and WSWTNN-l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV. The Alternating Direction Method of Multipliers (ADMM) and the Augmented Lagrange Multiplier (ALM) are employed to solve the l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV model and TLR-l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV model, respectively. In both simulated and real data, the proposed models achieve superior performances in mixed noise removal of HSI. Especially, HSI classification accuracy is improved more effectively after denoising by the proposed TLR-l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> TV method.

Purpose. The total variation (TV) minimization algorithm is an effective image reconstruction algorithm capable of accurately reconstructing images from sparse and/or noisy data. The TV model consists of two terms: a data fidelity term and a TV regularization term. Two constrained TV models, data divergence-constrained TV minimization (DDcTV) and TV-constrained data divergence minimization (TVcDM), have been successfully applied to computed tomography (CT) and electron paramagnetic resonance imaging (EPRI). In this work, we propose a new constrained TV model, a doubly constrained TV (dcTV) model, which has the potential to further improve the reconstruction accuracy for the two terms which are both of constraint forms. Methods. We perform an inverse crime study to validate the model and its Chambolle-Pock (CP) solver and characterize the performance of the dcTV-CP algorithm in the context of CT. To demonstrate the superiority of the dcTV model, we compare the convergence rate and the reconstruction accuracy with the DDcTV and TVcDM models via simulated data. Results and Conclusions. The performance-characterizing study shows that the dcTV-CP algorithm is an accurate and convergent algorithm, with the model parameters impacting the reconstruction accuracy and the algorithm parameters impacting the convergence path and rate. The comparison studies show that the dcTV-CP algorithm has a relatively fast convergence rate and can achieve higher reconstruction accuracy from sparse projections or noisy projections relative to the other two single-constrained TV models. The knowledge and insights gained in the work may be utilized in the application of the new model in other imaging modalities including divergence-beam CT, magnetic resonance imaging (MRI), positron emission tomography (PET), and EPRI.

Although the traditional TV (Total Variation) model owns excellent image denoising ability, there are staircase effect problems for TV model. In this article, two detection operators for staircase effect problem are proposed. The staircase effect problem can be solved effectively by introducing two operators into traditional TV model. On the basis, it proposes an adaptive total variation model for image denoising. When dealing with image edge, it can still use the traditional TV model. Its purpose is to maintain the advantages in edge protection for TV model. When it is in the smooth area of image, linear diffusion is used to avoid the staircase effect.

Although the Total Variation (TV) model has good performance in the image inpainting including both maintaining damaged images' edge and reducing numerical calculation, it should be improved in the inpainting domain with rich texture. In this paper, an image multi-level-inpainting method based on TV model and texture synthesis scheme is proposed. It is the main research topic to improve the visual result of inpainted images with scratches including rich texture. At the first inpainting level, damaged images are calculated following the TV model, and then the patch-based texture synthesis scheme is used to improve the inpainted results of rich texture domain in the first level. Experimental results prove that the method has better performance in restoring an incomplete 2-D image in every detail that it looks more `complete' and `natural'.

Fractional-order derivative is attracting more and more interest from researchers working on image processing because it helps to preserve more texture than total variation when noise is removed. In the existing works, the Grunwald–Letnikov fractional-order derivative is usually used, where the Dirichlet homogeneous boundary condition can only be considered and therefore the full lower triangular Toeplitz matrix is generated as the discrete partial fractional-order derivative operator. In this paper, a modified truncation is considered in generating the discrete fractional-order partial derivative operator and a truncated fractional-order total variation (tFoTV) model is proposed for image restoration. Hopefully, first any boundary condition can be used in the numerical experiments. Second, the accuracy of the reconstructed images by the tFoTV model can be improved. The alternating directional method of multiplier is applied to solve the tFoTV model. Its convergence is also analyzed briefly. In the numerical experiments, we apply the tFoTV model to recover images that are corrupted by blur and noise. The numerical results show that the tFoTV model provides better reconstruction in peak signal-to-noise ratio (PSNR) than the full fractional-order variation and total variation models. From the numerical results, we can also see that the tFoTV model is comparable with the total generalized variation (TGV) model in accuracy. In addition, we can roughly fix a fractional order according to the structure of the image, and therefore, there is only one parameter left to determine in the tFoTV model, while there are always two parameters to be fixed in TGV model.

Following the traditional total variational denoising model in removing medical image noise with blurred image texture details, among other problems, an adaptive medical image fractional-order total variational denoising model with an improved sparrow search algorithm is proposed in this study. This algorithm combines the characteristics of fractional-order differential operators and total variational models. The model preserves the weak texture region of the image improvement based on the unique amplitude-frequency characteristics of the fractional-order differential operator. The order of the fractional-order differential operator is adaptively determined by the improved sparrow search algorithm using both the sine search strategy and the diversity variation processing strategy, which can greatly improve the denoising ability of the fractional-order differential operator. The experimental results reveal that the model not only achieves the adaptivity of fractional-order total variable differential order, but also can effectively remove noise, preserve the texture structure of the image to the maximum extent, and improve the peak signal-to-noise ratio of the image; it also displays favorable prospects for applications in medical image denoising.

In this paper, we introduce two novel total variation models to deal with speckle noise in ultrasound image in order to retain the fine details more effectively and to improve the speed of energy diffusion during the process. Firstly, two new convex functions are introduced as regularization term in the adaptive total variation model, and then, the diffusion performances of Hypersurface Total Variation (HYPTV) model and Logarithmic Total Variation (LOGTV) model are analyzed mathematically through the physical characteristics of local coordinates. We have shown that the larger positive parameter in the model is set, the greater energy diffusion speed appears to be, but it will cause the image to be too smooth that required adequate attention. Numerical experimental results show that our proposed LOGTV model for speckle noise removal is superior to traditional models, not only in visual effect but also in quantitative measures.

Non-blind image deblurring method by local and nonlocal total variation models

By analyzing three important denoising models: the harmonical model, the TV (total variation) model and the generalized TV model, we have proposed an adaptive one which is named `adaptive TV image denoising model'. On the basis of SNR of noisy images, this model can pretreat them with Gaussian filter, so as to overcome the staircase effect in the TV model. Then by utilizing the gradient information of every pixel point of the image, we can adaptively select the most appropriate denoising scheme. The results of numerical experiments show that this method can preserve significant image details while removing the noise. Compared with other variational denoising methods, especially at high noise levels, the method achieves at least about 1.0dB gain for Peak Signal to the Noise Ratio (as PSNR for short) measurement.

The traditional total variational (TV) model performs well for most noise image. However, the method will lose some information and details for the image which has rich texture and tiny boundary. Therefore, according to the requirements of the OCT pearl image, a novel denoising approach based on the TV model is proposed in this paper. This method combined the adaptive image denoising model and the novel fidelity term. Numerical experiments show that the proposed method can remove the noise while preserving significant image details. At pearl OCT image the method achieves at least 0.1dB gain over other existing denoising methods for Signal-Noise Ratio (SNR) measurement and Peak Signal-Noise Ratio (PSNR) measurement.

In this study, a novel image edge detection technique based on the combination of total variation (TV) and anisotropic diffusion (PM) models is presented. In the proposed technique, the authors first use the gradient magnitude to eliminate the noise, then utilise the adaptive weight function to detect the edges of the image. The adaptive weight function has a high ability to adapt and change according to the areas information (edges or flats areas). More specifically, TV filter is applied on the areas which suffer from double and false edges, whereas, anisotropic diffusion filter is applied on the areas which suffer from weak and discontinuous edges. Applying TV filter on the double edges areas will allow one to remove most of the false edges, and thus to obtain much sharper edges. While, applying anisotropic diffusion filter on the discontinuous edges areas will lead to obtaining robust and continuous edges. Consequently, less false edges besides high localisation accuracy were obtained. Experimental results demonstrate the superiority of the new approach in terms of removing the false edges and improving the localisation accuracy of the edges. As objective quantitative performance measures, the peak signal‐to‐noise ratio (PSNR) and Pratt's figure of merit (FOM) were used.

Image restoration is a key step in the field of image processing. Total Variation (TV) model is widely applied in image denoising because it preserves edges and image details. However, TV model has some shortcomings, such as staircase artifacts and excessive smoothing of image texture area. Then we purpose a truncated L1-L2 Total Variational model, which is nonconvex and nonsmooth, for image restoration with impulse noise. In this proper, two algorithms, the alternating direction method of multiplier (ADMM) and the penalty-Gaussian Seidel type inertial proximal alternating linearized minimization (P-GiPALM), are designed to solve the nonconvex optimization. The subproblems are solved by the proximal difference-of -convex algorithm with extrapolation (pDCAe) and GiPALM with global convergence, respectively. The experimental results show that the new model has higher peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) values than those of median filter and the cutting-edge Cauchy denoising method.

The total variation (TV) model is attractive in that it is able to preserve sharp attributes in images. However, the restored images from TV-based methods do not usually stay in a given dynamic range, and hence projection is required to bring them back into the dynamic range for visual presentation or for storage in digital media. This will affect the accuracy of the restoration as the projected image will no longer be the minimizer of the given TV model. In this paper, we show that one can get much more accurate solutions by imposing box constraints on the TV models and solving the resulting constrained models. Our numerical results show that for some images where there are many pixels with values lying on the boundary of the dynamic range, the gain can be as great as 10.28 decibel in the peak signal-to-noise ratio. One traditional hindrance using the constrained model is that it is difficult to solve. However, in this paper, we propose using the alternating direction method of multipliers (ADMM) to solv...