基于支持向量机(SVM)的图像去噪方法

提出了一种基于支持向量机进行图像去噪的方法。该方法利用支持向量回归技术构造图像去噪所需的滤波器．其中特征的提取和训练样本的设计旨在抑制不同类型的噪声。实验结果表明，该方法能够有效去除噪声，并能较好地保护边缘信息，适用于边缘检测等操作的预处理。     

Estimation of 2-D noisy fractional Brownian motion and itsapplications using wavelets

The two-dimensional (2-D) fractional Brownian motion (fBm) model is useful in describing natural scenes and textures. Most fractal estimation algorithms for 2-D isotropic fBm images are simple extensions of the one-dimensional (1-D) fBm estimation method. This method does not perform well when the image size is small (say, 32x32). We propose a new algorithm that estimates the fractal parameter from the decay of the variance of the wavelet coefficients across scales. Our method places no restriction on the wavelets. Also, it provides a robust parameter estimation for small noisy fractal images. For image denoising, a Wiener filter is constructed by our algorithm using the estimated parameters and is then applied to the noisy wavelet coefficients at each scale. We show that the averaged power spectrum of the denoised image is isotropic and is a nearly 1/f process. The performance of our algorithm is shown by numerical simulation for both the fractal parameter and the image estimation. Applications to coastline detection and texture segmentation in a noisy environment are also demonstrated.     

全变差数字滤波器与Ridgelet变换相结合的图像去噪方法

针对Gurvelet变换采用的金字塔分解对图像细节表现的不足,我们提出利用全变差数字滤波器提取图像细节,然后对其采用基于分数阶傅立叶变换和投影－切片定理的Ridgelet变换,在变换域中由极小化极大误差准则进行阈值估计并对变换域系数进行阈值处理,以实现图像去噪.与金字塔分解相比,全变差数字滤波器能够简化图像分解并得到包含几乎所有细节的单幅图像,从而更有利于在Ridgelet域中进行降噪处理.实验结果表明,相对于Ridgelet和Curvelet变换的去噪方法,本文方法在抑制噪声的同时具有更有效的边缘保护能力,同时消除了边缘处的振荡,并且相对于Curvelet变换节省了计算.     

A new framework for particle detection in low-SNR fluorescence live-cell images and its application for improved particle tracking

Image denoising and signal enhancement are two common steps to improve particle contrast for detection in low-signal-to-noise ratio (SNR) fluorescence live-cell images. However, denoising may oversmooth features of interest, particularly weak features, leading to false negative detection. Here, we propose a robust framework for particle detection in which image denoising in the grayscale image is not needed, so avoiding image oversmoothing. A key to our approach is the new development of a particle enhancement filter based on the recently proposed particle probability image to obtain significantly enhanced particle features and greatly suppressed background in low-SNR and low-contrast environments. The new detection method is formed by combining foreground and background markers with watershed transform operating in both particle probability and grayscale spaces; dynamical switchings between the two spaces can optimally make use the information in images for accurate determination of particle position, size, and intensity. We further develop the interacting multiple mode filter for particle motion modeling and data association by incorporating the extra information obtained from our particle detector to enhance the efficiency of multiple particle tracking. We find that our methods lead to significant improvements in particle detection and tracking efficiency in fluorescence live-cell applications.     

Smoothing low-SNR molecular images via anisotropic median-diffusion

We propose a new anisotropic diffusion filter for denoising low-signal-to-noise molecular images. This filter, which incorporates a median filter into the diffusion steps, is called an anisotropic median-diffusion filter. This hybrid filter achieved much better noise suppression with minimum edge blurring compared with the original anisotropic diffusion filter when it was tested on an image created based on a molecular image model. The universal quality index, proposed in this paper to measure the effectiveness of denoising, suggests that the anisotropic median-diffusion filter can retain adherence to the original image intensities and contrasts better than other filters. In addition, the performance of the filter is less sensitive to the selection of the image gradient threshold during diffusion, thus making automatic image denoising easier than with the original anisotropic diffusion filter. The anisotropic median-diffusion filter also achieved good denoising results on a piecewise-smooth natural image and real Raman molecular images.     

An image denoising algorithm for mixed noise combining nonlocal means filter and sparse representation technique

Nonlocal means (NLM) filtering or sparse representation based denoising method has obtained a remarkable denoising performance. In order to integrate the advantages of two methods into a unified framework, we propose an image denoising algorithm through skillfully combining NLM and sparse representation technique to remove Gaussian noise mixed with random-valued impulse noise. In the non-Gaussian circumstance, we propose a customized blockwise NLM (CBNLM) filter to generate an initial denoised image. Based on it, we classify the different noisy pixels according to the three-sigma rule. Besides, an overcomplete dictionary is trained on the initial denoised image. Then, a complementary sparse coding technique is used to find the sparse vector for each input noisy patch over the overcomplete dictionary. Through solving a more reasonable variational denoising model, we can reconstruct the clean image. Experimental results verify that our proposed algorithm can obtain the best denoising performance, compared with some typical methods.     

Multivariate statistical modeling for image denoising using wavelet transforms

Recently a variety of efficient image denoising methods using wavelet transforms have been proposed by many researchers. In this paper, we derive the general estimation rule in the wavelet domain to obtain the denoised coefficients from the noisy image based on the multivariate statistical theory. The multivariate distributions of the original clean image can be estimated empirically from a sample image set. We define a parametric multivariate generalized Gaussian distribution (MGGD) model which closely fits the sample distribution. Multivariate model makes it possible to exploit the dependency between the estimated wavelet coefficients and their neighbours or other coefficients in different subbands. Also it can be shown that some of the existing methods based on statistical modeling are subsets of our multivariate approach. Our method could achieve high quality image denoising. Among the existing image denoising methods using the same type of wavelet (Daubechies 8) filter, our results produce the highest peak signal-to-noise ratio (PSNR).     

Image denoising via local and nonlocal circulant similarity

A patch based image denoising method is developed in this paper by introducing a new type of image self-similarity. This self-similarity is obtained by cyclic shift, which is called “circulant similarity”. Given a corrupted image patch, it can be estimated by incorporating circulant similarity into a weighted averaging filter. By choosing an appropriate kernel as weight function, the patch filter is implemented by circular convolution, and can be efficiently solved using fast Fourier transform. In addition, the circulant similarity can be enhanced by using nonlocal modeling. We stack the similar image patches into 3D groups, and propose a denoising scheme based on group estimation across the patches. Numerical experiments demonstrate that the proposed method with local circulant similarity outperforms much its local filtering based counterparts, and the proposed method with nonlocal circulant similarity shows very competitive performance with state-of-the-art denoising method, especially on images corrupted by strong noise.     

Monte-Carlo sure: a black-box optimization of regularization parameters for general denoising algorithms

We consider the problem of optimizing the parameters of a given denoising algorithm for restoration of a signal corrupted by white Gaussian noise. To achieve this, we propose to minimize Stein's unbiased risk estimate (SURE) which provides a means of assessing the true mean-squared error (MSE) purely from the measured data without need for any knowledge about the noise-free signal. Specifically, we present a novel Monte-Carlo technique which enables the user to calculate SURE for an arbitrary denoising algorithm characterized by some specific parameter setting. Our method is a black-box approach which solely uses the response of the denoising operator to additional input noise and does not ask for any information about its functional form. This, therefore, permits the use of SURE for optimization of a wide variety of denoising algorithms. We justify our claims by presenting experimental results for SURE-based optimization of a series of popular image-denoising algorithms such as total-variation denoising, wavelet soft-thresholding, and Wiener filtering/smoothing splines. In the process, we also compare the performance of these methods. We demonstrate numerically that SURE computed using the new approach accurately predicts the true MSE for all the considered algorithms. We also show that SURE uncovers the optimal values of the parameters in all cases.     

The nonsubsampled contourlet transform: theory, design, and applications.

In this paper, we develop the nonsubsampled contourlet transform (NSCT) and study its applications. The construction proposed in this paper is based on a nonsubsampled pyramid structure and nonsubsampled directional filter banks. The result is a flexible multiscale, multidirection, and shift-invariant image decomposition that can be efficiently implemented via the à trous algorithm. At the core of the proposed scheme is the nonseparable two-channel nonsubsampled filter bank (NSFB). We exploit the less stringent design condition of the NSFB to design filters that lead to a NSCT with better frequency selectivity and regularity when compared to the contourlet transform. We propose a design framework based on the mapping approach, that allows for a fast implementation based on a lifting or ladder structure, and only uses one-dimensional filtering in some cases. In addition, our design ensures that the corresponding frame elements are regular, symmetric, and the frame is close to a tight one. We assess the performance of the NSCT in image denoising and enhancement applications. In both applications the NSCT compares favorably to other existing methods in the literature.     

Online denoising method to handle intraindividual variability of signal-to-noise ratio in continuous glucose monitoring

In the last decade, the availability of new minimally invasive subcutaneous sensors for monitoring glucose level continuously stimulated research on new online strategies for improving the treatment of diabetes, including hyper/hypoglycemic alert generators and artificial pancreas. An important aspect that has to be dealt with in these applications is the random measurement noise that affects continuous glucose monitoring (CGM) signals. One major difficulty is that for a given sensor technology, the signal-to-noise ratio (SNR) can vary from subject to subject (interindividual variability) and also within subject (intraindividual variability). Recently, a denoising approach implemented through a Kalman filter with parameters automatically tuned, once for all, in a burn-in interval was proposed to cope with the interindividual variability of SNR. In this paper, we propose a new denoising method able to cope also with the intraindividual variability of the SNR. The method resorts to a Bayesian smoothing procedure that uses a statistically-based criterion to determine, and continuously update, filter parameters in real time. The performance of the method is assessed on both Monte Carlo simulation and 24 real CGM time series obtained with the Glucoday system (Menarini, Florence, Italy). The method has a general applicability, also outside from the CGM context.     

Edge-preserving image denoising via optimal color space projection

Denoising of color images can be done on each color component independently. Recent work has shown that exploiting strong correlation between high-frequency content of different color components can improve the denoising performance. We show that for typical color images high correlation also means similarity, and propose to exploit this strong intercolor dependency using an optimal luminance/color-difference space projection. Experimental results confirm that performing denoising on the projected color components yields superior denoising performance, both in peak signal-to-noise ratio and visual quality sense, compared to that of existing solutions. We also develop a novel approach to estimate directly from the noisy image data the image and noise statistics, which are required to determine the optimal projection.     

Optimal spatial adaptation for patch-based image denoising.

A novel adaptive and patch-based approach is proposed for image denoising and representation. The method is based on a pointwise selection of small image patches of fixed size in the variable neighborhood of each pixel. Our contribution is to associate with each pixel the weighted sum of data points within an adaptive neighborhood, in a manner that it balances the accuracy of approximation and the stochastic error, at each spatial position. This method is general and can be applied under the assumption that there exists repetitive patterns in a local neighborhood of a point. By introducing spatial adaptivity, we extend the work earlier described by Buades et al. which can be considered as an extension of bilateral filtering to image patches. Finally, we propose a nearly parameter-free algorithm for image denoising. The method is applied to both artificially corrupted (white Gaussian noise) and real images and the performance is very close to, and in some cases even surpasses, that of the already published denoising methods.     

Multi-stage image denoising based on correlation coefficient matching and sparse dictionary pruning

We present a novel image denoising method based on multiscale sparse representations. In tackling the conflicting problems of structure extraction and artifact suppression, we introduce a correlation coefficient matching criterion for sparse coding so as to extract more meaningful structures from the noisy image. On the other hand, we propose a dictionary pruning method to suppress noise. Based on the above techniques, an effective dictionary training method is developed. To further improve the denoising performance, we propose a multi-stage sparse coding framework where sparse representations are obtained in different scales to capture multiscale image features for effective denoising. The multi-stage coding scheme not only reduces the computational burden of previous multiscale denoising approaches, but more importantly, it also contributes to artifact suppression. Experimental results show that the proposed method achieves a state-of-the-art denoising performance in terms of both objective and subjective quality and provides significant improvements over other methods at high noise levels.     

A Robust Hidden Markov Gauss Mixture Vector Quantizer for a Noisy Source

Noise is ubiquitous in real life and changes image acquisition, communication, and processing characteristics in an uncontrolled manner. Gaussian noise and Salt and Pepper noise, in particular, are prevalent in noisy communication channels, camera and scanner sensors, and medical MRI images. It is not unusual for highly sophisticated image processing algorithms developed for clean images to malfunction when used on noisy images. For example, hidden Markov Gauss mixture models (HMGMM) have been shown to perform well in image segmentation applications, but they are quite sensitive to image noise. We propose a modified HMGMM procedure specifically designed to improve performance in the presence of noise. The key feature of the proposed procedure is the adjustment of covariance matrices in Gauss mixture vector quantizer codebooks to minimize an overall minimum discrimination information distortion (MDI). In adjusting covariance matrices, we expand or shrink their elements based on the noisy image. While most results reported in the literature assume a particular noise type, we propose a framework without assuming particular noise characteristics. Without denoising the corrupted source, we apply our method directly to the segmentation of noisy sources. We apply the proposed procedure to the segmentation of aerial images with Salt and Pepper noise and with independent Gaussian noise, and we compare our results with those of the median filter restoration method and the blind deconvolution-based method, respectively. We show that our procedure has better performance than image restoration-based techniques and closely matches to the performance of HMGMM for clean images in terms of both visual segmentation results and error rate.     

Patch-Based Nonlocal Functional for Denoising Fluorescence Microscopy Image Sequences

We present a nonparametric regression method for denoising 3-D image sequences acquired via fluorescence microscopy. The proposed method exploits the redundancy of the 3-D+time information to improve the signal-to-noise ratio of images corrupted by Poisson-Gaussian noise. A variance stabilization transform is first applied to the image-data to remove the dependence between the mean and variance of intensity values. This preprocessing requires the knowledge of parameters related to the acquisition system, also estimated in our approach. In a second step, we propose an original statistical patch-based framework for noise reduction and preservation of space-time discontinuities. In our study, discontinuities are related to small moving spots with high velocity observed in fluorescence video-microscopy. The idea is to minimize an objective nonlocal energy functional involving spatio-temporal image patches. The minimizer has a simple form and is defined as the weighted average of input data taken in spatially-varying neighborhoods. The size of each neighborhood is optimized to improve the performance of the pointwise estimator. The performance of the algorithm (which requires no motion estimation) is then evaluated on both synthetic and real image sequences using qualitative and quantitative criteria.      

A low light natural image statistical model for joint contrast enhancement and denoising

We study the problem of joint low light image contrast enhancement and denoising using a statistical approach. The low light natural image in the band pass domain is modeled by statistically relating a Gaussian scale mixture model for the pristine image, to the low light image, through a detail loss coefficient and Gaussian noise. The detail loss coefficient is statistically described using a posterior distribution with respect to its estimate based on a prior contrast enhancement algorithm. We then design our low light enhancement and denoising (LLEAD) method by computing the minimum mean squared error estimate of the pristine image band pass coefficients. We create the Indian Institute of Science low light image dataset of well-lit and low light image pairs to learn the model parameters and evaluate our enhancement method. We show through extensive experiments on multiple datasets that our method helps better enhance the contrast while simultaneously controlling the noise when compared to other state of the art joint contrast enhancement and denoising methods.     

PSO-based learning of sub-band adaptive thresholding function for image denoising

In this paper, a new computationally efficient approach has been proposed for denoising the images which are corrupted by Gaussian noise. In this approach, relatively recent category of stochastic global optimization technique i.e., particle swarm optimization (PSO) technique have been proposed for learning the parameters of adaptive thresholding function required for optimum performance. The proposed PSO-based denoising approach not only speeds up the optimization but also improves the performance in comparison with wavelet transform-based thresholding neural network (WT-TNN) approach. The results obtained shows better edge preservation performance with bior6.8 wavelet filter when compared to db8 wavelet filter. Further, problem of dependency of learning time on initial value of thresholding parameters and noise level in the image have been sorted out in the proposed approach.     

Robust NL-Means Filter With Optimal Pixel-Wise Smoothing Parameter for Statistical Image Denoising

Most denoising methods require that some smoothing parameters be set manually to optimize their performance. Among these methods, a new filter based on nonlocal weighting (NL-means filter) has been shown to have a very attractive denoising capacity. In this paper, we propose fixing the smoothing parameter of this filter automatically. The smoothing parameter corresponds to the bandwidth h of a local constant regression. We use the C_p statistic embedded in Newton's method to optimize h in a point-wise fashion. This statistic also has the advantage of being a reliable measure of the quality of the denoising process for each pixel. In addition, we introduce a robust regression in the NL-means filter designed to greatly reduce the blur yielded by the weighting. Finally, we show how the automatic denoising model can be extended to images degraded by multiplicative noise. Experiments conducted on images with additive and multiplicative noise demonstrate a high denoising power with a degree of detail preservation...     

B-spline wavelets for signal denoising and image compression

In this paper we propose to develop novel techniques for signal/image decomposition, and reconstruction based on the B-spline mathematical functions. Our proposed B-spline based multiscale/resolution representation is based upon a perfect reconstruction analysis/synthesis point of view. Our proposed B-spline analysis can be utilized for different signal/imaging applications such as compression, prediction, and denoising. We also present a straightforward computationally efficient approach for B-spline basis calculations that is based upon matrix multiplication and avoids any extra generated basis. Then we propose a novel technique for enhanced B-spline based compression for different image coders by preprocessing the image prior to the decomposition stage in any image coder. This would reduce the amount of data correlation and would allow for more compression, as will be shown with our correlation metric. Extensive simulations that have been carried on the well-known SPIHT image coder with and without the proposed correlation removal methodology are presented. Finally, we utilized our proposed B-spline basis for denoising and estimation applications. Illustrative results that demonstrate the efficiency of the proposed approaches are presented.