Non-local Means Algorithm Research Articles

Image Denoising Methods. A New Nonlocal Principle

The search for efficient image denoising methods is still a valid challenge at the crossing of functional analysis and statistics. In spite of the sophistication of the recently proposed methods, most algorithms have not yet attained a desirable level of applicability. All show an outstanding performance when the image model corresponds to the algorithm assumptions but fail in general and create artifacts or remove fine structures in images. The main focus of this paper is, first, to define a general mathematical and experimental methodology to compare and classify classical image denoising algorithms and, second, to propose a nonlocal means (NL-means) algorithm addressing the preservation of structure in a digital image. The mathematical analysis is based on the analysis of the “method noise,” defined as the difference between a digital image and its denoised version. The NL-means algorithm is proven to be asymptotically optimal under a generic statistical image model. The denoising performance of all considered methods is compared in four ways; mathematical: asymptotic order of magnitude of the method noise under regularity assumptions; perceptual-mathematical: the algorithms artifacts and their explanation as a violation of the image model; quantitative experimental: by tables of $L^2$ distances of the denoised version to the original image. The fourth and perhaps most powerful evaluation method is, however, the visualization of the method noise on natural images. The more this method noise looks like a real white noise, the better the method.

SURE-Based Non-Local Means

Non-local means (NLM) provides a powerful framework for denoising. However, there are a few parameters of the algorithm-most notably, the width of the smoothing kernel-that are data-dependent and difficult to tune. Here, we propose to use Stein's unbiased risk estimate (SURE) to monitor the mean square error (MSE) of the NLM algorithm for restoration of an image corrupted by additive white Gaussian noise. The SURE principle allows to assess the MSE without knowledge of the noise-free signal. We derive an explicit analytical expression for SURE in the setting of NLM that can be incorporated in the implementation at low computational cost. Finally, we present experimental results that confirm the optimality of the proposed parameter selection.

A moment-based nonlocal-means algorithm for image denoising

Image denoising is a crucial step to increase image quality and to improve the performance of all the tasks needed for quantitative imaging analysis. The nonlocal (NL) means filter is a very successful technique for denoising textured images. However, this algorithm is only defined up to translation without considering the orientation and scale for each image patch. In this paper, we introduce the Zernike moments into NL-means filter, which are the magnitudes of a set of orthogonal complex moments of the image. The Zernike moments in small local windows of each pixel in the image are computed to obtain the local structure information for each patch, and then the similarities according to this information are computed instead of pixel intensity. For the rotation invariant of the Zernike moments, we can get much more pixels or patches with higher similarity measure and make the similarity of patches translation-invariant and rotation-invariant. The proposed algorithm is demonstrated on real images corrupted by white Gaussian noise (WGN). The comparative experimental results show that the improved NL-means filter achieves better denoising performance.

Iterative Weighted Maximum Likelihood Denoising With Probabilistic Patch-Based Weights

Image denoising is an important problem in image processing since noise may interfere with visual or automatic interpretation. This paper presents a new approach for image denoising in the case of a known uncorrelated noise model. The proposed filter is an extension of the nonlocal means (NL means) algorithm introduced by Buades , which performs a weighted average of the values of similar pixels. Pixel similarity is defined in NL means as the Euclidean distance between patches (rectangular windows centered on each two pixels). In this paper, a more general and statistically grounded similarity criterion is proposed which depends on the noise distribution model. The denoising process is expressed as a weighted maximum likelihood estimation problem where the weights are derived in a data-driven way. These weights can be iteratively refined based on both the similarity between noisy patches and the similarity of patches extracted from the previous estimate. We show that this iterative process noticeably improves the denoising performance, especially in the case of low signal-to-noise ratio images such as synthetic aperture radar (SAR) images. Numerical experiments illustrate that the technique can be successfully applied to the classical case of additive Gaussian noise but also to cases such as multiplicative speckle noise. The proposed denoising technique seems to improve on the state of the art performance in that latter case.

Denoising of Dynamic Contrast-Enhanced MR Images Using Dynamic Nonlocal Means

This paper presents a new algorithm for denoising dynamic contrast-enhanced (DCE) MR images. It is a novel variation on the nonlocal means (NLM) algorithm. The algorithm, called dynamic nonlocal means (DNLM), exploits the redundancy of information in the temporal sequence of images. Empirical evaluations of the performance of the DNLM algorithm relative to seven other denoising methods-simple Gaussian filtering, the original NLM algorithm, a trivial extension of NLM to include the temporal dimension, bilateral filtering, anisotropic diffusion filtering, wavelet adaptive multiscale products threshold, and traditional wavelet thresholding-are presented. The evaluations include quantitative evaluations using simulated data and real data (20 DCE-MRI data sets from routine clinical breast MRI examinations) as well as qualitative evaluations using the same real data (24 observers: 14 image/signal-processing specialists, 10 clinical breast MRI radiographers). The results of the quantitative evaluation using the simulated data show that the DNLM algorithm consistently yields the smallest MSE between the denoised image and its corresponding original noiseless version. The results of the quantitative evaluation using the real data provide evidence, at the alpha = 0.05 level of significance, that the DNLM algorithm yields the smallest MSE between the denoised image and its corresponding original noiseless version. The results of the qualitative evaluation provide evidence, at the alpha = 0.05 level of significance, that the DNLM algorithm performs visually better than all of the other algorithms. Collectively the qualitative and quantitative results suggest that the DNLM algorithm more effectively attenuates noise in DCE MR images than any of the other algorithms.

SNR enhancement of highly-accelerated real-time cardiac MRI acquisitions based on non-local means algorithm

Real-time cardiac MRI appears as a promising technique to evaluate the mechanical function of the heart. However, ultra-fast MRI acquisitions come with an important signal-to-noise ratio (SNR) penalty, which drastically reduces the image quality. Hence, a real-time denoising approach would be desirable for SNR amelioration. In the clinical context of cardiac dysfunction assessment, long acquisitions are required and for most patients the acquisition takes place with free breathing. Hence, it is necessary to compensate respiratory motion in real-time. In this article, a real-time and interactive method for sequential registration and denoising of real-time MR cardiac images is presented. The method has been experimented on 60 fast MRI acquisitions in five healthy volunteers and five patients. These experiments assessed the feasibility of the method in a real-time context.

Modified similarity metric for non-local means algorithm

The non-local means (NLM) algorithm exploits the self-similarity property of images to suppress noise. Similarities are measured by neighbourhood comparisons; however, the original NLM algorithm uses only translational neighbourhoods, which do not fully exploit the symmetric characteristics that exist in many images. Several neighbourhood transformations are introduced for similarity comparison so that the self-similarity property of images can be better exploited. Experimental results show that, compared with the original algorithm, substantial PSNR improvements can be achieved when appropriate neighbourhood transformations are used in the similarity comparison.

Generalizing the Nonlocal-Means to Super-Resolution Reconstruction

Super-resolution reconstruction proposes a fusion of several low-quality images into one higher quality result with better optical resolution. Classic super-resolution techniques strongly rely on the availability of accurate motion estimation for this fusion task. When the motion is estimated inaccurately, as often happens for nonglobal motion fields, annoying artifacts appear in the super-resolved outcome. Encouraged by recent developments on the video denoising problem, where state-of-the-art algorithms are formed with no explicit motion estimation, we seek a super-resolution algorithm of similar nature that will allow processing sequences with general motion patterns. In this paper, we base our solution on the Nonlocal-Means (NLM) algorithm. We show how this denoising method is generalized to become a relatively simple super-resolution algorithm with no explicit motion estimation. Results on several test movies show that the proposed method is very successful in providing super-resolution on general sequences.

A Robust and Fast Non-Local Means Algorithm for Image Denoising

In the paper, we propose a robust and fast image denoising method. The approach integrates both 'Non-Local means algorithm and Laplacian Pyramid. Given an image to be denoised, we first decompose it into Laplacian pyramid. Exploiting the redundancy property of Laplacian pyramid, we then perform non-local means on every level image of Laplacian pyramid. Essentially, we use the similarity of image features in Laplacian pyramid to act as weight to denoise image. Since the features extracted in Laplacian pyramid are localized in spatial position and scale, they are much more able to describe image, and computing the similarity between them is more reasonable and more robust. Also, based on the efficient Summed Square Image (SSI) scheme and Fast Fourier Transform (FFT), we present an accelerating algorithm to break the bottleneck of non-local means algorithm -similarity computation of compare windows. After speedup, our algorithm is fifty times faster than original non-local means algorithm. Experiments demonstrated the effectiveness of our algorithm.

Robust Speech Recognition by Nonlocal Means Denoising Processing

The nonlocal means (NL-means) algorithm recently proposed for image denoising has proved highly effective for removing additive noise while to a large extent maintaining image details. The algorithm performs denoising by averaging each pixel with other pixels that have similar characteristics in the image. This letter considers the real and imaginary parts of complex speech spectrogram each as a separate image and presents a modified NL-means algorithm to them for denoising to improve the noise robustness of speech recognition. Recognition results on a noisy speech database show that the proposed method is superior to classical methods such as spectral subtraction.

Statistical interpretation of non-local means

Noise filtering is a common step in image processing, and is particularly effective in improving the subjective quality of images. A large number of techniques have been developed, many of which concentrate on the problem of removing noise without damaging small structures such as edges. One recent approach that demonstrates empirical merit is the non-local means (NLM) algorithm. However, in order to use noise filtering algorithms in quantitative or clinical image analysis tasks an understanding of their behaviour that goes beyond subjective appearance must be developed. The purpose of this study is to investigate the statistical basis of NLM in order to attempt to understand the conditions required for its use. The theory is illustrated on synthetic data and clinical magnetic resonance images of the brain.