Nonlocal means with dimensionality reduction and SURE-based parameter selection

Application of Fast Non-Local Means Algorithm for Noise Reduction Using Separable Color Channels in Light Microscopy Images

The purpose of this study is to evaluate the various control parameters of a modeled fast non-local means (FNLM) noise reduction algorithm which can separate color channels in light microscopy (LM) images. To achieve this objective, the tendency of image characteristics with changes in parameters, such as smoothing factors and kernel and search window sizes for the FNLM algorithm, was analyzed. To quantitatively assess image characteristics, the coefficient of variation (COV), blind/referenceless image spatial quality evaluator (BRISQUE), and natural image quality evaluator (NIQE) were employed. When high smoothing factors and large search window sizes were applied, excellent COV and unsatisfactory BRISQUE and NIQE results were obtained. In addition, all three evaluation parameters improved as the kernel size increased. However, the kernel and search window sizes of the FNLM algorithm were shown to be dependent on the image processing time (time resolution). In conclusion, this work has demonstrated that the FNLM algorithm can effectively reduce noise in LM images, and parameter optimization is important to achieve the algorithm's appropriate application.

Projection onto Epigraph Sets for Rapid Self-Tuning Compressed Sensing MRI

The compressed sensing (CS) framework leverages the sparsity of MR images to reconstruct from the undersampled acquisitions. CS reconstructions involve one or more regularization parameters that weigh sparsity in transform domains against fidelity to acquired data. While parameter selection is critical for reconstruction quality, the optimal parameters are subject and dataset specific. Thus, commonly practiced heuristic parameter selection generalizes poorly to independent datasets. Recent studies have proposed to tune parameters by estimating the risk of removing significant image coefficients. Line searches are performed across the parameter space to identify the parameter value that minimizes this risk. Although effective, these line searches yield prolonged reconstruction times. Here, we propose a new self-tuning CS method that uses computationally efficient projections onto epigraph sets of the l₁ and total-variation norms to simultaneously achieve parameter selection and regularization. In vivo demonstrations are provided for balanced steady-state free precession, time-of-flight, and T1-weighted imaging. The proposed method achieves an order of magnitude improvement in computational efficiency over line-search methods while maintaining near-optimal parameter selection.

Bounded Self-Weights Estimation Method for Non-Local Means Image Denoising Using Minimax Estimators

A non-local means (NLM) filter is a weighted average of a large number of non-local pixels with various image intensity values. The NLM filters have been shown to have powerful denoising performance, excellent detail preservation by averaging many noisy pixels, and using appropriate values for the weights, respectively. The NLM weights between two different pixels are determined based on the similarities between two patches that surround these pixels and a smoothing parameter. Another important factor that influences the denoising performance is the self-weight values for the same pixel. The recently introduced local James-Stein type center pixel weight estimation method (LJS) outperforms other existing methods when determining the contribution of the center pixels in the NLM filter. However, the LJS method may result in excessively large self-weight estimates since no upper bound is assumed, and the method uses a relatively large local area for estimating the self-weights, which may lead to a strong bias. In this paper, we investigated these issues in the LJS method, and then propose a novel local self-weight estimation methods using direct bounds (LMM-DB) and reparametrization (LMM-RP) based on the Baranchik's minimax estimator. Both the LMM-DB and LMM-RP methods were evaluated using a wide range of natural images and a clinical MRI image together with the various levels of additive Gaussian noise. Our proposed parameter selection methods yielded an improved bias-variance trade-off, a higher peak signal-to-noise (PSNR) ratio, and fewer visual artifacts when compared with the results of the classical NLM and LJS methods. Our proposed methods also provide a heuristic way to select a suitable global smoothing parameters that can yield PSNR values that are close to the optimal values.

Iterative reconstruction for CT perfusion with a prior-image induced hybrid nonlocal means regularization: Phantom studies

PURPOSE

In computed tomography perfusion (CTP) imaging, an initial phase CT acquired with a high-dose protocol can be used to improve the image quality of later phase CT acquired with a low-dose protocol. For dynamic regions, signals in the later low-dose CT may not be completely recovered if the initial CT heavily regularizes the iterative reconstruction process. The authors propose a hybrid nonlocal means (hNLM) regularization model for iterative reconstruction of low-dose CTP to overcome the limitation of the conventional prior-image induced penalty.

METHODS

The hybrid penalty was constructed by combining the NLM of the initial phase high-dose CT in the stationary region and later phase low-dose CT in the dynamic region. The stationary and dynamic regions were determined by the similarity between the initial high-dose scan and later low-dose scan. The similarity was defined as a Gaussian kernel-based distance between the patch-window of the same pixel in the two scans, and its measurement was then used to weigh the influence of the initial high-dose CT. For regions with high similarity (e.g., stationary region), initial high-dose CT played a dominant role for regularizing the solution. For regions with low similarity (e.g., dynamic region), the regularization relied on a low-dose scan itself. This new hNLM penalty was incorporated into the penalized weighted least-squares (PWLS) for CTP reconstruction. Digital and physical phantom studies were performed to evaluate the PWLS-hNLM algorithm.

RESULTS

Both phantom studies showed that the PWLS-hNLM algorithm is superior to the conventional prior-image induced penalty term without considering the signal changes within the dynamic region. In the dynamic region of the Catphan phantom, the reconstruction error measured by root mean square error was reduced by 42.9% in PWLS-hNLM reconstructed image.

CONCLUSIONS

The PWLS-hNLM algorithm can effectively use the initial high-dose CT to reconstruct low-dose CTP in the stationary region while reducing its influence in the dynamic region.

Bayesian Inference for Neighborhood Filters With Application in Denoising

Range-weighted neighborhood filters are useful and popular for their edge-preserving property and simplicity, but they are originally proposed as intuitive tools. Previous works needed to connect them to other tools or models for indirect property reasoning or parameter estimation. In this paper, we introduce a unified empirical Bayesian framework to do both directly. A neighborhood noise model is proposed to reason and infer the Yaroslavsky, bilateral, and modified non-local means filters by joint maximum a posteriori and maximum likelihood estimation. Then, the essential parameter, range variance, can be estimated via model fitting to the empirical distribution of an observable chi scale mixture variable. An algorithm based on expectation-maximization and quasi-Newton optimization is devised to perform the model fitting efficiently. Finally, we apply this framework to the problem of color-image denoising. A recursive fitting and filtering scheme is proposed to improve the image quality. Extensive experiments are performed for a variety of configurations, including different kernel functions, filter types and support sizes, color channel numbers, and noise types. The results show that the proposed framework can fit noisy images well and the range variance can be estimated successfully and efficiently.

Fault diagnosis of rolling bearing based on fast nonlocal means and envelop spectrum

The nonlocal means (NL-Means) method that has been widely used in the field of image processing in recent years effectively overcomes the limitations of the neighborhood filter and eliminates the artifact and edge problems caused by the traditional image denoising methods. Although NL-Means is very popular in the field of 2D image signal processing, it has not received enough attention in the field of 1D signal processing. This paper proposes a novel approach that diagnoses the fault of a rolling bearing based on fast NL-Means and the envelop spectrum. The parameters of the rolling bearing signals are optimized in the proposed method, which is the key contribution of this paper. This approach is applied to the fault diagnosis of rolling bearing, and the results have shown the efficiency at detecting roller bearing failures.

Monte Carlo non-local means: random sampling for large-scale image filtering

We propose a randomized version of the nonlocal means (NLM) algorithm for large-scale image filtering. The new algorithm, called Monte Carlo nonlocal means (MCNLM), speeds up the classical NLM by computing a small subset of image patch distances, which are randomly selected according to a designed sampling pattern. We make two contributions. First, we analyze the performance of the MCNLM algorithm and show that, for large images or large external image databases, the random outcomes of MCNLM are tightly concentrated around the deterministic full NLM result. In particular, our error probability bounds show that, at any given sampling ratio, the probability for MCNLM to have a large deviation from the original NLM solution decays exponentially as the size of the image or database grows. Second, we derive explicit formulas for optimal sampling patterns that minimize the error probability bound by exploiting partial knowledge of the pairwise similarity weights. Numerical experiments show that MCNLM is competitive with other state-of-the-art fast NLM algorithms for single-image denoising. When applied to denoising images using an external database containing ten billion patches, MCNLM returns a randomized solution that is within 0.2 dB of the full NLM solution while reducing the runtime by three orders of magnitude.

Adaptive regularization of the NL-means: application to image and video denoising

Image denoising is a central problem in image processing and it is often a necessary step prior to higher level analysis such as segmentation, reconstruction, or super-resolution. The nonlocal means (NL-means) perform denoising by exploiting the natural redundancy of patterns inside an image; they perform a weighted average of pixels whose neighborhoods (patches) are close to each other. This reduces significantly the noise while preserving most of the image content. While it performs well on flat areas and textures, it suffers from two opposite drawbacks: it might over-smooth low-contrasted areas or leave a residual noise around edges and singular structures. Denoising can also be performed by total variation minimization-the Rudin, Osher and Fatemi model-which leads to restore regular images, but it is prone to over-smooth textures, staircasing effects, and contrast losses. We introduce in this paper a variational approach that corrects the over-smoothing and reduces the residual noise of the NL-means by adaptively regularizing nonlocal methods with the total variation. The proposed regularized NL-means algorithm combines these methods and reduces both of their respective defaults by minimizing an adaptive total variation with a nonlocal data fidelity term. Besides, this model adapts to different noise statistics and a fast solution can be obtained in the general case of the exponential family. We develop this model for image denoising and we adapt it to video denoising with 3D patches.

Novel speed-up strategies for non-local means denoising with patch and edge patch based dictionaries

In this paper, a novel technique to speed-up a nonlocal means (NLM) filter is proposed. In the original NLM filter, most of its computational time is spent on finding distances for all the patches in the search window. Here, we build a dictionary in which patches with similar photometric structures are clustered together. Dictionary is built only once with high resolution images belonging to different scenes. Since the dictionary is well organized in terms of indexing its entries, it is used to search similar patches very quickly for efficient NLM denoising. We achieve a substantial reduction in computational cost compared with the original NLM method, especially when the search window of NLM is large, without much affecting the PSNR. Second, we show that by building a dictionary for edge patches as opposed to intensity patches, it is possible to reduce the dictionary size; thus, further improving the computational speed and memory requirement. The proposed method preclassifies similar patches with the same distance measure as used by NLM method. The proposed algorithm is shown to outperform other prefiltering based fast NLM algorithms computationally as well as qualitatively.

How to SAIF-ly boost denoising performance

Spatial domain image filters (e.g., bilateral filter, non-local means, locally adaptive regression kernel) have achieved great success in denoising. Their overall performance, however, has not generally surpassed the leading transform domain-based filters (such as BM3-D). One important reason is that spatial domain filters lack efficiency to adaptively fine tune their denoising strength; something that is relatively easy to do in transform domain method with shrinkage operators. In the pixel domain, the smoothing strength is usually controlled globally by, for example, tuning a regularization parameter. In this paper, we propose spatially adaptive iterative filtering (SAIF) is the Middle Eastern/Arabic name for sword. This acronym somehow seems appropriate for what the algorithm does by precisely tuning the value of the iteration number. a new strategy to control the denoising strength locally for any spatial domain method. This approach is capable of filtering local image content iteratively using the given base filter, and the type of iteration and the iteration number are automatically optimized with respect to estimated risk (i.e., mean-squared error). In exploiting the estimated local signal-to-noise-ratio, we also present a new risk estimator that is different from the often-employed SURE method, and exceeds its performance in many cases. Experiments illustrate that our strategy can significantly relax the base algorithm's sensitivity to its tuning (smoothing) parameters, and effectively boost the performance of several existing denoising filters to generate state-of-the-art results under both simulated and practical conditions.

LLSURE: local linear SURE-based edge-preserving image filtering

In this paper, we propose a novel approach for performing high-quality edge-preserving image filtering. Based on a local linear model and using the principle of Stein's unbiased risk estimate as an estimator for the mean squared error from the noisy image only, we derive a simple explicit image filter which can filter out noise while preserving edges and fine-scale details. Moreover, this filter has a fast and exact linear-time algorithm whose computational complexity is independent of the filtering kernel size; thus, it can be applied to real time image processing tasks. The experimental results demonstrate the effectiveness of the new filter for various computer vision applications, including noise reduction, detail smoothing and enhancement, high dynamic range compression, and flash/no-flash denoising.

Non-Local Euclidean Medians

In this letter, we note that the denoising performance of Non-Local Means (NLM) can be improved at large noise levels by replacing the mean by the Euclidean median. We call this new denoising algorithm the Non-Local Euclidean Medians (NLEM). At the heart of NLEM is the observation that the median is more robust to outliers than the mean. In particular, we provide a simple geometric insight that explains why NLEM performs better than NLM in the vicinity of edges, particularly at large noise levels. NLEM can be efficiently implemented using iteratively reweighted least squares, and its computational complexity is comparable to that of NLM. We provide some preliminary results to study the proposed algorithm and to compare it with NLM.

Regularization parameter selection for nonlinear iterative image restoration and MRI reconstruction using GCV and SURE-based methods

Regularized iterative reconstruction algorithms for imaging inverse problems require selection of appropriate regularization parameter values. We focus on the challenging problem of tuning regularization parameters for nonlinear algorithms for the case of additive (possibly complex) Gaussian noise. Generalized cross-validation (GCV) and (weighted) mean-squared error (MSE) approaches (based on Steinfs Unbiased Risk Estimate. SURE) need the Jacobian matrix of the nonlinear reconstruction operator (representative of the iterative algorithm) with respect to the data. We derive the desired Jacobian matrix for two types of nonlinear iterative algorithms: a fast variant of the standard iterative reweighted least-squares method and the contemporary split-Bregman algorithm, both of which can accommodate a wide variety of analysis- and synthesis-type regularizers. The proposed approach iteratively computes two weighted SURE-type measures: Predicted-SURE and Projected-SURE (that require knowledge of noise variance Ð2), and GCV (that does not need Ð2) for these algorithms. We apply the methods to image restoration and to magnetic resonance image (MRI) reconstruction using total variation (TV) and an analysis-type .1-regularization. We demonstrate through simulations and experiments with real data that minimizing Predicted-SURE and Projected-SURE consistently lead to near-MSE-optimal reconstructions. We also observed that minimizing GCV yields reconstruction results that are near-MSE-optimal for image restoration and slightly suboptimal for MRI. Theoretical derivations in this work related to Jacobian matrix evaluations can be extended, in principle, to other types of regularizers and reconstruction algorithms.

A CURE for noisy magnetic resonance images: chi-square unbiased risk estimation

n this article we derive an unbiased expression for the expected mean-squared error associated with continuously differentiable estimators of the noncentrality parameter of a chisquare random variable. We then consider the task of denoising squared-magnitude magnetic resonance image data, which are well modeled as independent noncentral chi-square random variables on two degrees of freedom. We consider two broad classes of linearly parameterized shrinkage estimators that can be optimized using our risk estimate, one in the general context of undecimated filterbank transforms, and another in the specific case of the unnormalized Haar wavelet transform. The resultant algorithms are computationally tractable and improve upon most state-of-the-art methods for both simulated and actual magnetic resonance image data.

A signal processing approach for enriched region detection in RNA polymerase II ChIP-seq data

Background

RNA polymerase II (PolII) is essential in gene transcription and ChIP-seq experiments have been used to study PolII binding patterns over the entire genome. However, since PolII enriched regions in the genome can be very long, existing peak finding algorithms for ChIP-seq data are not adequate for identifying such long regions.

Methods

Here we propose an enriched region detection method for ChIP-seq data to identify long enriched regions by combining a signal denoising algorithm with a false discovery rate (FDR) approach. The binned ChIP-seq data for PolII are first processed using a non-local means (NL-means) algorithm for purposes of denoising. Then, a FDR approach is developed to determine the threshold for marking enriched regions in the binned histogram.

Results

We first test our method using a public PolII ChIP-seq dataset and compare our results with published results obtained using the published algorithm HPeak. Our results show a high consistency with the published results (80-100%). Then, we apply our proposed method on PolII ChIP-seq data generated in our own study on the effects of hormone on the breast cancer cell line MCF7. The results demonstrate that our method can effectively identify long enriched regions in ChIP-seq datasets. Specifically, pertaining to MCF7 control samples we identified 5,911 segments with length of at least 4 Kbp (maximum 233,000 bp); and in MCF7 treated with E2 samples, we identified 6,200 such segments (maximum 325,000 bp).

Conclusions

We demonstrated the effectiveness of this method in studying binding patterns of PolII in cancer cells which enables further deep analysis in transcription regulation and epigenetics. Our method complements existing peak detection algorithms for ChIP-seq experiments.