Non-local Filter Research Articles

Spatially adaptive denoising for X-ray cardiovascular angiogram images

Abstract The X-ray angiogram image denoising is always one of the most popular research in the field of computer vision. While the methods removed the noise, the useful structure (such as peripheral vascular) had also been smoothed, the fundamental reason is that the denoising methods cannot efficiently distinguish structural areas from flat areas. In this paper, we have proposed a spatially adaptive image denoising (SAID) method which contains two steps: spatially adaptive gradient descent (SAGD) image denoising and dual-domain filter (DDF). The SAGD denoising method contains the following parts: first of all, the wavelet shrinkage method is used to estimate redundant information which is composed of the noise and useful structures; secondly, according to the characteristic of second order matrix, a spatially adaptive gradient factor (SAGF) has been constructed to distinguish the structure from flat areas; finally, the SAGF replaces the original gradient factor and then the SAGD image denoising method is formed. To further improve the quality of the SAGD image, the SAGD image is re-denoised by a modified DDF which is guided with a rotationally invariant non-local filter (RINLF) in spatial domain and gets structural details by wavelet shrinkage in frequency domain. The results of simulation experiments verify that the proposed SAID method can get well quantitative and qualitative results which are even superior to those using the state-of-the-art denoising methods. Even more, the fluctuation of peak signal-to-noise ratio (PSNR) value is very small with a small disturbance of SAGF, which illustrates that our algorithm is more robust than the prior progressive image denoising (PID) method. Moreover, the comparison results of the extensive experiments on clinical X-ray cardiovascular angiogram images further illustrate that our method can yield clearer cardiovascular images which can provide more useful vascular information for clinicians to analyze and diagnose the cardiovascular diseases.

A Spatial and Temporal Nonlocal Filter-Based Data Fusion Method

The trade-off in remote sensing instruments that balances the spatial resolution and temporal frequency limits our capacity to monitor spatial and temporal dynamics effectively. The spatiotemporal data fusion technique is considered as a cost-effective way to obtain remote sensing data with both high spatial resolution and high temporal frequency, by blending observations from multiple sensors with different advantages or characteristics. In this paper, we develop the spatial and temporal non-local filter based fusion model (STNLFFM) to enhance the prediction capacity and accuracy, especially for complex changed landscapes. The STNLFFM method provides a new transformation relationship between the fine-resolution reflectance images acquired from the same sensor at different dates with the help of coarse-resolution reflectance data, and makes full use of the high degree of spatiotemporal redundancy in the remote sensing image sequence to produce the final prediction. The proposed method was tested over both the Coleambally Irrigation Area study site and the Lower Gwydir Catchment study site. The results show that the proposed method can provide a more accurate and robust prediction, especially for heterogeneous landscapes and temporally dynamic areas.

A group-based signal filtering approach for trajectory abstraction and restoration

Trajectory abstraction is used to summarize the large amount of information delivered by the trajectory data, and trajectory restoration is used to reconstruct lost parts of trajectories. To cope with complex trajectory data, in this paper, we propose a new strategy for abstracting and restoring trajectories from the perspective of signal processing. That is, trajectories are treated as signals that bear copious information that varies with time and space, and information filtering is exploited to concisely communicate the trajectory data. As for trajectory abstraction, the resampling of trajectory data is first introduced based on achieving the minimum Jensen---Shannon divergence of the trajectories before and after being resampled. Then, a non-local filtering approach is developed to perform wavelet transformations of similarity groups of these resampled trajectories to produce the trajectory summaries. Trajectory abstraction can not only offer multi-granularity summaries of trajectory data, but also identify outliers by utilizing a probabilistic definition of a group of trajectories and the Shannon entropy. Furthermore, to handle incomplete trajectory data for which some sample points are lost, the proposed non-local filtering idea is exploited to restore the incomplete data. Extensive experimental studies have shown that the proposed trajectory abstraction and restoration can obtain very encouraging results, in terms of both objective evaluation metrics and subjective visual effects. To the best of our knowledge, this is the first attempt to deploy the group-based signal filtering technique in the context of dealing with trajectory data. In addition, as a preprocessing step, the proposed trajectory abstraction can be employed to improve the performance of trajectory clustering.

Interferogram denoising using an iteratively refined nonlocal InSAR filter

ABSTRACTInterferogram denoising is important for height reconstruction and deformation measurement. For high-resolution interferograms over heterogeneous areas, local biases and resolution losses may appear due to the violation of the local stationarity assumption. To address this problem, an iteratively refined nonlocal filter is proposed, whose estimation is refined iteratively by jointly using the amplitude, interferometric phase, coherence, and the pre-estimated patches. For nonlocal interferometric synthetic aperture radar (InSAR) techniques, the similarity of two pixels is computed via their surrounding patches, followed by the maximum likelihood weighted averaging of similar pixels. In this letter, the outliers in the search window is identified before the weight calculation. If the normalized probability density function (NPDF) of the central pixel and other surrounding pixels in the search window is less than the preset threshold, the pixel will be assigned with the minimum weight in the search window. Moreover, the denoising weight is calculated not only depending on the probabilistic patch-based (PPB) similarity, but also the coherence of the pixels in the search window. Both simulated and real data experiments are used to validate the effectiveness of the proposed method.

RETRACTED ARTICLE: Adaptive hexagonal fuzzy hybrid filter for Rician noise removal in MRI images

Magnetic resonance images (MRIs) are sensitive to redundant Rician noise. The proposed adaptive hexagonal fuzzy hybrid filtering technique adapts itself to remove Rician noise variances. The removal of noise variance is performed by constructing a hexagonal membership function along with local and nonlocal filters. The statistical feature such as local mean (μ i) and global mean (μ g) is determined to find fuzzy weights by constructing a hexagonal membership function for nonlocal filter to preserve the structural information and for local filter to preserve edges. The restoration is performed by multiplying its corresponding fuzzy weight with the restored image of local and nonlocal filter in order to improve the quality of an image. Detailed simulation is performed for Brain Web database and real MRI images at various noise levels using the proposed adaptive hexagonal fuzzy hybrid filtering algorithm and existing algorithms. The visual and diagnostic qualities of the denoised image are well preserved for the proposed adaptive hexagonal fuzzy hybrid filter both at low and high densities of Rician noise.

Mapping Glacier Elevations and Their Changes in the Western Qilian Mountains, Northern Tibetan Plateau, by Bistatic InSAR

Accurate measurements of glacier surface topography and their changes play an essential role in various glaciological studies related to glacier dynamics and mass balance. The focus of this study is on mapping glacier digital elevation model (DEM) and elevation changes in the western Qilian Mountains, northern Tibetan Plateau, by synergistically using the TanDEM-X (TDX) bistatic Interferometric Synthetic Aperture Radar (InSAR) data in 2013 and Shuttle Radar Topography Mission (SRTM) DEM in 2000. The first high-resolution and high-precision glacier DEM is derived in this region by a TDX InSAR procedure with a nonlocal (NL) filter. Validated against the Ice, Cloud, and land Elevation Satellite (ICESat) height references, the absolute height error of the TanDEM-X DEM derived with the NL filter and the Goldstein filter with the parameters investigated is, respectively, 1.493 ± 0.747 and 1.857 ± 1.709 m. Further, four combinations of differential phase method (DiffPha) and DEM differencing method (DiffDem) with Goldstein filter and NL filter are applied to estimate glacier elevation changes between 2000 and 2013. The synergistic use of the DiffPha method and the NL filter is superior to other three combinations in terms of uncertainty and noise reduction. Generally, a clear surface thinning can be found in most glacier tongue regions, the maximum value of elevation lowering up to approximately −40 m, whereas a slight thickening is detected in accumulation areas, which are in agreement with the height difference results between GPS measurements and SRTM DEM over Laohugou Glacier No.12. This study demonstrates the potential of the TanDEM-X bistatic InSAR in mapping surface topography and elevation changes of valley glaciers in the Tibetan Plateau.

Yet Another Cost Aggregation Over Models

In the recent decades, we have witnessed the advent of local or non-local filters for cost aggregation in stereo matching, pushing the envelope of local methods to the degree of global methods, while maintaining the efficiency. A specific filter with a specific parameter setting may have a potential to best work for an image pair, but may not guarantee equally good performance for other image pairs. To address this problem, we propose a mixture-of-experts model, which applies a heterogeneous set of filters on the cost volume and adaptively combines the results. We employ supervised learning to estimate per-pixel mixing coefficients, which are used to adaptively control the weight of the filter responses. Through experiments, we show that the mixture model significantly reduces errors in disparity estimation and even outperforms the strategy of selecting the best per-pixel filter from the pool of filters in the average sense.

Noise Estimation and Reduction in Magnetic Resonance Imaging Using a New Multispectral Nonlocal Maximum-likelihood Filter.

Denoising of magnetic resonance (MR) images enhances diagnostic accuracy, the quality of image manipulations such as registration and segmentation, and parameter estimation. The first objective of this paper is to introduce a new, high-performance, nonlocal filter for noise reduction in MR image sets consisting of progressively-weighted, that is, multispectral, images. This filter is a multispectral extension of the nonlocal maximum likelihood filter (NLML). Performance was evaluated on synthetic and in-vivo T2 - and T1 -weighted brain imaging data, and compared to the nonlocal-means (NLM) and its multispectral version, that is, MS-NLM, and the nonlocal maximum likelihood (NLML) filters. Visual inspection of filtered images and quantitative analyses showed that all filters provided substantial reduction of noise. Further, as expected, the use of multispectral information improves filtering quality. In addition, numerical and experimental analyses indicated that the new multispectral NLML filter, MS-NLML, demonstrated markedly less blurring and loss of image detail than seen with the other filters evaluated. In addition, since noise standard deviation (SD) is an important parameter for all of these nonlocal filters, a multispectral extension of the method of maximum likelihood estimation (MLE) of noise amplitude is presented and compared to both local and nonlocal MLE methods. Numerical and experimental analyses indicated the superior performance of this multispectral method for estimation of noise SD.

ВІДНОВЛЕННЯ ЧАСТОТНО-ЧАСОВИХ ПРЕДСТАВЛЕНЬ: ПІДХІД З ЗАСТОСУВАННЯМ МЕТОДІВ ФІЛЬТРАЦІЇ ЗОБРАЖЕНЬ

The task of filtering of the time-frequency representations, obtained by the S-method, using advanced digital image processing filters, both local and nonlocal is considered. Such enhancement is important for design of the time-varying filters for processing of nonstationary frequency modulated signals. The class of local filters is represented by spatial domain filtering using median and related filters. Orthogonal transform based denoising is represented by DCT domain filtering. The block matching 3-D filter is considered as a representative of nonlocal filter class. It is demonstrated that the noise in the time-frequency representations based on Smethod has rather complicated nature: non-Gaussian pdf, spatially correlated properties with varying parameters. It is shown that direct application of the considered filters to such a challenging noisy environment is not possible. Then, several filter modifications are proposed and analyzed with respect to integral and local parameters – MSE and MAE. The block matching 3-D filter is shown to provide the best results but at the expense of quality loss in representation of weak components.

Visual Attention Detection By Adaptive Non-Local Filter

Regarding global and local factors of a set of features, a given single image or multiple images is a common approach in image processing. This paper introduces an application of an adaptive version of non-local filter whose original version searches non-local similarity for removing noise. Since most images involve texture partner in both foreground and background, extraction of signified regions with texture is a challenging task. Aiming to the detection of visual attention regions for images with texture, we present the contrast analysis of image patches located in a whole image but not nearby with assistance of the adaptive filter for estimation of non-local divergence. The method allows extraction of signified regions with texture of images of wild life. Experimental results for a benchmark demonstrate the ability of the proposed method to deal with the mentioned challenge.

Monitoring reclaimed lands subsidence in Hong Kong with InSAR technique by persistent and distributed scatterers

This paper introduced an advanced SBAS algorithm to investigate the subsidence time-series of reclaimed lands. A new method for fusing persistent and distributed scatterers in time-series images was presented in this algorithm. Moreover, nonlocal filter based on DS was employed for the interferometric phase which improved results quality with high spatial resolution. The reclaimed lands near Hong Kong Science Park and Hong Kong Disneyland (HKD) were selected for the investigation by high-resolution TerraSAR-X images. The reclaimed lands area was classified into three types labeled as undeveloped area, developing area and developed area. The results showed that: Undeveloped area had significant subsidence due to soft soil consolidation, especially in HKD’s reclaimed lands with deformation rate up to −459 mm/year; developing and developed area also had subsidence phenomenon due to building pressure caused by mass constructions of infrastructure. In particular, in the preliminary stage after construction, there was a dramatic subsidence trend, which easily threatened the security and stability of infrastructure facilities such as underground pipes and drainage system.

Assessment of SAR speckle filters in the context of object-based image analysis

ABSTRACTThe initial step in most object-based classification methodologies is the application of a segmentation algorithm to define objects. In the context of synthetic aperture radar (SAR) image analysis, the presence of speckle noise might hamper the segmentation quality. The aim of this study is to assess the segmentation performance of SAR images when no filter or different filters are applied before segmentation. In particular, the performance of the mean-shift segmentation algorithm combined with different adaptive and non-adaptive filters is assessed based on both synthetic and natural SAR images. Studied filters include the non-adaptive Boxcar filter and four adaptive filters: the well-known Refined Lee filter and three recently proposed non-local filters differing, in particular, in their dissimilarity criteria: the Hellinger and the Kullback–Leibler filters are based on stochastic distances, whereas the NL-SAR filter is based on the generalized likelihood ratio. Two measures were used for quality assessment: -index and -index. Over-segmentation was assessed by the -index, the ratio of the resulting number of segments to the number of connected components of the ground-truth classes. The accuracy of the best possible classification given on the segmentation result was assessed with ground truth information by maximizing the -index. A Monte Carlo experiment conducted on synthetic images shows that the quality measures significantly differ for the applied filters. Our results indicate that the use of an adaptive filter improves the performance of the segmentation. In particular, the combination of the mean-shift segmentation algorithm with the NL-SAR filter gives the best results and the resulting process is less sensitive to variations in the mean-shift operational parameters than when applying other filters or no filter. The results obtained may help improve the reliability of land-cover classification analyses based on an object-based approach on SAR data.

Adaptive Switching Non-local Filter for the Restoration of Salt and Pepper Impulse-Corrupted Digital Images

The paper presents an effective nonlinear adaptive switching non-local filter for the restoration of impulse-corrupted digital images by using distinct impulse detection and correction stages. The correction scheme of the filter adaptively switches between details-preserving non-local mode and signal restoration-based local mode to facilitate high fidelity in the restored image. The non-local filtering operation replaces impulses with a remote pixel that better suits the local image conditions. The algorithm works in this non-local mode only when there are sufficient uncorrupted pixels in the local neighborhood of the corrupted pixel to be replaced. Otherwise, the algorithm replaces impulsive pixels with the median of the uncorrupted pixels from the local neighborhood. Experimental results from various impulse noise levels support the improved performance of the proposed algorithm over other algorithms both subjectively and objectively.

Interferometric Phase Denoising by Median Patch-Based Locally Optimal Wiener Filter

This letter presents a new filtering technique for interferometric synthetic aperture radar (InSAR) phase images. Traditional local denoising algorithms all suffer from the drawback of removing texture detail information. In contrast, several nonlocal methods have attained good performance in InSAR applications. However, these methods only take radiometric similarity. The patch-based locally optimal Wiener filter (PLOW) utilizes both geometrically and radiometrically similar patch information by clustering analysis and nonlocal filtering; thus, it can better balance between detail preservation and denoising. Nevertheless, PLOW itself is not fitted for InSAR. In this letter, we modify and improve the original algorithm while considering the coherence coefficient and the characteristics of InSAR. This new method provides better filtering results, but with a higher computational cost. Moreover, we introduce the box dimension in fractal geometry as a new index. Experiments on simulated and real data demonstrate that this algorithm outperforms traditional denoising methods.

Nonlocal PDE morphology: a generalized shock operator on graph

This paper presents an adaptation and extension of the shock filters on weighted graphs using the formalism of partial difference equations. This adaptation leads to new morphological operators that alternate between nonlocal dilation and nonlocal erosion filter type on graphs. Furthermore, this adaptation extends the shock filter applications to any data that can be represented by graphs. This approach is illustrated through image, data defined on region maps, and 3D point cloud processing.

Linear fractional-based filter as a pre-classifier to map burned areas in Mediterranean countries

Wildfires in Southern Europe burn thousands of square kilometres every year, causing extensive economic and ecological losses. Accurate mapping of fire-burned areas is a decisive factor in guiding forest management decisions. In this work a linear fractional-based filter is considered as a pre-classifier for burned area estimation from Moderate Resolution Imaging Spectroradiometer (MODIS) accurate satellite imagery. Three vegetation indices (normalized difference vegetation index, enhanced vegetation index, and global environment monitoring index) and three spectral indices specifically designed for burned area identification (normalized burnt ratio, burned area index, and burned area adapted for MODIS) have been used as inputs for the proposed filter. The filtered images were classified and the accuracy of the burned area estimates was computed by kappa () statistic. Burned area perimeters measured on the ground by global positioning system were used as reference truth. A linear Gaussian pre-classification filter was used as reference to check the burned area estimates accuracy improvements. When using the proposed fractional-type filter, an accurate estimation () of areas burned by forest fires in the four study areas located in Central Spain was achieved. The results showed that the non-local filter, used as a pre-classifier, allowed higher accuracy than the same inputs both without filtering and with the Gaussian filter ( index increased up to 30% with statistical significance). McNemar test confirmed that such accuracy improvement had statistical significance, and a statistical separability test showed that filtering increased the inter-class distance, helping to improve the latter classification. Burned areas in Central Spain were accurately mapped when the linear fractional-based filter proposed here was used as a pre-classifier.

Fine feature retention of magnetic resonance images using intensity inhomogeneity weighted non-local filtering

Electronic noise in the presence of intensity inhomogeneity severely inhibits the robustness of many traditional filtering algorithms. We propose an adaptive filter that utilises the intensity inhomogeneity bias field often observed in magnetic resonance imaging as a map for directing the magnitude of smoothing. This adaptive filter allows for controlled filtering of images where high signal-to-noise (SNR) regions are smoothed less, while low SNR regions are smoothed more intensely. We validated our method with a phantom and MRIs of the lumbar spine. Results showed that the proposed algorithm improved filtering of noise in the presence of intensity inhomogeneity.

Nonlocal Adaptive Multilooking in SAR Multipass Differential Interferometry

Filtering of interferometric synthetic aperture radar (InSAR) data has been the object of a growing number of papers, in recent years, aimed at improving the quality of differential InSAR (DInSAR) and tomography products based on multibaseline/multitemporal data. In this work, we investigate the potential of nonlocal adaptive multilooking (AML) techniques for the filtering of interferometric stacks. Nonlocal filtering has been already successfully applied to SAR data in many contexts, including the restoration of single interferograms. We propose several workflows, with different solutions for the data preprocessing and for the estimation of similarity, at the core of all nonlocal methods. Experiments on simulated and real data, the latter both at low and high spatial resolution, prove the proposed methods to provide significant improvements over nonadaptive multilooking in terms of both resolution and detail preservation, allowing for the generation of better interferometric products.

Polarimetric SAR Speckle Filtering and the Extended Sigma Filter

The advancement of synthetic aperture radar (SAR) technology with high-resolution and quad-polarization data demands better and efficient polarimetric SAR (PolSAR) speckle-filtering algorithms. Two requirements on PolSAR speckle filtering are proposed: 1) speckle filtering should be applied to distributed media only, and strong hard targets should be kept unfiltered; and 2) scattering mechanism preservation should be taken into consideration, in addition to speckle reduction. The purpose of this paper is twofold: 1) to propose an effective algorithm that is an extension of the improved sigma filter developed for single-polarization SAR; and 2) to investigate speckle characteristics and the need for speckle filtering for very high resolution (decimeter) PolSAR data. The proposed filter was specifically developed to account for the aforementioned two requirements. Its effectiveness is demonstrated with Jet Propulsion Laboratory airborne synthetic aperture radar data, and comparisons are made with a boxcar filter, the refined Lee filter, and a Wishart-based nonlocal filter. For very high resolution PolSAR systems, such as the German Aerospace Center F-SAR and Japanese Pi-SAR2, with decimeter spatial resolution, we found that the complex Wishart distribution is still valid to describe PolSAR speckle characteristics of distributed media and that speckle filtering may be needed depending on the size of objects to be analyzed. F-SAR X-band data with 25-cm resolution is used for illustration.

Optical-Driven Nonlocal SAR Despeckling

We propose a new synthetic aperture radar (SAR) despeckling technique based on nonlocal filtering and driven by a coregistered optical image. A preliminary homogeneous versus heterogeneous classification of the image is used to decide where the optical guide can be safely used, thus preventing any distortion of the SAR geometry. Even in regions where the use of optical data is enabled, despeckling is carried out exclusively in the SAR domain, and the optical guide is used only to improve the predictor selection in nonlocal filtering and, hence, in the estimation process. Experiments on real-world imagery confirm the potential of the proposed approach.