Fast High-Dimensional Bilateral and Nonlocal Means Filtering

Nair, Pravin; Chaudhury, Kunal N.

doi:10.1109/tip.2018.2878955

Cited by 35 publications

(20 citation statements)

References 48 publications

(255 reference statements)

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“…The weighted average matrix R can be chosen as the arithmetic mean, geometric mean or geometric median. In each case, the matrix R is still HPD and this defines a map from a HPD matrix to another HPD matrix: R → R. Analogous to the filter in image denoising, the arithmetic mean can be viewed as a mean filter [26] and the geometric mean or median can be viewed as nonlocal mean filters [45]. In this paper, we choose the arithmetic mean as the weighted average matrix.…”

Section: Manifold Filtermentioning

confidence: 99%

MIG Median Detectors with Manifold Filter

Hua,

Peng

2021

Preprint

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In this paper, we propose a class of median-based matrix information geometry (MIG) detectors with a manifold filter and apply them to signal detection in nonhomogeneous environments. As customary, the sample data is assumed to be modeled as Hermitian positive-definite (HPD) matrices, and the geometric median of a set of HPD matrices is interpreted as an estimate of the clutter covariance matrix (CCM). Then, the problem of signal detection can be reformulated as discriminating two points on the manifold of HPD matrices, one of which is the HPD matrix in the cell under test while the other represents the CCM. By manifold filter, we map a set of HPD matrices to another set of HPD matrices by weighting them, that consequently improves the discriminative power by reducing the intra-class distances while increasing the inter-class distances. Three MIG median detectors are designed by resorting to three geometric measures on the matrix manifold, and the corresponding geometric medians are shown to be robust to outliers. Numerical simulations show the advantage of the proposed MIG median detectors in comparison with their state-of-the-art counterparts as well as the conventional detectors in nonhomogeneous environments.

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Section: Manifold Filtermentioning

confidence: 99%

MIG Median Detectors with Manifold Filter

Hua,

Peng

2021

Preprint

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“…This allows one to transform the HSI data into a multispectral image (MSI). The bands in the resulting MSI can be estimated by the weighted linear combination of the HSI, conditioned by its bilateral filtered version [52]. This approach produces a MSI or even a RGB image that focuses on the texture and spatial content while strongly condensing the spectral information.…”

Section: Spatial Context Capturementioning

confidence: 99%

A Robust Stochastic Approach to Mineral Hyperspectral Analysis for Geometallurgy

et al. 2020

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Most mining companies have registered important amounts of drill core composite spectra using different acquisition equipment and by following diverse protocols. These companies have used classic spectrography based on the detection of absorption features to perform semi-quantitative mineralogy. This methodology requires ideal laboratory conditions in order to obtain normalized spectra to compare. However, the inherent variability of spectral features—due to environmental conditions and geological context, among others—is unavoidable and needs to be managed. This work presents a novel methodology for geometallurgical sample characterization consisting of a heterogeneous, multi-pixel processing pipeline which addresses the effects of ambient conditions and geological context variability to estimate critical geological and geometallurgical variables. It relies on the assumptions that the acquisition of hyperspectral images is an inherently stochastic process and that ore sample information is deployed in the whole spectrum. The proposed framework is basically composed of: (a) a new hyperspectral image segmentation algorithm, (b) a preserving-information dimensionality reduction scheme and (c) a stochastic hierarchical regression model. A set of experiments considering white reference spectral characterization and geometallurgical variable estimation is presented to show promising results for the proposed approach.

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“…These inspired some researchers to expect better denoising performance by exploiting the nonlocal information during the noise removal procedure. However, initially, the nonlocal techniques were only for removal of additive Guassian noise and random-valued impulse noise [29]; and subsequently, some researchers ingeniously proposed the improved versions of nonlocal techniques for fixed-valued impulse noise removal. Wang et al [30] proposed an iterative nonlocal means filter (INLM); the concept of nonlocal means filter is based on the fact that there exist lots of similar patches with repeat patterns in natural image, and the central pixels of these similar patches share the same intensity value distribution; the central noisy pixel under processing is thus replaced by the weighted mean of central pixels of all similar patterns.…”

Section: Related Workmentioning

confidence: 99%

Adaptive Sequentially Weighted Median Filter for Image Highly Corrupted by Impulse Noise

2019

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To tackle the difficulties in the detection and removal of impulse noise faced by the existing filters, and to further improve the denoising performance, we propose an adaptive sequentially weighted median filter for image corrupted by impulse noise. In the proposed method, a noise detector employing the 3σ principle of normal distribution and the local intensity statistics, is proposed; and a sequentially weighted median filter with a neighborhood of adaptive size, is proposed for noise removal, in which the weighted operator is derived in reference to the spatial distances from central noisy pixel, i.e., the weighting coefficients are sequentially inversely proportional to the spatial distances. The experimental results confirm that the proposed method outperforms the existing filters, excelling in the capability of noise removal, structure and edge information preservation. INDEX TERMSImage denoising, median filter, noise detection, noise removal, sequentially weighted median filter, 3σ principle.

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Fast High-Dimensional Bilateral and Nonlocal Means Filtering

Cited by 35 publications

References 48 publications

MIG Median Detectors with Manifold Filter

MIG Median Detectors with Manifold Filter

A Robust Stochastic Approach to Mineral Hyperspectral Analysis for Geometallurgy

Adaptive Sequentially Weighted Median Filter for Image Highly Corrupted by Impulse Noise

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