Nonlinear multivariate image filtering techniques

Multispectral image denoising with optimized vector bilateral filter

Vector bilateral filtering has been shown to provide good tradeoff between noise removal and edge degradation when applied to multispectral/hyperspectral image denoising. It has also been demonstrated to provide dynamic range enhancement of bands that have impaired signal to noise ratios (SNRs). Typical vector bilateral filtering described in the literature does not use parameters satisfying optimality criteria. We introduce an approach for selection of the parameters of a vector bilateral filter through an optimization procedure rather than by ad hoc means. The approach is based on posing the filtering problem as one of nonlinear estimation and minimization of the Stein's unbiased risk estimate of this nonlinear estimator. Along the way, we provide a plausibility argument through an analytical example as to why vector bilateral filtering outperforms bandwise 2D bilateral filtering in enhancing SNR. Experimental results show that the optimized vector bilateral filter provides improved denoising performance on multispectral images when compared with several other approaches.

Multi-channel morphological profiles for classification of hyperspectral images using support vector machines

Hyperspectral imaging is a new remote sensing technique that generates hundreds of images, corresponding to different wavelength channels, for the same area on the surface of the Earth. Supervised classification of hyperspectral image data sets is a challenging problem due to the limited availability of training samples (which are very difficult and costly to obtain in practice) and the extremely high dimensionality of the data. In this paper, we explore the use of multi-channel morphological profiles for feature extraction prior to classification of remotely sensed hyperspectral data sets using support vector machines (SVMs). In order to introduce multi-channel morphological transformations, which rely on ordering of pixel vectors in multidimensional space, several vector ordering strategies are investigated. A reduced implementation which builds the multi-channel morphological profile based on the first components resulting from a dimensional reduction transformation applied to the input data is also proposed. Our experimental results, conducted using three representative hyperspectral data sets collected by NASA's Airborne Visible-Infrared Imaging Spectrometer (AVIRIS) sensor and the German Digital Airborne Imaging Spectrometer (DAIS 7915), reveal that multi-channel morphological profiles can improve single-channel morphological profiles in the task of extracting relevant features for classification of hyperspectral data using small training sets.

Partition-based vector filtering technique for suppression of noise in digital color images

A partition-based adaptive vector filter is proposed for the restoration of corrupted digital color images. The novelty of the filter lies in its unique three-stage adaptive estimation. The local image structure is first estimated by a series of center-weighted reference filters. Then the distances between the observed central pixel and estimated references are utilized to classify the local inputs into one of preset structure partition cells. Finally, a weighted filtering operation, indexed by the partition cell, is applied to the estimated references in order to restore the central pixel value. The weighted filtering operation is optimized off-line for each partition cell to achieve the best tradeoff between noise suppression and structure preservation. Recursive filtering operation and recursive weight training are also investigated to further boost the restoration performance. The proposed filter has demonstrated satisfactory results in suppressing many distinct types of noise in natural color images. Noticeable performance gains are demonstrated over other prior-art methods in terms of standard objective measurements, the visual image quality and the computational complexity.

A robust structure-adaptive hybrid vector filter for color image restoration

A robust structure-adaptive hybrid vector filter is proposed for digital color image restoration in this paper. At each pixel location, the image vector (i.e., pixel) is first classified into several different signal activity categories by applying a modified quadtree decomposition to luminance component (image) of the input color image. A weight-adaptive vector filtering operation with an optimal window is then activated to achieve the best tradeoff between noise suppression and detail preservation. Through extensive simulation experiments conducted using a wide range of test color images, the filter has demonstrated superior performance to that of a number of well known benchmark techniques, in terms of both standard objective measurements and perceived image quality, in suppressing several distinct types of noise commonly considered in color image restoration, including Gaussian noise, impulse noise, and mixed noise.

Building robust wavelet estimators for multicomponent images using Stein's principle

Multichannel imaging systems provide several observations of the same scene which are often corrupted by noise. In this paper, we are interested in multispectral image denoising in the wavelet domain. We adopt a multivariate statistical approach in order to exploit the correlations existing between the different spectral components. Our main contribution is the application of Stein's principle to build a new estimator for arbitrary multichannel images embedded in additive Gaussian noise. Simulation tests carried out on optical satellite images show that the proposed method outperforms conventional wavelet shrinkage techniques.

MRI diffusion-based filtering: a note on performance characterisation

Frequently MRI data is characterised by a relatively low signal to noise ratio (SNR) or contrast to noise ratio (CNR). When developing automated Computer Assisted Diagnostic (CAD) techniques the errors introduced by the image noise are not acceptable. Thus, to limit these errors, a solution is to filter the data in order to increase the SNR. More importantly, the image filtering technique should be able to reduce the level of noise, but not at the expense of feature preservation. In this paper we detail the implementation of a number of 3D diffusion-based filtering techniques and we analyse their performance when they are applied to a large collection of MR datasets of varying type and quality.

Multi-exponential analysis of magnitude MR images using a quantitative multispectral edge-preserving filter

A solution for discrete multi-exponential analysis of T(2) relaxation decay curves obtained in current multi-echo imaging protocol conditions is described. We propose a preprocessing step to improve the signal-to-noise ratio and thus lower the signal-to-noise ratio threshold from which a high percentage of true multi-exponential detection is detected. It consists of a multispectral nonlinear edge-preserving filter that takes into account the signal-dependent Rician distribution of noise affecting magnitude MR images. Discrete multi-exponential decomposition, which requires no a priori knowledge, is performed by a non-linear least-squares procedure initialized with estimates obtained from a total least-squares linear prediction algorithm. This approach was validated and optimized experimentally on simulated data sets of normal human brains.

Generalized multichannel image-filtering structures

Recent works in multispectral image processing advocate the employment of vector approaches for this class of signals. Vector processing operators that involve the minimization of a suitable error criterion have been proposed and shown appropriate for this task. In this framework, two main classes of vector processing filters have been reported in the literature. Astola et al. (1990) introduce the well-known class of vector median filters (VMF), which are derived as maximum likelihood (ML) estimates from exponential distributions. Trahanias et al. (see ibid., vol.2, no.4, p.528-34, 1993 and vol.5, no.6, p.868-80, 1996) study the processing of color image data using directional information, considering the class of vector directional filters (VDF). We introduce a new filter structure, the directional-distance filters (DDF), which combine both VDF and VMF in a novel way. We show that DDF are robust signal estimators under various noise distributions, they have the property of chromaticity preservation and, finally, compare favorably to other multichannel image processing filters.

A new approach to vector median filtering based on space filling curves

The availability of a wide set of multidimensional information sources in different application fields (e.g., color cameras, multispectral remote sensing imagery devices, etc.) is the basis for the interest of image processing research on extensions of scalar nonlinear filtering approaches to multidimensional data filtering. A new approach to multidimensional median filtering is presented. The method is structured into two steps. Absolute sorting of the vectorial space based on Peano space filling curves is proposed as a preliminary step in order to map vectorial data onto an appropriate one-dimensional (1-D) space. Then, a scalar median filtering operation is applied. The main advantage of the proposed approach is the computational efficiency of the absolute sorting step, which makes the method globally faster than existing median filtering techniques. This is particularly important when dealing with a large amount of data (e.g., image sequences). Presented results also show that the filtering performances of the proposed approach are comparable with those of vector median filters presented in the literature.