Ivica Kopriva

Wavelet packets approach to blind separation of statistically dependent sources

Sub-band decomposition independent component analysis (SDICA) assumes that wide-band source signals can be dependent but some of their sub-components are independent. Thus, it extends applicability of standard independent component analysis (ICA) through the relaxation of the independence assumption. In this paper, firstly, we introduce novel wavelet packets (WPs) based approach to SDICA obtaining adaptive sub-band decomposition of the wideband signals. Secondly, we introduce small cumulant based approximation of the mutual information (MI) as a criterion for the selection of the sub-band with the least-dependent components. Although MI is estimated for measured signals only, we have provided a proof that shows that index of the sub-band with least dependent components of the measured signals will correspond with the index of the sub-band with least dependent components of the sources. Unlike in the case of the competing methods, we demonstrate consistent performance in terms of accuracy and robustness as well as computational efficiency of WP SDICA algorithm.

Independent-component analysis for hyperspectral remote sensing imagery classification

We investigate the application of independent-component analysis ICA to remotely sensed hyperspectral image classification. We focus on the performance of two well-known and frequently used ICA algorithms: joint approximate diagonalization of eigenmatrices JADE and FastICA; but the proposed method is applicable to other ICA algo- rithms. The major advantage of using ICA is its ability to classify objects with unknown spectral signatures in an unknown image scene, i.e., un- supervised classification. However, ICA suffers from computational ex- pensiveness, which limits its application to high-dimensional data analy- sis. In order to make it applicable or reduce the computation time in hyperspectral image classification, a data-preprocessing procedure is employed to reduce the data dimensionality. Instead of using principal- component analysis PCA, a noise-adjusted principal-components NAPC transform is employed for this purpose, which can reorganize the original data with respect to the signal-to-noise ratio, a more appro- priate image-ranking criterion than variance in PCA. The experimental results demonstrate that the major principal components from the NAPC transform can better maintain the object information in the original data than those from PCA. As a result, an ICA algorithm can provide better object classification.

Approach to blind image deconvolution by multiscale subband decomposition and independent component analysis

A single-frame multichannel blind image deconvolution technique has been formulated recently as a blind source separation problem solved by independent component analysis (ICA). The attractive feature of this approach is that neither origin nor size of the spatially invariant blurring kernel has to be known. To enhance the statistical independence among the hidden variables, we employ multiscale analysis implemented by wavelet packets and use mutual information to locate a subband with the least dependent components, where the basis matrix is learned by means of standard ICA. We show that the proposed algorithm is capable of performing blind deconvolution of nonstationary signals that are not independent and identically distributed processes. The image poses these properties. The algorithm is tested on experimental data and compared with state-of-the-art single-frame blind image deconvolution algorithms. Our good experimental results demonstrate the viability of the proposed concept.

Sparse coding blind source separation through Powerline

Without multiplexing, Powerline (PL) can support the concept of smart sensor webb roadcasting of an N -sensors-to-single-owner (N -to-1) for household=stadium=mall=metro=city surveillance. In order to make the single user scenario feasible, the underdetermined blind source separation (BSS) problem x(k )= � * a; * s (k)� + n(k) has to be solved so that only inner product time series signal x(k) is known. Our contribution is based on the understanding that the 3nite alphabet property of the binary sources * s (k) can resolve the underdetermined PL BSS case. For example, the alphabet of two binary sources consists of four states (1 1, 1 −1, − 11 ,−1 −1), which mixing vector * a and noise n(k) will spread in the mixed signal x(k), around the four centroids. We apply self-organizing maps to compute centroids from which the impulse response vector * a is determined. Then, the source vector * s (k) is recovered using the standard LMS method. Published by Elsevier Science B.V.

Independent component analysis approach to resolve the multi-source limitation of the nutating rising-sun reticle based optical trackers

Independent component analysis (ICA) is described for a number of signals from different sources and a number of receivers. When applied to nutating rising-sun reticle optical trackers, ICA enables the discrimination of optical sources with an appropriate number of detectors. The main contribution of this paper is the conclusion that coherence between optical sources results in a nonlinear ICA problem that becomes linear when the optical fields are incoherent. It is shown that requirements necessary for the ICA theory to work are fulfilled for both coherent and incoherent optical sources. Moreover, it is shown additionally that by the proper design of the optical tracker the nonlinear model can be converted into linear one by simple linear bandpass filtering operation. Consequently, the multisource limitation of the nutating rising-sun reticle based optical trackers can in principle be overcome for both coherent and incoherent optical sources.

Unsupervised decomposition of low-intensity low-dimensional multi-spectral fluorescent images for tumour demarcation

Unsupervised decomposition of static linear mixture model (SLMM) with ill-conditioned basis matrix and statistically dependent sources is considered. Such situation arises when low-dimensional low-intensity multi-spectral image of the tumour in the early stage of development is represented by the SLMM, wherein tumour is spectrally similar to the surrounding tissue. The original contribution of this paper is in proposing an algorithm for unsupervised decomposition of low-dimensional multi-spectral image for high-contrast tumour visualisation. It combines nonlinear band generation (NBG) and dependent component analysis (DCA) that itself combines linear pre-processing transform and independent component analysis (ICA). NBG is necessary to improve conditioning of the extended mixing matrix in the SLMM, while DCA is necessary to increase statistical independence between spectrally similar sources. We demonstrate good performance of the method on both computational model and experimental low-intensity red-green-blue fluorescent image of the surface tumour (basal cell carcinoma). We believe that presented method can be of use in other multi-channel medical imaging systems.

An adaptive short-time frequency domain algorithm for blind separation of nonstationary convolved mixtures

We present a frequency domain algorithm derived for windowed-adaptive blind separation of convolved sources. Signal separation (filtering) is performed in short-time-windowed-frequency domain in terms of a finite filter length L obtaining faster convergence and better performance compared with the strictly time domain algorithms. In order to avoid the whitening effect the recurrent neural network, similar to the one proposed by Back and Tsoi (1994), is employed. A statistical independence test is done in time domain in order to determine the relative time-varying effect and solve the permutation indeterminacy problem. Corrections of the learning rules are introduced, which show to improve separation performance significantly. Additionally, the results developed by Amari et al. (2000) for the instantaneous mixtures are applied making learning equations computationally more efficient. To resolve the permutation problems the neural network outputs algorithm developed by Markowitz and Szu (1999) is applied.

INDEPENDENT COMPONENT ANALYSIS FOR CLASSIFYING MULTISPECTRAL IMAGES WITH DIMENSIONALITY LIMITATION

Airborne and spaceborne remote sensors can acquire invaluable information about earth surface, which have many important applications. The acquired information usually is represented as two-dimensional grids, i.e. images. One of techniques to processing such images is Independent Component Analysis (ICA), which is particularly useful for classifying objects with unknown spectral signatures in an unknown image scene, i.e. unsupervised classification. Since the weight matrix in ICA is a square matrix for the purpose of mathematical tractability, the number of objects that can be classified is equal to the data dimensionality, i.e. the number of spectral bands. When the number of sensors (or spectral channels) is very small (e.g. a 3-band CIR photograph and 6-band Landsat image with the thermal band being removed), it is impossible to classify all the different objects present in an image scene using the original data. In order to solve this problem, we present a data dimensionality expansion technique to generate artificial bands. Its basic idea is to use nonlinear functions to capture and highlight the similarity/dissimilarity between original spectral measurements, which can provide more data with additional information for detecting and classifying more objects. The results from such a nonlinear band generation approach are compared with a linear band generation method using cubic spline interpolation of pixel spectral signatures. The experiments demonstrate that nonlinear band generation approach can significantly improve unsupervised classification accuracy, while linear band generation method cannot since no new information can be provided. It is also demonstrated that ICA is more powerful than other frequently used unsupervised classification algorithms such as ISODATA.

Single-frame multichannel blind deconvolution by nonnegative matrix factorization with sparseness constraints

Single-frame multichannel blind deconvolution is formulated by applying a bank of Gabor filters to a blurred image. The key observation is that spatially oriented Gabor filters produce sparse images and that a multichannel version of the observed image can be represented as a product of an unknown nonnegative sparse mixing vector and an unknown nonnegative source image. Therefore a blind-deconvolution problem is formulated as a nonnegative matrix factorization problem with a sparseness constraint. No a priori knowledge about the blurring kernel or the original image is required. The good experimental results demonstrate the viability of the proposed concept.

Blind multispectral image decomposition by 3D nonnegative tensor factorization

Alpha-divergence-based nonnegative tensor factorization (NTF) is applied to blind multispectral image (MSI) decomposition. The matrix of spectral profiles and the matrix of spatial distributions of the materials resident in the image are identified from the factors in Tucker3 and PARAFAC models. NTF preserves local structure in the MSI that is lost as a result of vectorization of the image when nonnegative matrix factorization (NMF)- or independent component analysis (ICA)-based decompositions are used. Moreover, NTF based on the PARAFAC model is unique up to permutation and scale under mild conditions. To achieve this, NMF- and ICA-based factorizations, respectively, require enforcement of sparseness (orthogonality) and statistical independence constraints on the spatial distributions of the materials resident in the MSI, and these conditions do not hold. We demonstrate efficiency of the NTF-based factorization in relation to NMF- and ICA-based factorizations on blind decomposition of the experimental MSI with the known ground truth.