Subspace Projection Technique Research Articles

Author's reply to Comments on "Comparison between orthogonal subspace projection and background subtraction techniques applied to remote-sensing data"

Johnson's comments [Appl. Opt. 46, 4162 (2007)] represent a nice independent analytical proof of a specific aspect of the Ben-David and Ren [Appl. Opt. 44, 3846 (2005)] general analysis in which the effect of noise-angle statistics on the accuracy of the two techniques was addressed and demonstrated. When whitening is applied to the data, the noise-angle distribution becomes effectively uniform and is thus consistent with the predictions that the subtraction solution becomes superior to the orthogonal subspace projection solution.

An estimation method for InSAR interferometric phase combined with image auto-coregistration

In this paper we propose a method to estimate the InSAR interferometric phase of the steep terrain based on the terrain model of local plane by using the joint subspace projection technique proposed in our previous paper. The method takes advantage of the coherence information of neighboring pixel pairs to auto-coregister the SAR images and employs the projection of the joint signal subspace onto the corresponding joint noise subspace to estimate the terrain interferometric phase. The method can auto-coregister the SAR images and reduce the interferometric phase noise simultaneously. Theoretical analysis and computer simulation results show that the method can provide accurate estimate of the interferometric phase (interferogram) of very steep terrain even if the coregistration error reaches one pixel. The effectiveness of the method is verified via simulated data and real data.

Spectral feature projections that maximize Shannon mutual information with class labels

Determining optimal subspace projections that can maintain task-relevant information in the data is an important problem in machine learning and pattern recognition. In this paper, we propose a nonparametric nonlinear subspace projection technique that maintains class separability maximally under the Shannon mutual information (MI) criterion. Employing kernel density estimates for nonparametric estimation of MI makes possible an interesting marriage of kernel density estimation-based information theoretic methods and kernel machines, which have the ability to determine nonparametric nonlinear solutions for difficult problems in machine learning. Significant computational savings are achieved by translating the definition of the desired projection into the kernel-induced feature space, which leads to obtain analytical solution.

Dimension reduction for array processing with robust interference cancellation

We present a robust solution for data reduction in array processing. The purpose is to reduce the computation and improve the performance of applied signal processing algorithms by mapping the data into a lower dimension beamspace (BS) through a transformation. Nulls steering to interference are incorporated into a transformation using the subspace projection technique, and the BS spatial spectrum estimation accuracy is evaluated and maximized with a measure. The derived transformation tries to preserve the full-dimension Cramer-Rao bounds (CRBs) for the parameters of interest while rejecting undesired signals effectively. When compared with an optimal method and an adaptive approach, simulation results show that significant improvements are obtained in terms of BS direction-of-arrival (DOA) estimation root-mean-squared error (RMSE), bias, and resolution probability.

Comparison between orthogonal subspace projection and background subtraction techniques applied to remote-sensing data

The basic measurement equation r = B + alphad + n is solved for alpha (the weight or abundance of the spectral target vector d) by two methods: (a) by subtracting the stochastic spectral background vector B from the spectral measurement's vector r (subtraction solution) and (b) by orthogonal subspace projection (OSP) of the measurements to a subspace orthogonal to B (the OSP solution). The different geometry of the two solutions and in particular the geometry of the noise vector n is explored. The angular distribution of the noise angle between B and n is the key factor for determining and predicting which solution is better. When the noise-angle distribution is uniform, the subtraction solution is always superior regardless of the orientation of the spectral target vector d. When the noise is more concentrated in the direction orthogonal to B, the OSP solution becomes better (as expected). Simulations and one-dimensional hyperspectral measurements of vapor concentration in the presence of background radiation and noise are given to illustrate these two solutions.

An automated palmprint recognition system

Recently, biometric palmprint has received wide attention from researchers. It is well-known for several advantages such as stable line features, low-resolution imaging, low-cost capturing device, and user-friendly. In this paper, an automated scanner-based palmprint recognition system is proposed. The system automatically captures and aligns the palmprint images for further processing. Several linear subspace projection techniques have been tested and compared. In specific, we focus on principal component analysis (PCA), fisher discriminant analysis (FDA) and independent component analysis (ICA). In order to analyze the palmprint images in multi-resolution-multi-frequency representation, wavelet transformation is also adopted. The images are decomposed into different frequency subbands and the best performing subband is selected for further processing. Experimental result shows that application of FDA on wavelet subband is able to yield both FAR and FRR as low as 1.356 and 1.492% using our palmprint database.

Global spectral irradiance variability and material discrimination at Boulder, Colorado.

We analyze 7,258 global spectral irradiance functions over 0.4-2.2 microm that were acquired over a wide range of conditions at Boulder, Colorado, during the summer of 1997. We show that low-dimensional linear models can be used to capture the variability in these spectra over both the visible and the 0.4-2.2 microm spectral ranges. Using a linear model, we compare the Boulder data with the previous study of Judd et al. [J. Opt. Soc. Am. 54, 1031 (1964)] over the visible wavelengths. We also examine the agreement of the Boulder data with a spectral database generated by using the MODTRAN 4.0 radiative transfer code. We use a database of 223 minerals to consider the effect of the spectral variability in the global spectral irradiance functions on hyperspectral material identification. We show that the 223 minerals can be discriminated accurately over the variability in the Boulder data with subspace projection techniques.

Resonances and pseudoresonances in a potential with attractive coulomb tail: A study using analytic‐continuation techniques

AbstractThe performance of the complex absorbing potential (CAP) and the complex scaling (CS) methods in the detection and calculation of complex Siegert energies is studied using a 1‐D long‐range attractive model potential. This potential is constructed to mimic molecular properties, in particular an attractive Coulombic term, to allow one to draw conclusions on molecular ab initio studies. Analyzing the spectrum of the model potential, one compact bound state embedded in the manifold of Rydberg states is found that shows artificial resonance characteristics when applying the CAP and the CS methods. This pseudoresonance problem is less pronounced in the calculation using the CS method than in that using the CAP method. Despite this deficiency, the CAP method is shown to possess advantages over CS when dealing with physical resonances under conditions that simulate the application of standard basis sets in ab initio calculations. The accuracy of the Siegert energy is shown to be maintained when applying a subspace projection technique to the CAP method. This technique reduces the computational demand significantly and leads to an important improvement of the CAP method, which should be of particular significance in molecular applications. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003

GPS Antijam via Subspace Projection: A Performance Analysis for FM Interference in the C/A Code

Zhao, L., Amin, M. G., and Lindsey, A. R., GPS Antijam via Subspace Projection: A Performance Analysis for FM Interference in the C/A Code, Digital Signal Processing 12 (2002) 175–192 This paper is concerned with frequency modulated (FM) interference cancelation in GPS receivers. FM signals are instantaneously narrowband and have clear time–frequency signatures that are distinct from the GPS C/A spreading codes. Interference cancelation is performed by first constructing the interference subspace and then projecting the data onto the orthogonal subspace. Interference subspace estimation can be provided by the time–frequency distribution (TFD) or any other instantaneous frequency (IF) estimator. The GPS receiver signal-to-interference and noise ratio in the presence of IF or phase estimation errors is derived. The errors are assumed Gaussian and independent. From both analysis and simulations, it is shown that phase estimation errors can substantially impede interference rejection in GPS using subspace projection techniques.

Array processing for nonstationary interference suppression in DS/SS communications using subspace projection techniques

Combined spatial and time-frequency signatures of signal arrivals at a multisensor array are used for nonstationary interference suppression in direct-sequence spread-spectrum (DS/SS) communications. With random PN spreading code and deterministic nonstationary interferers, the use of antenna arrays offers increased DS/SS signal dimensionality relative to the interferers. Interference mitigation through a spatio-temporal subspace projection technique leads to reduced DS/SS signal distortion and improved performance over the case of a single antenna receiver. The angular separation between the interference and desired signals is shown to play a fundamental role in trading off the contribution of the spatial and time-frequency signatures to the interference mitigation process. The expressions of the receiver signal-to-interference-noise ratio (SINR) implementing subspace projections are derived, and numerical results are provided.

Stereo image coding: a projection approach

Recently, due to advances in display technology, three-dimensional (3-D) imaging systems are becoming increasingly popular. One way of stimulating 3-D perception is to use stereo pairs, a pair of images of the same scene acquired from different perspectives. Since there is an inherent redundancy between the images of a stereo pair, data compression algorithms should be employed to represent stereo pairs efficiently. This paper focuses on the stereo image coding problem. We begin with a description of the problem and a survey of current stereo coding techniques. A new stereo image coding algorithm that is based on disparity compensation and subspace projection is described. This algorithm, the subspace projection technique (SPT), is a transform domain approach with a space-varying transformation matrix and may be interpreted as a spatial-transform domain representation of the stereo data. The advantage of the proposed approach is that it can locally adapt to the changes in the cross-correlation characteristics of the stereo pairs. Several design issues and implementations of the algorithm are discussed. Finally, we present empirical results suggesting that the SPT approach outperforms current stereo coding techniques.

Tensor-GMRES Method for Large Systems of Nonlinear Equations

This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large systems of nonlinear equations. Krylov subspace projection techniques for asymmetric systems of linear equations are coupled with a tensor model formation and solution technique for nonlinear equations. Similar to traditional tensor methods, the new tensor method is shown to have significant computational advantages over the analogous Newton counterpart on a set of nonsingular and singular problems. For example, an application to the Euler equations for the flow through a nozzle with a given area ratio shows that the tensor-GMRES method can be much more efficient than the analogous Newton-GMRES method. The new tensor method is also consistent with preconditioning and matrix-free implementation.