Generalized Subspace Method Research Articles

From Pseudo to Real: Generalized Subspace Method for Power Spectrum Reconstruction

Subspace methods are widely used in statistical signal processing owing to their super-resolution. Conventional subspace methods, such as multiple signal classification (MUSIC) identify parameters containing frequency and direction of arrival by calculating pseudo-spectra without physical amplitudes. However, the real value of amplitude plays a significant role in fault diagnosis and condition monitoring. Additionally, due to hardware limitations and increased frequency, uniform (Nyquist) sampling becomes challenging. Nonuniform sampling, an alternative to high-rate sampling is common in practice. Consequently, Nonuniform (sub-Nyquist) signal processing methods are urgently required. In this paper, a generalized subspace method (GSM) is proposed to bridge the pseudo spectrum with the real spectrum. The proposed method is a supplement to the existing subspace methods and is applicable to both uniform and nonuniform sampling. In the GSM, the Fourier coefficient of the autocorrelation function is derived by signal subspace from the perspective of basis matching. Then, an alias-free real power spectrum is obtained by combining the power spectrum reconstructed by GSM with the classical pseudo spectrum. Finally, simulation and experiment demonstrate the performance of the proposed method in power spectrum reconstruction. Even under the dual influence of undersampled and nonuniform, the proposed method is still effective.

On pre-image iterations for speech enhancement.

In this paper, we apply kernel PCA for speech enhancement and derive pre-image iterations for speech enhancement. Both methods make use of a Gaussian kernel. The kernel variance serves as tuning parameter that has to be adapted according to the SNR and the desired degree of de-noising. We develop a method to derive a suitable value for the kernel variance from a noise estimate to adapt pre-image iterations to arbitrary SNRs. In experiments, we compare the performance of kernel PCA and pre-image iterations in terms of objective speech quality measures and automatic speech recognition. The speech data is corrupted by white and colored noise at 0, 5, 10, and 15 dB SNR. As a benchmark, we provide results of the generalized subspace method, of spectral subtraction, and of the minimum mean-square error log-spectral amplitude estimator. In terms of the scores of the PEASS (Perceptual Evaluation Methods for Audio Source Separation) toolbox, the proposed methods achieve a similar performance as the reference methods. The speech recognition experiments show that the utterances processed by pre-image iterations achieve a consistently better word recognition accuracy than the unprocessed noisy utterances and than the utterances processed by the generalized subspace method.

A sequential subspace method for blind identification of general FIR MIMO channels

This correspondence addresses the problem of blindly identifying multiple input multiple output (MIMO) finite impulse response (FIR) channels without the conventional assumption of identical column degrees. A subspace-based algorithm is developed that identifies the channel's columns sequentially from the lowest degree columns to the highest degree ones. Compared with the previous generalized subspace method by Gorokhov and Loubaton (1997), the new method is simpler and more accurate.

3D resistivity mapping of airborne EM data

A 3D resistivity mapping technique has been developed to provide fast estimates of resistivity distributions in airborne electromagnetic surveys. This proposed 3D mapping method consists of an approximate 3D linear inverse operator and a generalized subspace solver. The 3D inverse operator can be generated using any forward approximation that is linear in resistivity. The generalized subspace method is an alternative to the conjugate gradient method, and it reduces the original large linear system of equations to a much smaller but nonlinear one that is solved iteratively. The major benefit of using generalized subspace methods is that subspace vectors can be built based upon physical principles such as skin and investigation depths. Since the 3D mapping is a linear inverse problem, no iteration, and thus no forward modeling nor sensitivity updating, is needed. The 3D resistivity‐mapping technique can be used directly to estimate 3D resistivity distribution or to provide a model update during an intermediate iteration in a nonlinear 3D inversion. Synthetic and field data examples indicate that the 3D mapping can provide quantitative information about the resistivity and spatial distributions of the 3D targets.

Practical strategies for the solution of large‐scale electromagnetic inverse problems

Nonlinear inverse problems in electromagnetics are typically solved by dividing the Earth into cells of constant conductivity, linearizing the equations about a current model, computing the sensitivities, and then solving an optimization problem to obtain an updated estimate of the conductivity. In principle, this procedure can be implemented for any size problem, but in practice the computations involved may be too large for the available computing hardware. In electromagnetics this is currently the situation irrespective of whether the interpreter has access to a workstation or a supercomputer. In addition to the demands imposed by the need to compute the predicted responses from a specified model (i.e., invoking a forward mapping) there are two computational roadblocks encountered when solving an inverse problem: (1) calculation of the sensitivity matrix and (2) solution of the resultant large system of equations. If either of these operations cannot be carried out in reasonable time then an alternate strategy is required. Such strategies include generalized subspace methods, conjugate gradient methods, or approximate inverse mapping (AIM) procedures. The theoretical foundations and computational details of these strategies are explored in this paper with the ultimate goal that the inversionist, after assessing his/her computing power and knowing the time required to perform forward modeling, can generate a methodology by which to solve the problem. The methodologies are compared quantitatively by considering an archetypal inversion problem in electromagnetics, the inversion of dc potential data to recover the electrical conductivity.