Fast gradient algorithm for complex ICA and its application to the MIMO systems.

This paper proposes a new gradient-descent algorithm for complex independent component analysis and presents its application to the Multiple-Input Multiple-Output communication systems. Algorithm uses the Lie structure of optimization landscape and toral decomposition of gradient matrix. The theoretical results are validated by computer simulation and compared to several classes of algorithms, gradient descent, quasi-Newton as well as complex JADE. The simulations performed showed excellent results of the algorithm in terms of speed, stability of operation and the quality of separation. A characteristic feature of gradient methods is their quick response to changes in the input signal. The good results of the proposed algorithm indicate potential use in on-line applications.

Cutting Force during Surface Layer Milling of Selected Aluminium Alloys.

This paper presents the analysis of cutting force during surface layer milling of selected aluminium alloys, which are widely used in the aviation industry. The cutting force is one of the most important parameters determining the machinability of the material and also provides important information about the course of the cutting. The study analysed the influence of the technological parameters, i.e., cutting speed vc and depth of cut ap as well as the relation between cutting tool feed direction and rolling direction on the value of cutting force during milling of selected aluminium alloys, i.e., EN AW-2017A T451 and EN AW-2024 T351. The material anisotropy is a very important issue, since the engineering industry faces enormous problems related to the cutting of the tested materials that are usually supplied in the form of rolled plates. The surface layer was cut due to the fact that it accumulates the greatest residual stresses. The measurement process of cutting force was performed by using 9257B Kistler piezoelectric dynamometer. As part of the analysis of the results, the measurement uncertainty was also estimated, which was determined on the basis of two components obtained by using the A and B methods, respectively.

Single Channel Source Separation with ICA-Based Time-Frequency Decomposition.

This paper relates to the separation of single channel source signals from a single mixed signal by means of independent component analysis (ICA). The proposed idea lies in a time-frequency representation of the mixed signal and the use of ICA on spectral rows corresponding to different time intervals. In our approach, in order to reconstruct true sources, we proposed a novelty idea of grouping statistically independent time-frequency domain (TFD) components of the mixed signal obtained by ICA. The TFD components are grouped by hierarchical clustering and k-mean partitional clustering. The distance between TFD components is measured with the classical Euclidean distance and the ß distance of Gaussian distribution introduced by as. In addition, the TFD components are grouped by minimizing the negentropy of reconstructed constituent signals. The proposed method was used to separate source signals from single audio mixes of two- and three-component signals. The separation was performed using algorithms written by the authors in Matlab. The quality of obtained separation results was evaluated by perceptual tests. The tests showed that the automated separation requires qualitative information about time-frequency characteristics of constituent signals. The best separation results were obtained with the use of the ß distance of Gaussian distribution, a distance measure based on the knowledge of the statistical nature of spectra of original constituent signals of the mixed signal.

Lie Group Methods in Blind Signal Processing.

This paper deals with the use of Lie group methods to solve optimization problems in blind signal processing (BSP), including Independent Component Analysis (ICA) and Independent Subspace Analysis (ISA). The paper presents the theoretical fundamentals of Lie groups and Lie algebra, the geometry of problems in BSP as well as the basic ideas of optimization techniques based on Lie groups. Optimization algorithms based on the properties of Lie groups are characterized by the fact that during optimization motion, they ensure permanent bonding with a search space. This property is extremely significant in terms of the stability and dynamics of optimization algorithms. The specific geometry of problems such as ICA and ISA along with the search space homogeneity enable the use of optimization techniques based on the properties of the Lie groups O ( n ) and S O ( n ) . An interesting idea is that of optimization motion in one-parameter commutative subalgebras and toral subalgebras that ensure low computational complexity and high-speed algorithms.