Adaptive blind separation of underdetermined mixtures based on sparse component analysis

The independence priori is very often used in the conventional blind source separation （BSS）. Naturally, independent component analysis （ICA） is also employed to perform BSS very often. However, ICA is difficult to use in some challenging cases, such as underdetermined BSS or blind separation of dependent sources. Recently, sparse component analysis （SCA） has attained much attention because it is theoretically available for underdetermined BSS and even for blind dependent source separation sometimes. However, SCA has not been developed very sufficiently. Up to now, there are only few existing algorithms and they are also not perfect as well in practice. For example, although Lewicki-Sejnowski＇s natural gradient for SCA is superior to K-mean clustering, it is just an approximation without rigorously theoretical basis. To overcome these problems, a new natural gradient formula is proposed in this paper. This formula is derived directly from the cost function of SCA through matrix theory. Mathematically, it is more rigorous. In addition, a new and robust adaptive BSS algorithm is developed based on the new natural gradient. Simulations illustrate that this natural gradient formula is more robust and reliable than Lewicki-Sejnowski＇s gradient.

Inverse synthetic aperture radar imaging based on sparse signal processing

Based on the measurement model of inverse synthetic aperture radar (ISAR) within a small aspect sector,an imaging method was presented with the application of sparse signal processing.This method can form higher resolution inverse synthetic aperture radar images from compensating incomplete measured data,and improves the clarity of the images and makes the feature structure much more clear,which is helpful for target recognition.The simulation results indicate that this method can provide clear ISAR images with high contrast under complex motion case.

A contourlet-transform based sparse ICA algorithm for blind image separation

A contourlet-transform （CT） based sparse independent component analysis for blind image separation is proposed. The images are first decomposed into sets of local features with various degrees of sparsity, and then the intrinsic property is used to select the best （sparsest） subsets of features for further separation. Based on sparse description of the contourlet- transform, the proposed approach is able to yield better performance, including faster convergence and the certain order for the separated signals. Simulation results confirm the validity of the proposed method.

Mixing matrix estimation of underdetermined blind source separation based on the linear aggregation characteristic of observation signals

Under the underdetermined blind sources separation(UBSS) circumstance,it is difficult to estimate the mixing matrix with high-precision because of unknown sparsity of signals.The mixing matrix estimation is proposed based on linear aggregation degree of signal scatter plot without knowing sparsity,and the linear aggregation degree evaluation of observed signals is presented which obeys generalized Gaussian distribution(GGD).Both the GGD shape parameter and the signals' correlation features affect the observation signals sparsity and further affected the directionality of time-frequency scatter plot.So a new mixing matrix estimation method is proposed for different sparsity degrees,which especially focuses on unclear directionality of scatter plot and weak linear aggregation degree.Firstly,the direction of coefficient scatter plot by time-frequency transform is improved and then the single source coefficients in the case of weak linear clustering is processed finally the improved K-means clustering is applied to achieve the estimation of mixing matrix.The proposed algorithm reduces the requirements of signals sparsity and independence,and the mixing matrix can be estimated with high accuracy.The simulation results show the feasibility and effectiveness of the algorithm.