Multi-narrowband signals receiving method based on analog-to-information convertor and block sparsity

The analog-to-information convertor (AIC) is a successful practice of compressive sensing (CS) theory in the analog signal acquisition. This paper presents a multi-narrowband signals sampling and reconstruction model based on AIC and block sparsity. To overcome the practical problems, the block sparsity is divided into uniform block and non-uniform block situations, and the block restricted isometry property and sub-sampling limit in different situations are analyzed respectively in detail. Theoretical analysis proves that using the block sparsity in AIC can reduce the restricted isometric constant, increase the reconstruction probability and reduce the sub -sampling rate. Simulation results show that the proposed model can complete sub -sampling and reconstruction for multi-narrowband signals. This paper extends the application range of AIC from the finite information rate signal to the multi-narrowband signals by using the potential relevance of support sets. The proposed receiving model has low complexity and is easy to implement, which can promote the application of CS theory in the radar receiver to reduce the burden of analog-to digital convertor (ADC) and solve bandwidth limitations of ADC.

COMPRESSED SPEECH SIGNAL SENSING BASED ON THE STRUCTURED BLOCK SPARSITY WITH PARTIAL KNOWLEDGE OF SUPPORT

Structural and statistical characteristics of signals can improve the performance of Compressed Sensing (CS). Two kinds of features of Discrete Cosine Transform (DCT) coefficients of voiced speech signals are discussed in this paper. The first one is the block sparsity of DCT coefficients of voiced speech formulated from two different aspects which are the distribution of the DCT coefficients of voiced speech and the comparison of reconstruction performance between the mixed program and Basis Pursuit (BP). The block sparsity of DCT coefficients of voiced speech means that some algorithms of block-sparse CS can be used to improve the recovery performance of speech signals. It is proved by the simulation results of the mixed program which is an improved version of the mixed program. The second one is the well known large DCT coefficients of voiced speech focus on low frequency. In line with this feature, a special Gaussian and Partial Identity Joint (GPIJ) matrix is constructed as the sensing matrix for voiced speech signals. Simulation results show that the GPIJ matrix outperforms the classical Gaussian matrix for speech signals of male and female adults.

Adaptive block greedy algorithms for receiving multi-narrowband signal in compressive sensing radar reconnaissance receiver

This paper extends the application of compressive sensing(CS) to the radar reconnaissance receiver for receiving the multi-narrowband signal. By combining the concept of the block sparsity, the self-adaption methods, the binary tree search,and the residual monitoring mechanism, two adaptive block greedy algorithms are proposed to achieve a high probability adaptive reconstruction. The use of the block sparsity can greatly improve the efficiency of the support selection and reduce the lower boundary of the sub-sampling rate. Furthermore, the addition of binary tree search and monitoring mechanism with two different supports self-adaption methods overcome the instability caused by the fixed block length while optimizing the recovery of the unknown signal.The simulations and analysis of the adaptive reconstruction ability and theoretical computational complexity are given. Also, we verify the feasibility and effectiveness of the two algorithms by the experiments of receiving multi-narrowband signals on an analogto-information converter(AIC). Finally, an optimum reconstruction characteristic of two algorithms is found to facilitate efficient reception in practical applications.

Block Sparse Recovery via Mixed l_2/l_1 Minimization

We consider efficient methods for the recovery of block sparse signals from underdetermined system of linear equations. We show that if the measurement matrix satisfies the block RIP with δ2s 〈 0.4931, then every block s-sparse signal can be recovered through the proposed mixed l2/ll-minimization approach in the noiseless case and is stably recovered in the presence of noise and mismodeling error. This improves the result of Eldar and Mishali （in IEEE Trans. Inform. Theory 55： 5302-5316, 2009）. We also give another sufficient condition on block RIP for such recovery method： 58 〈 0.307.

AN EXTENDED BLOCK RESTRICTED ISOMETRY PROPERTY FOR SPARSE RECOVERY WITH NON-GAUSSIAN NOISE

We study the recovery conditions of weighted mixedl2/lp minimization for block sparse signal reconstruction from compressed measurements when partial block support information is available.We show theoretically that the extended block restricted isometry property can ensure robust recovery when the data fidelity constraint is expressed in terms of anlq norm of the residual error,thus establishing a setting wherein we are not restricted to Gaussian measurement noise.We illustrate the results with a series of numerical experiments.