Compress Sensing
A. Vakili; M. Shams Esfand Abadi; M. Kalantari
Abstract
Background and Objectives: In the realm of compressed sensing, most greedy sparse recovery algorithms necessitate former information about the signal's sparsity level, which may not be available in practical conditions. To address this, methods based on the Sparsity Adaptive Matching Pursuit (SAMP) algorithm ...
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Background and Objectives: In the realm of compressed sensing, most greedy sparse recovery algorithms necessitate former information about the signal's sparsity level, which may not be available in practical conditions. To address this, methods based on the Sparsity Adaptive Matching Pursuit (SAMP) algorithm have been developed to self-determine this parameter and recover the signal using only the sampling matrix and measurements. Determining a suitable Initial Value for the algorithm can greatly affect the performance of the algorithm.Methods: One of the latest sparsity adaptive methods is Correlation Calculation SAMP (CCSAMP), which relies on correlation calculations between the signals recovered from the support set and the candidate set. In this paper, we present a modified version of CCSAMP that incorporates a pre-estimation phase for determining the initial value of the sparsity level, as well as a modified acceptance criteria considering the variance of noise. Results: To validate the efficiency of the proposed algorithm over the previous approaches, random sparse test signals with various sparsity levels were generated, sampled at the compression ratio of 50%, and recovered with the proposed and previous methos. The results indicate that the suggested method needs, on average, 5 to 6 fewer iterations compared to the previous methods, just due to the pre-estimation of the initial guess for the sparsity level. Furthermore, as far as the least square technique is integrated in some parts of the algorithm, in presence of noise the modified acceptance criteria significantly improve the success rate while achieving a lower mean squared error (MSE) in the recovery process.Conclusion: The pre-estimation process makes it possible to recover signal with fewer iterations while keeping the recovery quality as before. The fewer the number of iterations, the faster the algorithm. By incorporating the noise variance into the accept criteria, the method achieves a higher success rate and a lower mean squared error (MSE) in the recovery process.
Compress Sensing
M. Kalantari
Abstract
Background and Objectives: Compressed sensing (CS) of analog signals in shift-invariant spaces can be used to reduce the complexity of the matched-filter (MF) receiver, in which we can be approached the standard MF performance with fewer filters. But, with a small number of filters the performance degrades ...
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Background and Objectives: Compressed sensing (CS) of analog signals in shift-invariant spaces can be used to reduce the complexity of the matched-filter (MF) receiver, in which we can be approached the standard MF performance with fewer filters. But, with a small number of filters the performance degrades quite rapidly as a function of SNR. In fact, the CS matrix aliases all the noise components, therefore the noise increases in the compressed measurements. This effect is referred to as noise folding. In this paper, an approach for compensating the noise folding effect is proposed. Methods: An approach for compensating of this effect is to use a sufficient number of filters. In this paper the aim is to reach the better performance with the same number of filter as in the previous work. This, can be approached using a weighting function embedded in the analog signal compressed sensing structure. In fact, using this weighting function we can remedy the effect of CS matrix on the noise variance. Results: Comparing with the approach based on using the sufficient number of filters to counterbalance the noise increase, experimental results show that with the same numbers of filters, in terms of probability of correct detection, the proposed approach remarkably outperforms the rival’s.Conclusion: Noise folding formation is the main factor in CS-based matched-filter receiver. The method previously presented to reduce this effect demanded using the sufficient number of filters which comes at a cost. In this paper we propose a new method based on using the weighting function embedded in the analog signal compressed sensing structure to achieve better performance.
Microphone Array Processing
M. Kalantari; M. Mohammadpour Tuyserkani; S.H. Amiri
Abstract
Background and Objectives: Operating frequency range of a microphone array is limited by the array configuration. Spatial aliasing occurs at frequencies considered to be out of the microphone array operating range that leads to side-lobes in the array beam pattern and consequently degrades the performance ...
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Background and Objectives: Operating frequency range of a microphone array is limited by the array configuration. Spatial aliasing occurs at frequencies considered to be out of the microphone array operating range that leads to side-lobes in the array beam pattern and consequently degrades the performance of the microphone array. In this paper, a general approach for increasing the operational bandwidth of the spherical microphone array without physical changes to the microphone array is proposed. Methods: Recently, Alon and Rafaely proposed a beamforming method with aliasing cancellation and formulated it for some well-known beamformers such as maximum directivity (MD), maximum white noise gain (WNG), and minimum variance distortionless response (MVDR) which have been called MDAC, MGAC, MVDR-AC beamformer respectively. In this paper, we derive MDAC method from different point of view. Then, based on our perspective, we propose a new method that is easily applicable for any beamforming algorithms.Results: Comparing with MDAC and MGAC beamformers, performance measures for our approach show improvement in directivity index (DI) and white noise gain (WNG) by nearly 19% and 15% respectively.Conclusion: Aliasing and, in consequence, unwanted side lobe formation is the main factor in spherical microphone arrays operational bandwidth determination. Most of the methods previously presented to reduce aliasing demanded physical changes in the array structure which comes at a cost. In this paper we propose a new method based on Alon and Rafaely’s approach via designing a constrained optimization problem using orthogonality property of spherical harmonics, to achieve better performance.
Microphone Array Processing
M. Kalantari
Abstract
Background and Objectives: One major problem in the minimum power distortionless response (MPDR) beamformer is the signal cancellation problem, i.e., the desired signal is canceled by the reflected signal, even though the distortionless response constraint is satisfied. Solving this problem is the objective ...
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Background and Objectives: One major problem in the minimum power distortionless response (MPDR) beamformer is the signal cancellation problem, i.e., the desired signal is canceled by the reflected signal, even though the distortionless response constraint is satisfied. Solving this problem is the objective of this paper. Methods: It is well known that the signal cancellation problem can be avoided by minimizing the cross-spectrum matrix of noise, i.e., using the minimum variance distortionless response (MVDR) beamformer. But, in the case of disturbance signals which have correlation with the desired signal, estimation of this matrix is a challenging problem. In this paper we propose an approach for estimating the cross-spectrum matrix of noise signal from which we can solve the signal cancellation problem. Results: Simulation examples show that using the proposed method we can bypass the signal cancellation problem completely. Conclusion: A common belief is that in the case of a disturbance that is a reflected version of the desired signal, due to cohesive appearance and disappearance of both the disturbance and the desired signal, the estimation of cross-spectrum matrix of noise signal is typically not possible in practice. So, based on this common belief, we can’t use the MVDR beamformer in this case. In this paper, we show that this common belief is a fault. We propose a general approach for estimating the cross-spectrum matrix of noise signal that is applicable even in the case of correlated disturbances.
