Sparse decomposition of two dimensional signals

Ghaffari, Aboozar; Babaie‐Zadeh, Massoud; Jutten, Christian

doi:10.1109/icassp.2009.4960294

Cited by 116 publications

(85 citation statements)

References 7 publications

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“…Recently, a new signal model with two-dimensional (2D) sparse parameters, called 2D sparse signal model, has been introduced [17,18], and some algorithms for 2D sparse reconstruction have been proposed [19][20][21][22][23][24]. Specifically, in [19], the 2D version of IAA is derived in which its computational cost is drastically reduced in comparison with the one-dimensional (1D) IAA.…”

Section: Introductionmentioning

confidence: 99%

Efficient two-dimensional compressive sensing in MIMO radar

Shahbazi

Abbasfar

Jabbarian-Jahromi

2017

EURASIP J. Adv. Signal Process.

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Compressive sensing (CS) has been a way to lower sampling rate leading to data reduction for processing in multiple-input multiple-output (MIMO) radar systems. In this paper, we further reduce the computational complexity of a pulse-Doppler collocated MIMO radar by introducing a two-dimensional (2D) compressive sensing. To do so, we first introduce a new 2D formulation for the compressed received signals and then we propose a new measurement matrix design for our 2D compressive sensing model that is based on minimizing the coherence of sensing matrix using gradient descent algorithm. The simulation results show that our proposed 2D measurement matrix design using gradient decent algorithm (2D-MMDGD) has much lower computational complexity compared to one-dimensional (1D) methods while having better performance in comparison with conventional methods such as Gaussian random measurement matrix.

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Section: Introductionmentioning

confidence: 99%

Efficient two-dimensional compressive sensing in MIMO radar

Shahbazi

Abbasfar

Jabbarian-Jahromi

2017

EURASIP J. Adv. Signal Process.

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“…To address these drawbacks, some 2D reconstruction algorithms that directly leverage the matrix structure of 2D sparse signals have been proposed recently [16][17][18][19][20][21], and some have been used in radar imaging systems. For example, a fast reconstruction algorithm, called two-dimensional smoothed L0 norm (2D-SL0) algorithm, has been proposed to reduce computational complexity and economize on the memory required by directly utilizes the matrix structure to recover the 2D sparse signals and is designed [20], but the reconstruction quality of the natural image is poor.…”

Section: Introductionmentioning

confidence: 99%

“…For example, a fast reconstruction algorithm, called two-dimensional smoothed L0 norm (2D-SL0) algorithm, has been proposed to reduce computational complexity and economize on the memory required by directly utilizes the matrix structure to recover the 2D sparse signals and is designed [20], but the reconstruction quality of the natural image is poor. Another novel algorithm called the 2D orthogonal matching pursuit (2D-OMP) algorithm, which was extended from 1D-OMP, has been developed to reconstruct 2D sparse signals [17].…”

Section: Introductionmentioning

confidence: 99%

2D Normalized Iterative Hard Thresholding Algorithm for Fast Compressive Radar Imaging

Yang

Wang

et al. 2017

Remote Sensing

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Abstract:Compressive radar imaging has attracted considerable attention because it substantially reduces imaging time through directly compressive sampling. However, a problem that must be addressed for compressive radar imaging systems is the high computational complexity of reconstruction of sparse signals. In this paper, a novel algorithm, called two-dimensional (2D) normalized iterative hard thresholding (NIHT) or 2D-NIHT algorithm, is proposed to directly reconstruct radar images in the matrix domain. The reconstruction performance of 2D-NIHT algorithm was validated by an experiment on recovering a synthetic 2D sparse signal, and the superiority of the 2D-NIHT algorithm to the NIHT algorithm was demonstrated by a comprehensive comparison of its reconstruction performance. Moreover, to be used in compressive radar imaging systems, a 2D sampling model was also proposed to compress the range and azimuth data simultaneously. The practical application of the 2D-NIHT algorithm in radar systems was validated by recovering two radar scenes with noise at different signal-to-noise ratios, and the results showed that the 2D-NIHT algorithm could reconstruct radar scenes with a high probability of exact recovery in the matrix domain. In addition, the reconstruction performance of the 2D-NIHT algorithm was compared with four existing efficient reconstruction algorithms using the two radar scenes, and the results illustrated that, compared to the other algorithms, the 2D-NIHT algorithm could dramatically reduce the computational complexity in signal reconstruction and successfully reconstruct 2D sparse images with a high probability of exact recovery.

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“…The concept of two-dimensional random projection is proposed in [15], and the idea of using 2D-SL0 to reconstruct the random projection is analyzed. Literature [16,17,18] proposed 2D iterative adaptive method for 2D signal reconstruction, and obtain a better reconstruction effect, but the method has higher computational complexity too.…”

Section: Introductionmentioning

confidence: 99%

Sparse Chirp Stepped-frequency ISAR Super-resolution Imaging Method Based on 2D-FISTA Algorithm

Zhou¹,

Xu²,

He³

et al. 2017

Proceedings of the 3rd International Conference on Wireless Communication and Sensor Networks (WCSN 2016)

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Abstract-The traditional Sparse Chirp Stepped-frequency ISAR imaging method has the problem of low imaging quality and large computational complexity. In view of the above problems, this paper studies a sparse Chirp Stepped-frequency ISAR imaging method based on two-dimensional fast iterative shrinkage threshold algorithm (2D-FISTA). Firstly, the two-dimensional echo model of Sparse Chirp Stepped-frequency signal is constructed. Based on this model, two-dimensional fast iterative shrinkage threshold algorithm is used to reconstruct the imaging result. This method can be reconstructed in the matrix domain directly, which avoids the computation of the vector processing method, and avoids the problem of the image quality loss of the decoupling method. The simulation results show that the proposed method is effective and has better imaging performance.

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Sparse decomposition of two dimensional signals

Cited by 116 publications

References 7 publications

Efficient two-dimensional compressive sensing in MIMO radar

Efficient two-dimensional compressive sensing in MIMO radar

2D Normalized Iterative Hard Thresholding Algorithm for Fast Compressive Radar Imaging

Sparse Chirp Stepped-frequency ISAR Super-resolution Imaging Method Based on 2D-FISTA Algorithm

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