A Fast Approach for Overcomplete Sparse Decomposition Based on Smoothed $\ell ^{0}$ Norm

Mohimani, Hosein; Babaie‐Zadeh, Massoud; Jutten, Christian

doi:10.1109/tsp.2008.2007606

Cited by 1,000 publications

(873 citation statements)

References 30 publications

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“…Simulations in [9] demonstrate the smoothed 0 norm algorithm converges fast. In [8] [4], the authors proposed to solve the Lagrange form of (1).…”

Section: Implementation Of the Combined Approachmentioning

confidence: 91%

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Compressed sensing MRI with combined sparsifying transforms and smoothed l<inf>0</inf> norm minimization

Cao

Guo

et al. 2010

2010 IEEE International Conference on Acoustics, Speech and Signal Processing

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Undersampling the k-space is an efficient way to speed up the magnetic resonance imaging (MRI). Recently emerged compressed sensing MRI shows promising results. However, most of them only enforce the sparsity of images in single transform, e.g. total variation, wavelet, etc. In this paper, based on the principle of basis pursuit, we propose a new framework to combine sparsifying transforms in compressed sensing MRI. Each transform can efficiently represent specific feature that the other can not. This framework is implemented via the state-of-art smoothed 0 norm in overcomplete sparse decomposition. Simulation results demonstrate that the proposed method can improve image quality when comparing to single sparsifying transform.

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“…Simulations in [9] demonstrate the smoothed 0 norm algorithm converges fast. In [8] [4], the authors proposed to solve the Lagrange form of (1).…”

Section: Implementation Of the Combined Approachmentioning

confidence: 91%

“…In order to solve equation (4), we extend sigma annealing method proposed in [9] to compressed sensing MRI with combined sparsifying transforms.…”

Section: Implementation Of the Combined Approachmentioning

confidence: 99%

Compressed sensing MRI with combined sparsifying transforms and smoothed l<inf>0</inf> norm minimization

Cao

Guo

et al. 2010

2010 IEEE International Conference on Acoustics, Speech and Signal Processing

View full text Add to dashboard Cite

show abstract

“…The strips are centred at (−10, 8, 5, 4, 3, 0, 3, 5, 7, 9) × λ/10 along the x-direction, respectively. [36]. The least square method is a widely used approach for solving inverse problems.…”

Section: Sparse Reconstruction Methodsmentioning

confidence: 99%

Performance Enhancement of Microwave Sub-Wavelength Imaging and Lens-Type Doa Estimation Systems by Using Signal Processing Techniques (Invited Paper)

Gu¹,

Mittra²,

Pelletti³

et al. 2014

PIER

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Abstract-In this work, we show how we can improve the image resolution capabilities of a Phase Conjugating (PC) lens as well as the angular resolution of Luneburg lens antennas by employing signal processing techniques such as the Correlation Method (CM), the Minimum Residual Power Search Method (MRPSM), the sparse reconstruction method, and the Singular-Value-Decomposition (SVD)-based basis matrix method. In the first part, we apply these techniques for sub-wavelength imaging in the microwave regime by combining them with the well-known phase conjugation principle. We begin by considering a one-dimensional microwave sub-wavelength imaging problem handled by using three signal processing methods, and then we move on to two-or three-dimensional problems by using the SVD-based basis matrix method. Numerical simulation results show that we can enhance the resolution significantly by using these methods, even if the measurement plane is not located in the very nearfield region of the source. We describe these proposed algorithms in detail and study their abilities to resolve at the sub-wavelength level. Next, we investigate the sparse reconstruction method for a normal Luneburg lens antenna and the Correlation Method and the SVD-based basis matrix method for a flat-base Luneburg lens antenna to estimate the Direction-of-Arrival (DOA). Numerical simulation results show that the signal processing techniques are capable of enhancing the angular resolution of the Luneburg lens antenna enabling the lens to locate multiple targets with different scattering cross-sections and achieving higher angular resolution.

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“…A variety of popular optimization algorithms have been developed to solve Eq. (6), such as smoothed l 0 norm (SL0) algorithm [16] and sparse Bayesian algorithm [17]. In practice, better recovery performance can be obtained if the structure of the sparse signal is exploited.…”

Section: Isar Imaging Modelmentioning

confidence: 99%

“…The parameters of the radar data are listed as follows: the carrier frequency is 10 GHz with signal bandwidth of 400 MHz, and a range resolution is 0.375 m. The pulse repetition frequency is 100 Hz, i.e., 256 pulses are used in this experiment. In order to investigate the role of the pulse number, three different amounts of pulses (16,32, and 64 pulses) are implemented. The experimental results are compared to those images obtained by some sparse signal recovery methods including BP method [20], SBL method [18], L 1 L 0 method [12] and S-method [21].…”

Section: A Isar Imaging Performance Versus Pulse Numbersmentioning

confidence: 99%

Isar Imaging Based on Iterative Reweighted Lp Block Sparse Reconstruction Algorithm

Feng¹,

Zhang²

2016

PIER M

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Abstract-Sparse signal recovery algorithms can be used to improve radar imaging quality by using the sparse property of strong scatterers. Traditional sparse inverse synthetic aperture radar (ISAR) imaging algorithms mainly consider the recovery of sparse scatterers. However, the scatterers of an ISAR target usually exhibit block or group sparse structure. By utilizing the inherent block sparse structure of ISAR target images, an iterative reweighted l p (0 < p ≤ 1) block sparse signal recovery algorithm is proposed to enhance imaging quality in this paper. Firstly, an ISAR imaging signal model is established with the aid of sparse basis, and the imaging is mathematically converted into block reweighted cost function optimization problem. Then, an iterative algorithm is used to solve the reweighted function minimization problem. In each iteration, the weights are updated based on the closed form solution of the previous iteration. The proposed method is effective to exploit the underlying block sparse structures which does not need the prior knowledge of the number of the blocks. Real data ISAR imaging results are provided to verify that the proposed algorithm in this paper can achieve better images than the images obtained by several popular sparse signal recovery algorithms.

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A Fast Approach for Overcomplete Sparse Decomposition Based on Smoothed $\ell ^{0}$ Norm

Cited by 1,000 publications

References 30 publications

Compressed sensing MRI with combined sparsifying transforms and smoothed l<inf>0</inf> norm minimization

Compressed sensing MRI with combined sparsifying transforms and smoothed l<inf>0</inf> norm minimization

Performance Enhancement of Microwave Sub-Wavelength Imaging and Lens-Type Doa Estimation Systems by Using Signal Processing Techniques (Invited Paper)

Isar Imaging Based on Iterative Reweighted Lp Block Sparse Reconstruction Algorithm

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