Efficient Multidimensional Diracs Estimation With Linear Sample Complexity

Pan, Haihua; Blu, Thierry; Vetterli, Martin

doi:10.1109/tsp.2018.2858213

Cited by 5 publications

(4 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The simulation results show that the proposed 2D-SGFRI algorithm has the best estimation performance under the same conditions. It is worth mentioning that the traditional DOA estimation algorithm based on the generalized FRI signal reconstruction model [22][23][24][25] can not be directly applied to the plane array DOA estimation problem. Therefore, in the simulation experiment of this paper, there is no comparison with this kind of algorithm.…”

Section: B Estimation Accuracymentioning

confidence: 99%

“…The FRIDA-V algorithm proposed in [24] directly processes the multi snapshots data received by the planar array, and no longer depends on the covariance data after vectorization, making the algorithm suitable for coherent signals. In [25], the generalized FRI signal reconstruction model is extended to two-dimensional and even higher dimensional cases, but it is not specifically applied to the problem of two-dimensional DOA estimation.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Two-Dimensional Separable Gridless Direction-of-Arrival Estimation Based on Finite Rate of Innovation

Wang¹,

Shi

Chen

2021

IEEE Access

View full text Add to dashboard Cite

In order to solve the problem that the gridless DOA estimation algorithms based on generalized finite rate of innovation (FRI) signal reconstruction model are not suitable for two-dimensional DOA estimation using planar array, a separable gridless DOA estimation algorithm exploiting bi-orthogonal sparse linear array (BSLA) structure is proposed in this paper, which is called 2D-SGFRI. The 2D-SGFRI algorithm firstly recovers the covariance data of the virtual array formed by BSLA through the matrix completion method, so as to obtain the complete covariance data vectors about two independent parameters respectively. Next, since the covariance data vector satisfies the constraints of annihilation filter equations, the generalized FRI signal reconstruction model can be utilized to retrieve DOA from the covariance data vector. Compared with the existing DOA estimation algorithms based on generalized FRI signal reconstruction model, the 2D-SGFRI algorithm can be can be effectively applied to twodimensional DOA estimation, and can obtain stable estimation results. At the same time, due to the reduction of the dimension of positive semidefinite matrix, the 2D-SGFRI algorithm can significantly reduce the computational complexity compared with the two-dimensional DOA estimation algorithms based on atomic norm minimization (ANM). A series of simulation experiments are shown to verify the effectiveness and superiority of 2D-SGFRI algorithm. INDEX TERMS Two-dimensional DOA estimation, bi-orthogonal sparse linear array (BSLA), finite rate of innovation (FRI), matrix completion, annihilation filter

show abstract

Section: B Estimation Accuracymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two-Dimensional Separable Gridless Direction-of-Arrival Estimation Based on Finite Rate of Innovation

Wang¹,

Shi

Chen

2021

IEEE Access

View full text Add to dashboard Cite

show abstract

“…The higher dimensional case was first discussed by Maravic [23], who proposed a first algorithm requiring O(N D ) samples, where D is the number of dimensions. More recently, Pan et al [32] came up with a multidimensional reconstruction algorithm using only O(N ) samples.…”

Section: A Acf Super Resolutionmentioning

confidence: 99%

Super Resolution Phase Retrieval for Sparse Signals

Baechler

Kreković

Ranieri

et al. 2019

IEEE Trans. Signal Process.

Self Cite

View full text Add to dashboard Cite

In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts to recover the phase information of a signal from the magnitude of its Fourier transform to enable the reconstruction of the original signal. Solving the phase retrieval problem is equivalent to recovering a signal from its auto-correlation function. In this paper, we assume the original signal to be sparse; this is a natural assumption in many applications, such as X-ray crystallography, speckle imaging and blind channel estimation. We propose an algorithm that resolves the phase retrieval problem in three stages, first, we leverage the finite rate of innovation sampling theory to super-resolve the autocorrelation function from a limited number of samples, second, we design a greedy algorithm that identifies the locations of a sparse solution given the super-resolved auto-correlation function, finally, we recover the amplitudes of the atoms given their locations and the measured auto-correlation function. Unlike traditional approaches that recover a discrete approximation of the underlying signal, our algorithm estimates the signal on a continuous domain, which makes it the first of its kind. Along with the algorithm, we derive its performance bound with a theoretical analysis and propose a set of enhancements to improve its computational complexity and noise resilience. Finally, we demonstrate the benefits of the proposed method via a comparison against Charge Flipping, a notable algorithm in crystallography.

show abstract

“…The Fourier transform, over-zero detection, and other conventional methods have the problem of low estimation accuracy [3]. The FRI algorithm [4][5][6][7][8] achieves the estimation of multiple signals based on the finite rate of innovation model through the zeroed filter with the polynomial ratio method, which has gained applications in DOA and frequency estimation.…”

Section: Introductionmentioning

confidence: 99%

Frequency estimation of underwater acoustic targets based on improved FRI method

Wang,

Guo,

Sun

2024

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

The line spectrum information of a ship’s radiated noise signal is often regarded as an important feature used to distinguish between targets. In this paper, an improved FRI (finite rate of innovation) method is proposed to estimate the low-frequency line spectra of the radiated noise from underwater acoustic passive targets under the condition of finite sampling points. First, a preliminary rough estimation of the frequency is performed using the Fourier transform. Then, the multichannel signal data are iteratively fitted based on the polynomial-ratio form model. The optimal estimation results are finally determined based on the residuals between the data and the model in the fitting process. Simulation experiments prove that compared with the original FRI algorithm, the method proposed in this paper can estimate line spectral frequency more efficiently under the condition of low signal-to-noise ratio (SNR), and can achieve fast convergence with shorter operation time. The experimental data processing results prove that the method can realize high-precision extraction of line spectrum information of ship noise.

show abstract

Efficient Multidimensional Diracs Estimation With Linear Sample Complexity

Cited by 5 publications

References 36 publications

Two-Dimensional Separable Gridless Direction-of-Arrival Estimation Based on Finite Rate of Innovation

Two-Dimensional Separable Gridless Direction-of-Arrival Estimation Based on Finite Rate of Innovation

Super Resolution Phase Retrieval for Sparse Signals

Frequency estimation of underwater acoustic targets based on improved FRI method

Contact Info

Product

Resources

About