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Study On Finite Rate Of Innovation Sparse Recovery And Underwater Acoustic Applications

Posted on:2023-12-08Degree:DoctorType:Dissertation
Country:ChinaCandidate:Y F LiFull Text:PDF
GTID:1520306809996269Subject:Information and Communication Engineering
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Sparse reconstruction has always been the heart of signal processing,and it plays an important role in biology,medicine,image,speech,radar,underwater acoustics,etc.Classical sparse reconstruction algorithms usually retrieve sparse signals on the discrete grids,which leads to a simpler optimization problem.However,it is not realistic,because the parameters of sparse signals do not always locate at grid points,leading to grid mismatch,spectral leakage,and inaccurate recovery.Moreover,the resolution of the algorithm is limited by the artificially imposed grid step-size,which is insufficient in many high-resolution underwater applications.And the computing resources are occupied by a large number of redundant grids,which also limits its real-time applications.In practical underwater signal processing issues,the noise is usually colored and correlated.However,many methods make unrealistic assumptions,e.g.,additive white Gaussian noise or known noise model,which leads to an inaccurate and unrobust recovery.Therefore,it is necessary to develop a fast and gridless sparse reconstruction algorithm.In recent years,with the development of sparse reconstruction methods,finite rate of innovation(FRI)methods have shown this potential.By establishing a sparse parameter model,FRI method successfully transforms the sparse reconstruction problem into a parameter estimation problem and achieves an accurate reconstruction in a continuous parameter domain.However,most existing FRI sparse algorithms can only deal with one-dimensional single-channel(or singlesensor)uniform samples,which cannot meet many application scenarios of underwater acoustic signal processing.Motivated by practical underwater applications,such as frequency estimation,interferogram reconstruction,direction of arrival(DOA)estimation for one-dimensional and twodimensional arrays,damped sinusoid reconstruction(e.g.,reconstruction of underwater acoustic field),coupled modes separation,etc,this paper abstracts the actual problem into different sparse reconstruction problems(e.g.,the joint sparse reconstruction of multi-channel/sensor data,sparse reconstruction of non-uniform samples,and sparse reconstruction of multi-dimensional signals),expands the FRI theory,and develops a fast,robust,gridless,and high-resolution algorithm to handle complex noise based on practical requirements.Both simulation and real data verify the effectiveness and robustness of the FRI sparse reconstruction algorithm.The main work of this paper is summarized as follows:The key idea of this paper is that the discrete Fourier transform(DFT)of FRI signal(a finite sum of sinusoids)can be represented as a ratio of two polynomials or a finite sum of Dirichlet sinc kernels.Therefore,the sparse reconstruction problem can essentially be transformed into a model-fitting problem or polynomial coefficients estimation.For the multi-sensor/channel data fusion in practical underwater applications(e.g.,joint frequency estimation for multi-sensor/channel data,wavenumber estimation,reconstruction of acoustic field,multi-snapshot DOA estimation,internal wave tracking,etc),this paper proposes a joint sparse model—vector FRI.By fitting the data with the parametric model,the vector FRI algorithm achieves an accurate sparse recovery even at a low signal-to-noise ratio(SNR).For the sparse reconstruction of multi-dimensional signals in practical underwater applications(e.g.,DOA estimation for two-dimensional arrays,interferogram reconstruction,etc),this paper proposes a sparse reconstruction algorithm of multi-dimensional signals.By decomposing a multidimensional FRI signal into multiple vector FRI signals along different dimensions,the vector FRI algorithm can also be directly generalized to the sparse reconstruction of multi-dimensional FRI signals,enjoying efficient implementation,strong robustness,and high accuracy.For the sparse reconstruction of non-uniform samples in practical underwater applications,such as frequency estimation with missing time series,direction of arrival(DOA)estimation of a sparse array,etc.,this paper also proposes a more generalized sparse framework,i.e.,sub-sampled FRI(ss-FRI).By reconstructing the mapping matrix between non-uniform samples and uniform samples,applying an alternate iteration strategy,the ss-FRI algorithm achieves an accurate sparse reconstruction for non-uniform samples.Unlike most sparse reconstruction algorithms whose computational complexity increases quickly with the number of samples and channels,the computational complexity of the FRI sparse reconstruction algorithm proposed in this paper changes very slowly with the number of samples and channels,which is mainly related to the sparseness of the signal.It is very suitable for sparse reconstruction of large-scale,multi-channel data,and is of great significance in many real-time applications.
Keywords/Search Tags:Sparse reconstruction, Finite rate of innovation(FRI), Multi-channel data fusion, Nonuniform samples, Mean square error(MSE) criterion, Direction of arrival(DOA), Signal processing in underwater, Coupled modes separation
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