Introduction to Sparse Blind

What is/are Sparse Blind?

Sparse Blind - Multi-channel sparse blind deconvolution, or convolutional sparse coding, refers to the problem of learning an unknown filter by observing its circulant convolutions with multiple input signals that are sparse. ^[1] This letter introduces the concept of antisparse Blind Source Separation (BSS), proposing a suitable criterion based on the $\ell_\infty$ norm to explore the antisparsity feature. ^[2] Two approaches in particular—singular value decomposition (SVD) and sparse blind deconvolution (SBD)—have been shown to effectively denoise GPR images and resolve a reflectivity model, respectively. ^[3] We normalize the convolution kernel to have unit Frobenius norm and cast the sparse blind deconvolution problem as a nonconvex optimization problem over the sphere. ^[4] We therefore investigate a new joint deconvolution/sparse blind source separation method dedicated for data sampled on the sphere, coined SDecGMCA. ^[5] We further develop a smoothed Riemannian algorithm to solve the sparse blind demixing optimization problem. ^[6] In this paper, to support low-latency communication for massive devices with sporadic traffic, we present a sparse blind demixing to simultaneously detect the active devices and decode multiple source signals without a priori channel state information in multi- in-multi-out (MIMO) networks. ^[7] We study the multi-channel sparse blind deconvolution (MCS-BD) problem, whose task is to simultaneously recover a kernel a and multiple sparse inputs $\left\{ {{{\mathbf{x}}_i}} \right\}_{i = 1}^p$ from their circulant convolution yi = a ⊛ xi (i = 1,⋯, p). ^[8] The method applies a sparse blind deconvolution (SBD) technique to obtain the optimized source wavelet and a sparse representation of the subsurface reflectivity series. ^[9] We normalize the convolution kernel to have unit Frobenius norm and cast the sparse blind deconvolution problem as a nonconvex optimization problem over the sphere. ^[10] We propose an effective method for sparse blind deconvolution (SBD) of ground penetrating radar data. ^[11] In this article, we investigate how the prior knowledge based on examples of physical spectra can be exploited in sparse Blind Source Separation (sBSS), based on the projection onto the barycentric span of these examples. ^[12]

Channel Sparse Blind

Multi-channel sparse blind deconvolution, or convolutional sparse coding, refers to the problem of learning an unknown filter by observing its circulant convolutions with multiple input signals that are sparse. ^[1] We study the multi-channel sparse blind deconvolution (MCS-BD) problem, whose task is to simultaneously recover a kernel a and multiple sparse inputs $\left\{ {{{\mathbf{x}}_i}} \right\}_{i = 1}^p$ from their circulant convolution yi = a ⊛ xi (i = 1,⋯, p). ^[2]

sparse blind deconvolution

Multi-channel sparse blind deconvolution, or convolutional sparse coding, refers to the problem of learning an unknown filter by observing its circulant convolutions with multiple input signals that are sparse. ^[1] Two approaches in particular—singular value decomposition (SVD) and sparse blind deconvolution (SBD)—have been shown to effectively denoise GPR images and resolve a reflectivity model, respectively. ^[2] We normalize the convolution kernel to have unit Frobenius norm and cast the sparse blind deconvolution problem as a nonconvex optimization problem over the sphere. ^[3] We study the multi-channel sparse blind deconvolution (MCS-BD) problem, whose task is to simultaneously recover a kernel a and multiple sparse inputs $\left\{ {{{\mathbf{x}}_i}} \right\}_{i = 1}^p$ from their circulant convolution yi = a ⊛ xi (i = 1,⋯, p). ^[4] The method applies a sparse blind deconvolution (SBD) technique to obtain the optimized source wavelet and a sparse representation of the subsurface reflectivity series. ^[5] We normalize the convolution kernel to have unit Frobenius norm and cast the sparse blind deconvolution problem as a nonconvex optimization problem over the sphere. ^[6] We propose an effective method for sparse blind deconvolution (SBD) of ground penetrating radar data. ^[7]

sparse blind source

This letter introduces the concept of antisparse Blind Source Separation (BSS), proposing a suitable criterion based on the $\ell_\infty$ norm to explore the antisparsity feature. ^[1] We therefore investigate a new joint deconvolution/sparse blind source separation method dedicated for data sampled on the sphere, coined SDecGMCA. ^[2] In this article, we investigate how the prior knowledge based on examples of physical spectra can be exploited in sparse Blind Source Separation (sBSS), based on the projection onto the barycentric span of these examples. ^[3]

sparse blind demixing

We further develop a smoothed Riemannian algorithm to solve the sparse blind demixing optimization problem. ^[1] In this paper, to support low-latency communication for massive devices with sporadic traffic, we present a sparse blind demixing to simultaneously detect the active devices and decode multiple source signals without a priori channel state information in multi- in-multi-out (MIMO) networks. ^[2]