This paper is concerned with the inverse problem of recovering the unknown signal components, along with extraction of their instantaneous frequencies (IFs), governed by the adaptive harmonic model (AHM), from discrete (and possibly non-uniform) samples of the blind-source composite signal.
None of the existing decomposition methods and algorithms, including the most popular empirical mode decomposition (EMD) computational scheme and its current modifications, is capable of solving this inverse problem.
In order to meet the AHM formulation and to extract the IFs of the decomposed components, called intrinsic mode functions (IMFs), each IMF of EMD is extended to an analytic function in the upper half of the complex plane via the Hilbert transform, followed by taking the real part of the polar form of the analytic extension.
Unfortunately, this approach most often fails to resolve the inverse problem satisfactorily.
More recently, to resolve the inverse problem, the notion of synchrosqueezed wavelet transform (SST) was proposed by Daubechies and Maes, and further developed in many other papers, while a more direct method, called signal separation operation (SSO), was proposed and developed in our previous work published in the journal, Applied and Computational Harmonic Analysis, vol. 30(2):243-261, 2016.
In the present paper, we propose a synthesis of SSO using a deep neural network, based directly on a discrete sample set, that may be non-uniformly sampled, of the blind-source signal.
Our method is localized, as illustrated by a number of numerical examples, including components with different signal arrival and departure times.
It also yields short-term prediction of the signal components, along with their IFs.
Our neural networks are inspired by theory, designed so that they do not require any training in the traditional sense.
Technical University of Munich（慕尼黑工业大学）；Munich Center for Machine Learning（慕尼黑机器学习中心）；Munich Data Science Institute（慕尼黑数据科学研究所）；KU Eichstätt-Ingolstadt（艾希施泰特-英戈尔施塔特天主教大学）
In this paper, we study the problem of recovering two unknown signals from their convolution, which is commonly referred to as blind deconvolution. Reformulation of blind deconvolution as a low-rank recovery problem has led to multiple theoretical recovery guarantees in the past decade due to the success of the nuclear norm minimization heuristic. In particular, in the absence of noise, exact recovery has been established for sufficiently incoherent signals contained in lower-dimensional subspaces. However, if the convolution is corrupted by additive bounded noise, the stability of the recover…
Convolutive blind source separation (BSS) is intended to recover the unknown components from their convolutive mixtures. Contrary to the contrast functions used in instantaneous cases, the spatial-temporal prewhitening stage and the para-unitary filters constraint are difficult to implement in a convolutive context. In this paper, we propose several modifications of FastICA to alleviate these difficulties. Our method performs the simple prewhitening step on convolutive mixtures prior to the separation and optimizes the contrast function under the diagonalization constraint implemented by singl…
One-bit compressive sensing is concerned with the accurate recovery of an underlying sparse signal of interest from its one-bit noisy measurements. The conventional signal recovery approaches for this problem are mainly developed based on the assumption that an exact knowledge of the sensing matrix is available. In this work, however, we present a novel data-driven and model-based methodology that achieves blind recovery; i.e., signal recovery without requiring the knowledge of the sensing matrix. To this end, we make use of the deep unfolding technique and develop a model-driven deep neural a…
Harvard University（哈佛大学）；Weizmann Institute of Science（魏茨曼科学研究所）
We propose a learned-structured unfolding neural network for the problem of compressive sparse multichannel blind-deconvolution. In this problem, each channel's measurements are given as convolution of a common source signal and sparse filter. Unlike prior works where the compression is achieved either through random projections or by applying a fixed structured compression matrix, this paper proposes to learn the compression matrix from data. Given the full measurements, the proposed network is trained in an unsupervised fashion to learn the source and estimate sparse filters. Then, given the…
Tsinghua University（清华大学）；University of Notre Dame（圣母大学）
Temporal drift of sensory data is a severe problem impacting the data quality of wireless sensor networks (WSNs). With the proliferation of large-scale and long-term WSNs, it is becoming more important to calibrate sensors when the ground truth is unavailable. This problem is called "blind calibration". In this paper, we propose a novel deep learning method named projection-recovery network (PRNet) to blindly calibrate sensor measurements online. The PRNet first projects the drifted data to a feature space, and uses a powerful deep convolutional neural network to recover the estimated drift-fr…
Technische Universität München（慕尼黑工业大学）；University of Southern California（南加州大学）
Low-rank matrix recovery from structured measurements has been a topic of intense study in the last decade and many important problems like matrix completion and blind deconvolution have been formulated in this framework. An important benchmark method to solve these problems is to minimize the nuclear norm, a convex proxy for the rank. A common approach to establish recovery guarantees for this convex program relies on the construction of a so-called approximate dual certificate. However, this approach provides only limited insight in various respects. Most prominently, the noise bounds exhibi…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；Nvidia Inc.（英伟达公司）；Xilinx Inc.（赛灵思公司）
Blindly decoding a signal requires estimating its unknown transmit parameters, compensating for the wireless channel impairments, and identifying the modulation type. While deep learning can solve complex problems, digital signal processing (DSP) is interpretable and can be more computationally efficient. To combine both, we propose the dual path network (DPN). It consists of a signal path of DSP operations that recover the signal, and a feature path of neural networks that estimate the unknown transmit parameters. By interconnecting the paths over several recovery stages, later stages benefit…
In this paper, we consider the highly ill-posed problem of jointly recovering two real-valued signals from the phaseless measurements of their circular convolution. The problem arises in various imaging modalities such as Fourier ptychography, X-ray crystallography, and in visible light communication. We propose to solve this inverse problem using alternating gradient descent algorithm under two pretrained deep generative networks as priors; one is trained on sharp images and the other on blur kernels. The proposed recovery algorithm strives to find a sharp image and a blur kernel in the range…
Sharif University of Technology（谢里夫理工大学）；Qom University of Technology（库姆理工大学）；Instituto Superior Técnico（高等理工学院）
This paper investigates the problem of sparse signal recovery in the presence of additive impulsive noise. The heavytailed impulsive noise is well modelled with stable distributions. Since there is no explicit formulation for the probability density function of $SαS$ distribution, alternative approximations like Generalized Gaussian Distribution (GGD) are used which impose $\ell_p$-norm fidelity on the residual error. In this paper, we exploit a Continuous Mixed Norm (CMN) for robust sparse recovery instead of $\ell_p$-norm. We show that in blind conditions, i.e., in case where the parameters …
University of Michigan（密歇根大学）；University of Illinois, Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Compressed sensing is a powerful tool in applications such as magnetic resonance imaging (MRI). It enables accurate recovery of images from highly undersampled measurements by exploiting the sparsity of the images or image patches in a transform domain or dictionary. In this work, we focus on blind compressed sensing (BCS), where the underlying sparse signal model is a priori unknown, and propose a framework to simultaneously reconstruct the underlying image as well as the unknown model from highly undersampled measurements. Specifically, our model is that the patches of the underlying image(s…
Extraction of latent sources of complex stimuli is critical for making sense of the world. While the brain solves this blind source separation (BSS) problem continuously, its algorithms remain unknown. Previous work on biologically-plausible BSS algorithms assumed that observed signals are linear mixtures of statistically independent or uncorrelated sources, limiting the domain of applicability of these algorithms. To overcome this limitation, we propose novel biologically-plausible neural networks for the blind separation of potentially dependent/correlated sources. Differing from previous wo…
TransitNet: A Compact Attention-Augmented Deep Learning Framework for Low-SNR Transit Blind Searches
Shanghai Astronomical Observatory, Shanghai 200030, China（上海天文台，上海200030，中国）；University of Chinese Academy of Sciences, Yanqi Lake Campus, East Road 1, Huairou, Beijing 101408, China（中国科学院大学，燕琦湖校区，东路1号，北京101408，中国）；Science Talent Training Center, Gainesville, FL, 32606 USA（科学人才培训中心，佛罗里达州盖恩斯维尔，32606美国）
The lack of interpretability in current deep learning models causes serious concerns as they are extensively used for various life-critical applications. Hence, it is of paramount importance to develop interpretable deep learning models. In this paper, we consider the problem of blind deconvolution and propose a novel model-aware deep architecture that allows for the recovery of both the blur kernel and the sharp image from the blurred image. In particular, we propose the Deep Unfolded Richardson-Lucy (Deep-URL) framework -- an interpretable deep-learning architecture that can be seen as an am…
Massachusetts Institute of Technology（麻省理工学院）；University of Oxford（牛津大学）；Rice University（莱斯大学）
We consider a blind identification problem in which we aim to recover a statistical model of a network without knowledge of the network's edges, but based solely on nodal observations of a certain process. More concretely, we focus on observations that consist of single snapshots taken from multiple trajectories of a diffusive process that evolves over the unknown network. We model the network as generated from an independent draw from a latent stochastic block model (SBM), and our goal is to infer both the partition of the nodes into blocks, as well as the parameters of this SBM. We discuss s…
The task of recovering a low-rank matrix from its noisy linear measurements plays a central role in computational science. Smooth formulations of the problem often exhibit an undesirable phenomenon: the condition number, classically defined, scales poorly with the dimension of the ambient space. In contrast, we here show that in a variety of concrete circumstances, nonsmooth penalty formulations do not suffer from the same type of ill-conditioning. Consequently, standard algorithms for nonsmooth optimization, such as subgradient and prox-linear methods, converge at a rapid dimension-independen…
