Shuffled Multi-Channel Sparse Signal Recovery

• URL: http://arxiv.org/abs/2212.07368v3
• Date: Mon, 24 Jul 2023 12:53:23 GMT
• Title: Shuffled Multi-Channel Sparse Signal Recovery
• Authors: Taulant Koka, Manolis C. Tsakiris, Michael Muma and Benjam\'in B\'ejar Haro
• Abstract summary: We pose it as a signal reconstruction problem where we have lost correspondences between the samples and their respective channels. We show that the problem is equivalent to a structured unlabeled sensing problem, and establish sufficient conditions for unique recovery. We propose a robust reconstruction method that combines sparse signal recovery with robust linear regression for the two-channel case.
• Score: 16.333381000882486
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Mismatches between samples and their respective channel or target commonly arise in several real-world applications. For instance, whole-brain calcium imaging of freely moving organisms, multiple-target tracking or multi-person contactless vital sign monitoring may be severely affected by mismatched sample-channel assignments. To systematically address this fundamental problem, we pose it as a signal reconstruction problem where we have lost correspondences between the samples and their respective channels. Assuming that we have a sensing matrix for the underlying signals, we show that the problem is equivalent to a structured unlabeled sensing problem, and establish sufficient conditions for unique recovery. To the best of our knowledge, a sampling result for the reconstruction of shuffled multi-channel signals has not been considered in the literature and existing methods for unlabeled sensing cannot be directly applied. We extend our results to the case where the signals admit a sparse representation in an overcomplete dictionary (i.e., the sensing matrix is not precisely known), and derive sufficient conditions for the reconstruction of shuffled sparse signals. We propose a robust reconstruction method that combines sparse signal recovery with robust linear regression for the two-channel case. The performance and robustness of the proposed approach is illustrated in an application related to whole-brain calcium imaging. The proposed methodology can be generalized to sparse signal representations other than the ones considered in this work to be applied in a variety of real-world problems with imprecise measurement or channel assignment.

Related papers

• Lazy Layers to Make Fine-Tuned Diffusion Models More Traceable [70.77600345240867]
  A novel arbitrary-in-arbitrary-out (AIAO) strategy makes watermarks resilient to fine-tuning-based removal. Unlike the existing methods of designing a backdoor for the input/output space of diffusion models, in our method, we propose to embed the backdoor into the feature space of sampled subpaths. Our empirical studies on the MS-COCO, AFHQ, LSUN, CUB-200, and DreamBooth datasets confirm the robustness of AIAO.
  arXiv  Detail & Related papers  (2024-05-01T12:03:39Z)
• Unsupervised Denoising for Signal-Dependent and Row-Correlated Imaging Noise [54.0185721303932]
  We present the first fully unsupervised deep learning-based denoiser capable of handling imaging noise that is row-correlated. Our approach uses a Variational Autoencoder with a specially designed autoregressive decoder. Our method does not require a pre-trained noise model and can be trained from scratch using unpaired noisy data.
  arXiv  Detail & Related papers  (2023-10-11T20:48:20Z)
• Consistent Signal Reconstruction from Streaming Multivariate Time Series [5.448070998907116]
  We formalize for the first time the concept of consistent signal reconstruction from streaming time-series data. Our method achieves a favorable error-rate decay with the sampling rate compared to a similar but non-consistent reconstruction.
  arXiv  Detail & Related papers  (2023-08-23T22:50:52Z)
• Simultaneous source separation of unknown numbers of single-channel underwater acoustic signals based on deep neural networks with separator-decoder structure [0.0]
  We propose a deep learning-based simultaneous separating solution with a fixed number of output channels equal to the maximum number of possible targets. This solution avoids the dimensional disaster caused by the permutation problem induced by the alignment of outputs to targets. Experiments conducted on simulated mixtures of radiated ship noise show that the proposed solution can achieve similar separation performance to that attained with a known number of signals.
  arXiv  Detail & Related papers  (2022-07-24T14:04:34Z)
• Self-Supervised Training with Autoencoders for Visual Anomaly Detection [61.62861063776813]
  We focus on a specific use case in anomaly detection where the distribution of normal samples is supported by a lower-dimensional manifold. We adapt a self-supervised learning regime that exploits discriminative information during training but focuses on the submanifold of normal examples. We achieve a new state-of-the-art result on the MVTec AD dataset -- a challenging benchmark for visual anomaly detection in the manufacturing domain.
  arXiv  Detail & Related papers  (2022-06-23T14:16:30Z)
• Deblurring via Stochastic Refinement [85.42730934561101]
  We present an alternative framework for blind deblurring based on conditional diffusion models. Our method is competitive in terms of distortion metrics such as PSNR.
  arXiv  Detail & Related papers  (2021-12-05T04:36:09Z)
• Meta-Learning Sparse Implicit Neural Representations [69.15490627853629]
  Implicit neural representations are a promising new avenue of representing general signals. Current approach is difficult to scale for a large number of signals or a data set. We show that meta-learned sparse neural representations achieve a much smaller loss than dense meta-learned models.
  arXiv  Detail & Related papers  (2021-10-27T18:02:53Z)
• Hierarchical compressed sensing [5.39680014668952]
  Compressed sensing is a paradigm within signal processing that provides the means for recovering structured signals from linear measurements. We present recovery algorithms based on efficient hierarchical hard-thresholding. Building upon this machinery, we sketch practical applications of this framework in machine-type communications and quantum tomography.
  arXiv  Detail & Related papers  (2021-04-06T18:00:01Z)
• Fast signal recovery from quadratic measurements [0.0]
  We present a novel approach for recovering a sparse signal from cross-correlated data. The main idea of our proposed approach is to reduce the dimensionality of the problem by recovering only the diagonal of the unknown matrix. Our theory shows that the proposed approach provides exact support recovery when the data is not too noisy, and that there are no false positives for any level of noise.
  arXiv  Detail & Related papers  (2020-10-11T23:36:51Z)
• Iterative Correction of Sensor Degradation and a Bayesian Multi-Sensor Data Fusion Method [0.0]
  We present a novel method for inferring ground-truth signal from degraded signals. The algorithm learns a multiplicative degradation effect by performing iterative corrections of two signals. We include theoretical analysis and prove convergence to the ground-truth signal for the noiseless measurement model.
  arXiv  Detail & Related papers  (2020-09-07T13:24:47Z)
• Analytic Signal Phase in $N-D$ by Linear Symmetry Tensor--fingerprint modeling [69.35569554213679]
  We show that the Analytic Signal phase, and its gradient have a hitherto unstudied discontinuity in $2-D $ and higher dimensions. This shortcoming can result in severe artifacts whereas the problem does not exist in $1-D $ signals. We suggest the use of Linear Symmetry phase, relying on more than one set of Gabor filters, but with a negligible computational add-on.
  arXiv  Detail & Related papers  (2020-05-16T21:17:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.