37 research outputs found
Efficient High-Dimensional Inference in the Multiple Measurement Vector Problem
In this work, a Bayesian approximate message passing algorithm is proposed
for solving the multiple measurement vector (MMV) problem in compressive
sensing, in which a collection of sparse signal vectors that share a common
support are recovered from undersampled noisy measurements. The algorithm,
AMP-MMV, is capable of exploiting temporal correlations in the amplitudes of
non-zero coefficients, and provides soft estimates of the signal vectors as
well as the underlying support. Central to the proposed approach is an
extension of recently developed approximate message passing techniques to the
amplitude-correlated MMV setting. Aided by these techniques, AMP-MMV offers a
computational complexity that is linear in all problem dimensions. In order to
allow for automatic parameter tuning, an expectation-maximization algorithm
that complements AMP-MMV is described. Finally, a detailed numerical study
demonstrates the power of the proposed approach and its particular suitability
for application to high-dimensional problems.Comment: 28 pages, 9 figure
Model Selection for Nonnegative Matrix Factorization by Support Union Recovery
Nonnegative matrix factorization (NMF) has been widely used in machine
learning and signal processing because of its non-subtractive, part-based
property which enhances interpretability. It is often assumed that the latent
dimensionality (or the number of components) is given. Despite the large amount
of algorithms designed for NMF, there is little literature about automatic
model selection for NMF with theoretical guarantees. In this paper, we propose
an algorithm that first calculates an empirical second-order moment from the
empirical fourth-order cumulant tensor, and then estimates the latent
dimensionality by recovering the support union (the index set of non-zero rows)
of a matrix related to the empirical second-order moment. By assuming a
generative model of the data with additional mild conditions, our algorithm
provably detects the true latent dimensionality. We show on synthetic examples
that our proposed algorithm is able to find an approximately correct number of
components
Grant-Free Massive MTC-Enabled Massive MIMO: A Compressive Sensing Approach
A key challenge of massive MTC (mMTC), is the joint detection of device
activity and decoding of data. The sparse characteristics of mMTC makes
compressed sensing (CS) approaches a promising solution to the device detection
problem. However, utilizing CS-based approaches for device detection along with
channel estimation, and using the acquired estimates for coherent data
transmission is suboptimal, especially when the goal is to convey only a few
bits of data.
First, we focus on the coherent transmission and demonstrate that it is
possible to obtain more accurate channel state information by combining
conventional estimators with CS-based techniques. Moreover, we illustrate that
even simple power control techniques can enhance the device detection
performance in mMTC setups.
Second, we devise a new non-coherent transmission scheme for mMTC and
specifically for grant-free random access. We design an algorithm that jointly
detects device activity along with embedded information bits. The approach
leverages elements from the approximate message passing (AMP) algorithm, and
exploits the structured sparsity introduced by the non-coherent transmission
scheme. Our analysis reveals that the proposed approach has superior
performance compared to application of the original AMP approach.Comment: Submitted to IEEE Transactions on Communication
A Generalized Framework for Learning and Recovery of Structured Sparse Signals
Engineering: 1st Place (The Ohio State University Edward F. Hayes Graduate Research Forum)We report on a framework for recovering single- or multi-timestep sparse signals that can learn and exploit a variety of probabilistic forms of structure. Message passing-based inference and empirical Bayesian parameter learning form the backbone of the recovery procedure. We further describe an object-oriented software paradigm for implementing our framework, which consists of assembling modular software components that collectively define a desired statistical signal model. Lastly, numerical results for an example structured sparse signal model are provided.A one-year embargo was granted for this item
Image Reconstruction for Multi-frequency Electromagnetic Tomography based on Multiple Measurement Vector Model
Imaging the bio-impedance distribution of a biological sample can provide
understandings about the sample's electrical properties which is an important
indicator of physiological status. This paper presents a multi-frequency
electromagnetic tomography (mfEMT) technique for biomedical imaging. The system
consists of 8 channels of gradiometer coils with adjustable sensitivity and
excitation frequency. To exploit the frequency correlation among each
measurement, we reconstruct multiple frequency data simultaneously based on the
Multiple Measurement Vector (MMV) model. The MMV problem is solved by using a
sparse Bayesian learning method that is especially effective for sparse
distribution. Both simulations and experiments have been conducted to verify
the performance of the method. Results show that by taking advantage of
multiple measurements, the proposed method is more robust to noisy data for
ill-posed problems compared to the commonly used single measurement vector
model.Comment: This is an accepted paper which has been submitted to I2MTC 2020 on
Nov. 201