Dehui Yang

Super-Resolution of Complex Exponentials From Modulations With Unknown Waveforms

In this paper, we investigate parametric estimation of complex exponentials from modulations with known waveforms. This problem arises naturally in radar systems and wireless communications, especially in applications which suffer from multipath effects. Viewing the problem as a group sparse recovery, we recast it naturally into an atomic norm minimization, which has an equivalent semidefinite program (SDP) characterization and thus can be solved efficiently. We experimentally demonstrate the advantage of our approach when compared with a super-resolution method that does not consider multipath effects.

Atomic norm minimization for modal analysis

Maintaining safely operable structures such as buildings and bridges requires periodic assessment of the health of the structure. We study the problem of identifying the characteristic modes and frequencies of a structure from small amounts of vibrational data collected from wireless sensors deployed across the structure. Using the recent technique of atomic norm minimization, we show that under certain conditions exact recovery of the mode shapes and frequencies is possible, and we survey several possible randomized sampling and compression schemes for minimizing the amount of data that is collected and transmitted by the sensors.

Non-stationary blind super-resolution

In this paper, we propose a new framework for parameter estimation of complex exponentials from their modulations with unknown waveforms via convex programming. Our model generalizes the recently developed blind sparse spike deconvolution framework by Y. Chi [1] to the non-stationary scenario and encompasses a wide spectrum of applications. Under the assumption that the unknown waveforms live in a common random subspace, we recast the problem into an atomic norm minimization framework by a lifting trick, and this problem can be solved using computationally efficient semidefinite programming. We show that the number of measurements for exact recovery is proportional to the number of degrees of freedom in the problem, up to polylogarithmic factors. Numerical experiments support our theoretical findings.

Weighted Matrix Completion and Recovery With Prior Subspace Information

An incoherent low-rank matrix can be efficiently reconstructed after observing a few of its entries at random, and then, solving a convex program that minimizes the nuclear norm. In many applications, in addition to these entries, potentially valuable prior knowledge about the column and row spaces of the matrix is also available to the practitioner. In this paper, we incorporate this prior knowledge in matrix completion—by minimizing a weighted nuclear norm—and precisely quantify any improvements. In particular, we find in theory that reliable prior knowledge reduces the sample complexity of matrix completion by a logarithmic factor, and the observed improvement in numerical simulations is considerably more magnified. We also present similar results for the closely related problem of matrix recovery from generic linear measurements.

Atomic norm minimization for modal analysis with random spatial compression

Identifying characteristic vibrational modes and frequencies is of great importance for monitoring the health of structures such as buildings and bridges. In this work, we address the problem of estimating the modal parameters of a structure from small amounts of vibrational data collected from wireless sensors distributed on the structure. We consider a randomized spatial compression scheme for minimizing the amount of data that is collected and transmitted by the sensors. Using the recent technique of atomic norm minimization, we show that under certain conditions exact recovery of the mode shapes and frequencies is possible. In addition, in a simulation based on synthetic data, our method outperforms a singular value decomposition (SVD) based method for modal analysis that uses the uncompressed data set.

Jazz: A companion to music for frequency estimation with missing data

Frequency estimation is a classical problem in signal processing, with applications ranging from sensor array processing to wireless communications and structural health monitoring. Modern algorithms based on atomic norm minimization can cope with missing data but incur a high computational cost. To recover missing data from an ensemble of frequency-sparse signals, we propose a computationally efficient low-rank tensor completion algorithm that exploits the fact that each signal in the ensemble can be associated with a Toeplitz matrix. We name our algorithm JAZZ in the spirit of the classical MUSIC algorithm for frequency estimation and in tribute to the random, improvisational nature of jazz music.

Modeling and recovering non-transitive pairwise comparison matrices

Pairwise comparison matrices arise in numerous applications including collaborative filtering, elections, economic exchanges, etc. In this paper, we propose a new low-rank model for pairwise comparison matrices that accommodates non-transitive pairwise comparisons. Based on this model, we consider the regime where one has limited observations of a pairwise comparison matrix and wants to reconstruct the whole matrix from these observations using matrix completion. To do this, we adopt a recently developed alternating minimization algorithm to this particular matrix completion problem and derive a theoretical guarantee for its performance. Numerical simulations using synthetic data support our proposed approach.

Stable 2nd order adaptive IIR filter structure for blind deconvolution

In this paper, blind system deconvolution using infinite impulse response (IIR) adaptive filters is studied. A new structure of input-balanced realizations is derived for 2nd order filter. It is showed that the adaptive IIR filter realized with such a structure is bounded-input bounded-output (BIBO) stable and suits for blind equalization based on Bussgang Criterion. Computer simulations are given and discussed to support our theoretical results. A series of the results show that the obtained filter structure is highly recommended for blind deconvolution due to its nice convergence and stability properties during adaptation.