Swayambhoo Jain

Backhaul-constrained multi-cell cooperation using compressive sensing and spectral clustering

Multi-cell cooperative processing with limited backhaul traffic is considered for cellular uplinks. To parsimoniously select a set of cooperating base stations, a sparse multi-cell receive-filter is obtained through convex optimization using compressive sensing techniques. Clustered cooperation is also considered, where sparsity is promoted on inter-cluster feedback. A joint equalizer design and dynamic partitioning problem is formulated and solved using an iterative spectral clustering approach. Numerical tests verify the efficacy of proposed methods.

Noisy Matrix Completion Under Sparse Factor Models

This paper examines a general class of noisy matrix completion tasks, where the goal is to estimate a matrix from observations obtained at a subset of its entries, each of which is subject to random noise or corruption. Our specific focus is on settings where the matrix to be estimated is well-approximated by a product of two (a priori unknown) matrices, one of which is sparse. Such structural models-referred to here as sparse factor models-have been widely used, for example, in subspace clustering applications, as well as in contemporary sparse modeling and dictionary learning tasks. Our main theoretical contributions are estimation error bounds for sparsity-regularized maximum likelihood estimators for the problems of this form, which are applicable to a number of different observation noise or corruption models. Several specific implications are examined, including scenarios where observations are corrupted by additive Gaussian noise or additive heavier-tailed (Laplace) noise, Poisson-distributed observations, and highly quantized (e.g., 1 b) observations. We also propose a simple algorithmic approach based on the alternating direction method of multipliers for these tasks, and provide experimental evidence to support our error analyses.

Compressive measurement designs for estimating structured signals in structured clutter: A Bayesian Experimental Design approach

This work considers an estimation task in compressive sensing, where the goal is to estimate an unknown signal from compressive measurements that are corrupted by additive pre-measurement noise (interference, or “clutter”) as well as post-measurement noise, in the specific setting where some (perhaps limited) prior knowledge on the signal, interference, and noise is available. The specific aim here is to devise a strategy for incorporating this prior information into the design of an appropriate compressive measurement strategy. Here, the prior information is interpreted as statistics of a prior distribution on the relevant quantities, and an approach based on Bayesian Experimental Design is proposed. Experimental results on synthetic data demonstrate that the proposed approach outperforms traditional random compressive measurement designs, which are agnostic to the prior information, as well as several other knowledge-enhanced sensing matrix designs based on more heuristic notions.

Backhaul-Constrained Multicell Cooperation Leveraging Sparsity and Spectral Clustering

Multicell cooperative processing with limited backhaul traffic is studied for cellular uplinks. Aiming at reduced backhaul overhead, a sparse multicell linear receive-filter design problem is formulated. Both unstructured distributed cooperation and clustered cooperation, in which base station groups are formed for tight cooperation, are considered. Dynamic clustered cooperation, where the sparse equalizer and the cooperation clusters are jointly determined, is solved via alternating minimization based on spectral clustering and group-sparse regression. Furthermore, decentralized implementations of both unstructured and clustered cooperation schemes are developed for scalability, robustness, and computational efficiency. Extensive numerical tests verify the efficacy of the proposed methods.

Error bounds for maximum likelihood matrix completion under sparse factor models

This paper examines a general class of matrix completion tasks where entry wise observations of the matrix are subject to random noise or corruption. Our particular focus here is on settings where the matrix to be estimated follows a sparse factor model, in the sense that it may be expressed as the product of two matrices, one of which is sparse. We analyze the performance of a sparsity-penalized maximum likelihood approach to such problems to provide a general-purpose estimation result applicable to any of a number of noise/corruption models, and describe its implications in two stylized scenarios - one characterized by additive Gaussian noise, and the other by highly-quantized one-bit observations. We also provide some supporting empirical evidence to validate our theoretical claims in the Gaussian setting.

Noisy inductive matrix completion under sparse factor models

Inductive Matrix Completion (IMC) is an important class of matrix completion problems that allows direct inclusion of available features to enhance estimation capabilities. These models have found applications in personalized recommendation systems, multilabel learning, dictionary learning, etc. This paper examines a general class of noisy matrix completion tasks where the underlying matrix is following an IMC model i.e., it is formed by a mixing matrix (a priori unknown) sandwiched between two known feature matrices. The mixing matrix here is assumed to be well approximated by the product of two sparse matrices — referred here to as “sparse factor models.” We leverage the main theorem of [1] and extend it to provide theoretical error bounds for the sparsity-regularized maximum likelihood estimators for the class of problems discussed in this paper. The main result is general in the sense that it can be used to derive error bounds for various noise models. In this paper, we instantiate our main result for the case of Gaussian noise and provide corresponding error bounds in terms of squared loss.

Locating material defects via wavefield demixing with morphologically germane dictionaries

This article introduces a methodology for the detection and localization of structural defects in solid media using morphological demixing algorithms. The demixing algorithms are designed to separate spatiotemporal response data into two morphologically antithetical components: one contribution captures the spatially sparse and temporally persistent features of the medium’s response, while the other provides a representation of the dominant, globally smooth component as it would be observed in a defect-free medium. Within the demixing paradigm, we explore two methods: in the first, we cast the demixing task in terms of a group Lasso regularization problem with simply structured orthonormal dictionaries; the second method makes use of a more morphologically germane dictionary whose additional structure allows for the localization of defects whose signature may be highly elusive, for example, buried in noise or masked by competing features. After the demixing is complete, an automatic visualization tool highlights the regions associated with potential anomalies and outputs their local coordinates. Since the method does not invoke any knowledge of the material properties of the medium, or of its behavior in its pristine conditions, and is solely based on data processing of current wavefield information, it is endowed with significant model agnostic and baseline-free attributes. These properties are desirable in systems where there exists limited or unreliable a priori knowledge of the constitutive model, when the physical domain is highly heterogeneous or compromised by large damage zones, or when accurate baseline simulations are unavailable. The efficacy of the proposed method is evaluated against synthetically generated data and experimental data obtained using a scanning laser Doppler vibrometer.

Locating rare and weak material anomalies by convex demixing of propagating wavefields

This paper considers the problem of detecting and localizing material anomalies in solid structures, given spatiotemporal observations at a pre-defined grid of points that collectively describe the material displacement resulting from an induced, propagating acoustic surface wave. We propose an approach that seeks to separate or “demix” each temporal snapshot of the propagating wavefield into its constituent components, which are assumed to be morphologically dissimilar in the vicinity of material defects. We cast this demixing approach as a group lasso regression task, characterized by morphologically dissimilar dictionaries, and establish conditions under which material anomalies may be accurately identified using this approach. We demonstrate and validate the performance of this approach on synthetic data as well as real-world data.

Noisy tensor completion for tensors with a sparse canonical polyadic factor

“To be considered for the 2017 IEEE Jack Keil Wolf ISIT Student Paper Award.” In this paper we study the problem of noisy tensor completion for tensors that admit a canonical polyadic or CANDE-COMP/PARAFAC (CP) decomposition with one of the factors being sparse. We present general theoretical error bounds for an estimate obtained by using a complexity-regularized maximum likelihood principle and then instantiate these bounds for the case of additive white Gaussian noise. We also provide an ADMM-type algorithm for solving the complexity-regularized maximum likelihood problem and validate the theoretical finding via experiments on synthetic data set.

Convolutional approximations to linear dimensionality reduction operators

This paper examines the existence of efficiently implementable approximations of a general real linear dimensionality reduction (LDR) operator. The specific focus is on approximating a given LDR operator with a partial circulant structured matrix (a matrix whose rows are related by circular shifts) as these constructions allow for low-memory footprint and computationally efficient implementations. Our main contributions are theoretical: we quantify how well general matrices may be approximated (in a Frobenius sense) by partial circulant structured matrices, and also consider a variation of this problem where the aim is only to accurately approximate the action of a given LDR operator on a restricted set of inputs. For the latter setting, we also propose a sparsity-regularized alternating minimization based algorithm for learning partial circulant approximations from data, and provide experimental evidence demonstrating the potential efficacy of this approach on real-world data.