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The theory behind compressive sampling pre-supposes that a given sequence of observations may be exactly represented by a linear combination of a small number of basis vectors. In practice, however, even small deviations from an exact…
The vibration analysis of the bearing is very crucial because of its non-stationary nature and low signal-to-noise ratio. Therefore, a novel scheme for detecting bearing defects is put forward based on the extraction of single-valued…
The decomposition of sounds into sines, transients, and noise is a long-standing research problem in audio processing. The current solutions for this three-way separation detect either horizontal and vertical structures or anisotropy and…
We study the problem of demixing a pair of sparse signals from noisy, nonlinear observations of their superposition. Mathematically, we consider a nonlinear signal observation model, $y_i = g(a_i^Tx) + e_i, \ i=1,\ldots,m$, where $x = \Phi…
We consider the demixing problem of two (or more) structured high-dimensional vectors from a limited number of nonlinear observations where this nonlinearity is due to either a periodic or an aperiodic function. We study certain families of…
Many fault diagnosis methods of rotating machines are based on discriminative features extracted from signals collected from the key components such as bearings. However, under complex operating conditions, periodic impulsive…
A pattern recognition (PR) based diagnostic scheme is presented to identify bearing faults, using time domain features. Vibration data is acquired from faulty bearings using a test rig. The features are extracted from the data, and…
This paper considers the problem of simultaneous sensor fault detection, isolation, and networked estimation of linear full-rank dynamical systems. The proposed networked estimation is a variant of single time-scale protocol and is based on…
In the pharmaceutical industry, the maintenance of production machines must be audited by the regulator. In this context, the problem of predictive maintenance is not when to maintain a machine, but what parts to maintain at a given point…
We consider a linear inverse problem whose solution is expressed as a sum of two components: one smooth and the other sparse. This problem is addressed by minimizing an objective function with a least squares data-fidelity term and a…
Time-frequency analysis is often used to study non stationary multicomponent signals, which can be viewed as the surperimposition of modes, associated with ridges in the TF plane. To understand such signals, it is essential to identify…
This paper proposes a sparse regression strategy for discovery of ordinary differential equations from incomplete and noisy data. Inference is performed over both equation parameters and state variables using a statistically motivated…
Tensor decomposition is a powerful tool for extracting physically meaningful latent factors from multi-dimensional nonnegative data, and has been an increasing interest in a variety of fields such as image processing, machine learning, and…
The characterization of multicomponent signals with a particular emphasis on musical and communication signals is one of the problems studied in the dissertation. In order to provide an efficient analysis of the multicomponent signals, the…
We consider composite linear inverse problems where the signal to recover is modeled as a sum of two functions. We study a variational framework formulated as an optimization problem over the pairs of components using two regularization…
To improve the performance in identifying the faults under strong noise for rotating machinery, this paper presents a dynamic feature reconstruction signal graph method, which plays the key role of the proposed end-to-end fault diagnosis…
Signals sparse in a transformation domain can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Simple re- construction algorithms are presented in the first part of the paper. The…
This paper studies the problem of recovering a signal vector and the corrupted noise vector from a collection of corrupted linear measurements through the solution of a l1 minimization, where the sensing matrix is a partial Fourier matrix…
In sparse coding, we attempt to extract features of input vectors, assuming that the data is inherently structured as a sparse superposition of basic building blocks. Similarly, neural networks perform a given task by learning features of…
In this paper, we propose a new method to reconstruct a signal corrupted by noise where both signal and noise are sparse but in different domains. The problem investigated in this paper arises in different applications such as impulsive…