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Exact recovery of $K$-sparse signals $x \in \mathbb{R}^{n}$ from linear measurements $y=Ax$, where $A\in \mathbb{R}^{m\times n}$ is a sensing matrix, arises from many applications. The orthogonal matching pursuit (OMP) algorithm is widely…
In statistics, series of ordinary least squares problems (OLS) are used to study the linear correlation among sets of variables of interest; in many studies, the number of such variables is at least in the millions, and the corresponding…
Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding…
This paper introduces a novel approach for recovering sparse signals using sorted L1/L2 minimization. The proposed method assigns higher weights to indices with smaller absolute values and lower weights to larger values, effectively…
Greedy sparse recovery has become a popular tool in many applications, although its complexity is still prohibitive when large sparsifying dictionaries or sensing matrices have to be exploited. In this paper, we formulate first a new class…
Compressive sampling (CoSa) is a new methodology which demonstrates that sparse signals can be recovered from a small number of linear measurements. Greedy algorithms like CoSaMP have been designed for this recovery, and variants of these…
Orthogonal matching pursuit (OMP) is a canonical greedy algorithm for sparse signal reconstruction. When the signal of interest is block sparse, i.e., it has nonzero coefficients occurring in clusters, the block version of OMP algorithm…
This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…
The optimal statistic (OS) is a frequentist estimator for the amplitude and significance of a spatially-correlated signal in pulsar timing array (PTA) data, and it is widely used to search for the gravitational wave background (GWB).…
Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least…
Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be…
This paper introduces two novel approaches for Online Multi-Task Learning (MTL) Regression Problems. We employ a high performance graph-based MTL formulation and develop two alternative recursive versions based on the Weighted Recursive…
We address the phase retrieval problem with errors in the sensing vectors. A number of recent methods for phase retrieval are based on least squares (LS) formulations which assume errors in the quadratic measurements. We extend this…
We propose a block least mean square (LMS) algorithm to monitor the longitudinal power profile of a fiber-optic link through receiver-based digital data from a coherent detector. Compared to the benchmark least squares (LS) method, the…
Sparse adaptive filtering has gained much attention due to its wide applicability in the field of signal processing. Among the main algorithm families, sparse norm constraint adaptive filters develop rapidly in recent years. However, when…
Because optical systems have huge bandwidth and are capable of generating low noise short pulses they are ideal for undersampling multi-band signals that are located within a very broad frequency range. In this paper we propose a new scheme…
As an extension of orthogonal matching pursuit (OMP) improving the recovery performance of sparse signals, generalized OMP (gOMP) has recently been studied in the literature. In this paper, we present a new analysis of the gOMP algorithm…
This paper concerns an application of the orthogonality sampling method (OSM) for a real-time identification of small objects from two-dimensional Fresnel experimental dataset in transverse electric polarization. First, we apply the OSM…
The recursive least-squares (RLS) algorithm has well-documented merits for reducing complexity and storage requirements, when it comes to online estimation of stationary signals as well as for tracking slowly-varying nonstationary…