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We address the problem of recovering a sparse signal from clipped or quantized measurements. We show how these two problems can be formulated as minimizing the distance to a convex feasibility set, which provides a convex and differentiable…
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…
Over the past decade, various matrix completion algorithms have been developed. Thresholded singular value decomposition (SVD) is a popular technique in implementing many of them. A sizable number of studies have shown its theoretical and…
We consider the classical 1D phase retrieval problem. In order to overcome the difficulties associated with phase retrieval from measurements of the Fourier magnitude, we treat recovery from the magnitude of the short-time Fourier transform…
The hierarchical sparsity framework, and in particular the HiHTP algorithm, has been successfully applied to many relevant communication engineering problems recently, particularly when the signal space is hierarchically structured. In this…
We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements. While the theoretical understanding of low rank…
Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be…
Free-discontinuity problems describe situations where the solution of interest is defined by a function and a lower dimensional set consisting of the discontinuities of the function. Hence, the derivative of the solution is assumed to be a…
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…
Estimating a sparse covariance matrix is a fundamental problem in high-dimensional statistics. However, thresholding methods developed for independent data are generally not directly applicable to high-dimensional time series, where…
We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…
We explore the impact of coarse quantization on matrix completion in the extreme scenario of dithered one-bit sensing, where the matrix entries are compared with time-varying threshold levels. In particular, instead of observing a subset of…
Low-rank recovery builds upon ideas from the theory of compressive sensing, which predicts that sparse signals can be accurately reconstructed from incomplete measurements. Iterative thresholding-type algorithms-particularly the normalized…
This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional…
This paper addresses the problem of identifying sparse linear time-invariant (LTI) systems from a single sample trajectory generated by the system dynamics. We introduce a Lasso-like estimator for the parameters of the system, taking into…
We study the problem of recovery of matrices that are simultaneously low rank and row and/or column sparse. Such matrices appear in recent applications in cognitive neuroscience, imaging, computer vision, macroeconomics, and genetics. We…
Single-snapshot direction-of-arrival (DOA) estimation using sparse linear arrays (SLAs) has gained significant attention in the field of automotive MIMO radars. This is due to the dynamic nature of automotive settings, where multiple…
Sparse phase retrieval plays an important role in many fields of applied science and thus attracts lots of attention. In this paper, we propose a \underline{sto}chastic alte\underline{r}nating \underline{m}inimizing method for…
In recent studies on sparse modeling, non-convex penalties have received considerable attentions due to their superiorities on sparsity-inducing over the convex counterparts. Compared with the convex optimization approaches, however, the…
In statistics, generalized linear models (GLMs) are widely used for modeling data and can expressively capture potential nonlinear dependence of the model's outcomes on its covariates. Within the broad family of GLMs, those with binary…