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Recovering structured models (e.g., sparse or group-sparse vectors, low-rank matrices) given a few linear observations have been well-studied recently. In various applications in signal processing and machine learning, the model of interest is structured in several ways, for example, a matrix that is simultaneously sparse and low rank. Often norms that(More)
Recovering sparse vectors and low-rank matrices from noisy linear measurements has been the focus of much recent research. Various reconstruction algorithms have been studied, including &#x2113;<inf>1</inf> and nuclear norm minimization as well as &#x2113;<inf>p</inf> minimization with p &#38;#60; 1. These algorithms are known to succeed if certain(More)
Nuclear norm minimization (NNM) has recently gained significant attention for its use in rank minimization problems. Similar to compressed sensing, using null space characterizations, recovery thresholds for NNM have been studied in [12, 4]. However simulations show that the thresholds are far from optimal, especially in the low rank region. In this paper(More)
We consider the problem of estimating an unknown but structured signal x<sub>0</sub> from its noisy linear observations y = Ax<sub>0</sub> + z &#x2208; &#x211D;<sup>m</sup>. To the structure of x<sub>0</sub> is associated a structure inducing convex function f(&#x00B7;). We assume that the entries of A are i.i.d. standard normal N(0, 1) and z ~ N(0,(More)
The problem of signal recovery from the autocorrelation, or equivalently, the magnitudes of the Fourier transform, is of paramount importance in various fields of engineering. In this work, for one-dimensional signals, we give conditions, which when satisfied, allow unique recovery from the autocorrelation with very high probability. In particular, for(More)
Recovering signals from their Fourier transform magnitudes is a classical problem referred to as phase retrieval and has been around for decades. In general, the Fourier transform magnitudes do not carry enough information to uniquely identify the signal and therefore additional prior information is required. In this paper, we shall assume that the(More)
We consider the problem of recovering signals from their power spectral densities. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In general, additional prior information about the signal is required to guarantee unique recovery as the mapping from(More)
<lb>Denoising has to do with estimating a signal x0 from its noisy observations y = x0 + z. In this paper,<lb>we focus on the “structured denoising problem”, where the signal x0 possesses a certain structure and z<lb>has independent normally distributed entries with mean zero and variance σ. We employ a structure-<lb>inducing convex function f(·) and(More)