Related papers: Signal Recovery from Time and Frequency Samples
The problem of phase retrieval is to determine a signal $f\in \mathcal{H}$, with $\mathcal{H}$ a Hilbert space, from intensity measurements $|F(\omega)|$, where $F(\omega):=\langle f , \varphi_\omega\rangle$ are measurements of $f$ with…
Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…
In many signal processing applications, one wishes to acquire images that are sparse in transform domains such as spatial finite differences or wavelets using frequency domain samples. For such applications, overwhelming empirical evidence…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…
We consider the geometry associated to the ambiguities of the one-dimensional Fourier phase retrieval problem for vectors in ${\mathbb C}^{N+1}$. Our first result states that the space of signals has a finite covering (which we call the…
We consider multi-variate signals spanned by the integer shifts of a set of generating functions with distinct frequency profiles and the problem of reconstructing them from samples taken on a random periodic set. We show that such a…
To obtain the initial pressure from the collected data on a planar sensor arrangement in Photoacoustic tomography, there exists an exact analytic frequency domain reconstruction formula. An efficient realization of this formula needs to…
The extraction of information carried by light plays an increasingly important role in optical communication, imaging, and detection. However, the information can only be successfully extracted when the light pulse is comparably strong,…
We consider the recovery of a continuous domain piecewise constant image from its non-uniform Fourier samples using a convex matrix completion algorithm. We assume the discontinuities/edges of the image are localized to the zero levelset of…
This paper introduces a novel technique for reconstructing the phase of modified spectrograms of audio signals. From the analysis of mixtures of sinusoids we obtain relationships between phases of successive time frames in the…
Time-frequency analysis, such as the Gabor transform, plays an important role in many signal processing applications. The redundancy of such representations is often directly related to the computational load of any algorithm operating in…
In this paper we study the performance of image reconstruction methods from incomplete samples of the 2D discrete Fourier transform. Inspired by requirements in parallel MRI, we focus on a special sampling pattern with a small number of…
Anisotropic two-dimensional diffraction signals encode additional structural information, including atom-pair angular distributions, beyond conventional isotropic scattering. However, experimental constraints such as beam stops result in…
In this paper, we provide a method to recover off-the-grid frequencies of a signal in two-dimensional (2-D) line spectral estimation. Most of the literature in this field focuses on the case in which the only information is spectral…
Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…
We study the problem of approximately recovering signals on a manifold from one-bit linear measurements drawn from either a Gaussian ensemble, partial circulant ensemble, or bounded orthonormal ensemble and quantized using Sigma-Delta or…
A core challenge for signal data recovery is to model the distribution of signal matrix (SM) data based on measured low-quality data in biomedical engineering of magnetic particle imaging (MPI). For acquiring the high-resolution…
Sonography techniques use multiple transducer elements for tissue visualization. Signals detected at each element are sampled prior to digital beamforming. The required sampling rates are up to 4 times the Nyquist rate of the signal and…
We study a sample complexity vs. conditioning tradeoff in modern signal recovery problems (including sparse recovery, low-rank matrix sensing, covariance estimation, and abstract phase retrieval), where convex optimization problems are…
We address the problem of reconstructing a multi-band signal from its sub-Nyquist point-wise samples. To date, all reconstruction methods proposed for this class of signals assumed knowledge of the band locations. In this paper, we develop…