Related papers: A Topological Lowpass Filter for Quasiperiodic Sig…
A variational approach to reconstruction of phase and amplitude of a complex-valued object from Poissonian intensity observations is developed. The observation model corresponds to the typical optical setups with a phase modulation of…
In the current paper, we have developed an analytical apparatus, allowing to calculate the phase error, produced by miscalibration of modulation parameters. The case of harmonic modulation is considered, the analysis is performed for cases…
The paper considers the phase retrieval problem in N-dimensional complex vector spaces. It provides two sets of deterministic measurement vectors which guarantee signal recovery for all signals, excluding only a specific subspace and a…
We suggest an adaptive sampling rule for obtaining information from noisy signals using wavelet methods. The technique involves increasing the sampling rate when relatively high-frequency terms are incorporated into the wavelet estimator,…
We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements…
Many real world problems exhibit patterns that have periodic behavior. For example, in astrophysics, periodic variable stars play a pivotal role in understanding our universe. An important step when analyzing data from such processes is the…
Generally, phase retrieval problem can be viewed as the reconstruction of a function/signal from only the magnitude of the linear measurements. These measurements can be, for example, the Fourier transform of the density function.…
We propose a new unsupervised and non-parametric method to detect change points in intricate quasi-periodic signals. The detection relies on optimal transport theory combined with topological analysis and the bootstrap procedure. The…
We present a two-stage least-squares method to inverse medium problems of reconstructing multiple unknown coefficients simultaneously from noisy data. A direct sampling method is applied to detect the location of the inhomogeneity in the…
Phase estimation is the most investigated protocol in quantum metrology, but its performance is affected by the presence of noise, also in the form of imperfect state preparation. Here we discuss how to address this scenario by using a…
In this paper we present a new multilevel quasi-interpolation algorithm for smooth periodic functions using scaled Gaussians as basis functions. Recent research in this area has focussed upon implementations using basis function with finite…
We consider the phase retrieval problem for signals that belong to a union of subspaces. We assume that amplitude measurements of the signal of length $n$ are observed after passing it through a random $m \times n$ measurement matrix. We…
We present a novel methodology able to distinguish meaningful level shifts from typical signal fluctuations. A two-stage regularization filtering can accurately identify the location of the significant level-shifts with an efficient…
We consider the problem of recovering of continuous multi-dimensional functions from the noisy observations over the regular grid. Our focus is at the adaptive estimation in the case when the function can be well recovered using a linear…
We propose a Bayesian nonparametric method for low-pass filtering that can naturally handle unevenly-sampled and noise-corrupted observations. The proposed model is constructed as a latent-factor model for time series, where the latent…
In this paper, we analyze the asymptotic properties of the Two-Stage (TS) estimator -- a simulation-based parameter estimation method that constructs estimators offline from synthetic data. While TS offers significant computational…
To achieve high data rates defined in 5G, the use of millimeter-waves and massive-MIMO are indispensable. To benefit from these technologies, an accurate estimation of the channel parameters is crucial. We propose a novel two-stage…
In this short note we propose a simple two-stage sparse phase retrieval strategy that uses a near-optimal number of measurements, and is both computationally efficient and robust to measurement noise. In addition, the proposed strategy is…
The phase estimation algorithm, which is at the heart of a variety of quantum algorithms, including Shor's factoring algorithm, allows a quantum computer to accurately determine an eigenvalue of an unitary operator. Quantum nondemolition…
The phase estimation algorithm is a powerful quantum algorithm with applications in cryptography, number theory, and simulation of quantum systems. We use this algorithm to simulate the time evolution of a system of two spin-1/2 particles…