Related papers: An algebraic characterization of injectivity in ph…
We tackle the problem of recovering a complex signal $\boldsymbol x\in\mathbb{C}^n$ from quadratic measurements of the form $y_i=\boldsymbol x^*\boldsymbol A_i\boldsymbol x$, where $\boldsymbol A_i$ is a full-rank, complex random…
We consider the question of estimating a real low-complexity signal (such as a sparse vector or a low-rank matrix) from the phase of complex random measurements. We show that in this "phase-only compressive sensing" (PO-CS) scenario, we can…
Advances in vectorial polarisation-resolved imaging are bringing new capabilities to applications ranging from fundamental physics through to clinical diagnosis. Imaging polarimetry requires determination of the Mueller matrix (MM) at every…
Phase retrieval problems occur in a wide range of applications in physics and engineering. Usually, these problems consist in the recovery of an unknown signal from the magnitudes of its Fourier transform. In some applications, however, the…
Phase retrieval aims to recover a signal from intensity-only measurements, a fundamental problem in many fields such as imaging, holography, optical computing, crystallography, and microscopy. Although there are several well-known phase…
A matrix network is a family of matrices, with relatedness modeled by a weighted graph. We consider the task of completing a partially observed matrix network. We assume a novel sampling scheme where a fraction of matrices might be…
The phase retrieval from multi-frequency intensity (power) observations is considered. The object to be reconstructed is complex-valued. A novel algorithm is presented that accomplishes both the object phase (absolute phase) retrieval and…
We consider frames in a finite-dimensional Hilbert space where frames are exactly the spanning sets of the vector space. A factor poset of a frame is defined to be a collection of subsets of $I$, the index set of our vectors, ordered by…
Recovering the transmission matrix of a disordered medium is a challenging problem in disordered photonics. Usually, its reconstruction relies on a complex inversion that aims at connecting a fully-controlled input to the deterministic…
Eyeframe lens tracing is an important process in the optical industry that requires sub-millimeter precision to ensure proper lens fitting and optimal vision correction. Traditional frame tracers rely on mechanical tools that need precise…
To obtain an electron-density map from a macromolecular crystal the phase-problem needs to be solved, which often involves the use of heavy-atom derivative crystals and concomitantly the determination of the heavy atom substructure. This is…
Consider a scenario in which an unknown signal is transformed by a known linear operator, and then the pointwise absolute value of the unknown output function is reported. This scenario appears in several applications, and the goal is to…
Accurate determination of the complex effective permittivity is fundamental to optical material engineering, but it remains a critical metrology challenge for heterogeneous systems. In polymer blends and optical composites, scattering and…
We consider the recovery of a (real- or complex-valued) signal from magnitude-only measurements, known as phase retrieval. We formulate phase retrieval as a convex optimization problem, which we call PhaseMax. Unlike other convex methods…
We study the phase retrieval problem for the short-time Fourier transform on the groups $\mathbb{Z}$, $\mathbb{Z}_d$ and $\mathbb{R}^d$. As is well-known, phase retrieval is possible, once the window's ambiguity function vanishes nowhere.…
Motivated by non-destructive testing of optical fiber, we consider the problem of determining the index of refraction of a two-dimensional medium from magnitude of the total field resulting from known incident plane waves at a fixed…
A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a -…
Recurrence networks are a powerful nonlinear tool for time series analysis of complex dynamical systems. {While there are already many successful applications ranging from medicine to paleoclimatology, a solid theoretical foundation of the…
Complex field imaging, which captures both the amplitude and phase information of input optical fields or objects, can offer rich structural insights into samples, such as their absorption and refractive index distributions. However,…
Programmable photonic integrated circuits (PICs), offering diverse signal processing functions within a single chip, are promising solutions for applications ranging from optical communications to artificial intelligence. While the scale…