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We describe a self calibrating optical technique that allows to perform absolute measurements of scattering cross sections for the light scattered at extremely small angles. Very good performances are obtained by using a very simple optical…
Compton scattering is a well-established technique that can provide detailed information about electronic states in solids. Making use of the principle of tomography, it is possible to determine the Fermi surface from sets of…
We address the problem of compressed sensing (CS) with prior information: reconstruct a target CS signal with the aid of a similar signal that is known beforehand, our prior information. We integrate the additional knowledge of the similar…
Classical compressed sensing (CS) allows us to recover structured signals from far few linear measurements than traditionally prescribed, thereby efficiently decreasing sampling rates. However, if there exist nonlinearities in the…
Compressive sensing (CS) is a technique for estimating a sparse signal from the random measurements and the measurement matrix. Traditional sparse signal recovery methods have seriously degeneration with the measurement matrix uncertainty…
From many fewer acquired measurements than suggested by the Nyquist sampling theory, compressive sensing (CS) theory demonstrates that, a signal can be reconstructed with high probability when it exhibits sparsity in some domain. Most of…
The theory of Compressed Sensing, the emerging sampling paradigm 'that goes against the common wisdom', asserts that 'one can recover signals in Rn from far fewer samples or measurements, if the signal has a sparse representation in some…
The linear inverse source and scattering problems are studied from the perspective of compressed sensing, in particular the idea that sufficient incoherence and sparsity guarantee uniqueness of the solution. By introducing the sensor as…
We prove small data scattering in the mass-subcritical regime for the NLS equation with double nonlinearities, where a focusing leading term is perturbed by a lower order defocusing nonlinear term. Our proof relies on the pseudo-conformal…
Small-angle neutron scattering (SANS) is a powerful technique for probing the nanoscale structure of materials. However, the fundamental limitations of neutron flux pose significant challenges for rapid, high-fidelity data acquisition…
We propose a new technique for adaptive identification of sparse systems based on the compressed sensing (CS) theory. We manipulate the transmitted pilot (input signal) and the received signal such that the weights of adaptive filter…
Using the two-dimensional nonlinear Schr\"odinger equation (NLS) as a model example, we present a general method for recovering the nonlinearity of a nonlinear dispersive equation from its small-data scattering behavior. We prove that under…
The l1-norm minimization problem plays an important role in the compressed sensing (CS) theory. We present in this letter an algorithm for solving the problem of l1-norm minimization for quaternion signals by converting it to second-order…
We introduce a new constrained minimization problem that performs template and pattern detection on a multispectral image in a compressive sensing context. We use an original minimization problem from Guo and Osher that uses $L_1$…
Several powerful machines, such as the D-Wave 2000Q, dedicated to solving combinatorial optimization problems through the Ising-model formulation have been developed. To input problems into the machines, the unknown parameters on the Ising…
This paper considers a compressive sensing (CS) approach for hyperspectral data acquisition, which results in a practical compression ratio substantially higher than the state-of-the-art. Applying simultaneous low-rank and joint-sparse…
We developed a method to infer the calibration parameters of multichannel measurement systems, such as channel variations of sensitivity and noise amplitude, from experimental data. We regard such uncertainties of the calibration parameters…
We study relativistic scattering when one only has access to a subset of the particles, using the language of quantum measurement theory. We give an exact, non-perturbative formula for the von Neumann entanglement entropy of an apparatus…
The recent theory of compressive sensing leverages upon the structure of signals to acquire them with much fewer measurements than was previously thought necessary, and certainly well below the traditional Nyquist-Shannon sampling rate.…
This paper proposes a compressed sensing (CS) framework for the acquisition and reconstruction of frequency-sparse signals with chaotic dynamical systems. The sparse signal is acting as an excitation term of a discrete-time chaotic system…