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A new method of quantum state tomography for quantum information processing is described. The method based on two-dimensional Fourier transform technique involves detection of all the off-diagonal elements of the density matrix in a…
We introduce an ordinate method for noisy data analysis, based solely on rank information and thus insensitive to outliers. The method is nonparametric, objective, and the required data processing is parsimonious. Main ingredients are a…
Several novel imaging applications have lead recently to a variety of Radon type transforms, where integration is done over a family of conical surfaces. We call them \emph{cone transforms} (in 2D they are also called \emph{V-line} or…
Multi input multi output (MIMO) systems\' capability of using seperate signals brings many advantages to radar signal processing and time frequency analysis. In this paper, a variety of properties of MIMO ambiguity functions related with…
Quantum states are successfully reconstructed using the maximum likelihood estimation on the subspace where the measured projectors reproduce the identity operator. Reconstruction corresponds to normalization of incompatible observations.…
Learned denoisers play a fundamental role in various signal generation (e.g., diffusion models) and reconstruction (e.g., compressed sensing) architectures, whose success derives from their ability to leverage low-dimensional structure in…
The characterization of a binary function by partial frequency information is considered. We show that it is possible to reconstruct binary signals from incomplete frequency measurements via the solution of a simple linear optimization…
A Forster transform is an operation that turns a distribution into one with good anti-concentration properties. While a Forster transform does not always exist, we show that any distribution can be efficiently decomposed as a disjoint…
We introduce a new method for robust beamforming, where the goal is to estimate a signal from array samples when there is uncertainty in the angle of arrival. Our method offers state-of-the-art performance on narrowband signals and is…
We present a pure machine learning process for synthesizing radar spectrograms from Motion-Capture (MoCap) data. We formulate MoCap-to-spectrogram translation as a windowed sequence-to-sequence task using a transformer-based model that…
Moment methods to reconstruct images from their Radon transforms are both natural and useful. They can be used to suppress noise or other spurious effects and can lead to highly efficient reconstructions from relatively few projections. We…
The ability to measure polarisation, spectrum, temporal dynamics, and spatial amplitude and phase of optical beams is essential to study fundamental phenomena in laser dynamics, telecommunications and nonlinear optics. Current…
Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…
Characterizing complex quantum systems is a vital task in quantum information science. Quantum tomography, the standard tool used for this purpose, uses a well-designed measurement record to reconstruct quantum states and processes. It is,…
This paper extends the Radon transform, a classical image processing tool for fast tomography and denoising, to the quantum computing platform. A new kind of periodic discrete Radon transform (PDRT), called quantum Radon transform (QRT), is…
Representation learning seeks meaningful sensory representations without supervision and can model aspects of human development. Although many neural networks empirically learn useful features, a principled account of what makes a…
The robustness of image recognition algorithms remains a critical challenge, as current models often depend on large quantities of labeled data. In this paper, we propose a hybrid approach that combines the adaptability of neural networks…
We present an efficient and robust method for the reconstruction of photon number distributions by using solely thermal noise as a probe. The method uses a minimal number of pre-calibrated quantum devices, only one on/off single-photon…
The limited angle Radon transform is notoriously difficult to invert due to its ill-posedness. In this work, we give a mathematical explanation that data-driven approaches can stably reconstruct more information compared to traditional…
Signal analysis is built upon various resolutions of the identity in signal vector spaces, e.g. Fourier, Gabor, wavelets, etc. Similar resolutions are used as quantizers of functions or distributions, paving the way to a time-frequency or…