Related papers: Absolute Uniqueness of Phase Retrieval with Random…
Reconstructing the geometry and appearance of objects from photographs taken in different environments is difficult as the illumination and therefore the object appearance vary across captured images. This is particularly challenging for…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…
We establish a sharp quantum advantage in determining the parity (even/odd) of an unknown permutation applied to any number $n \ge 3$ of particles. Classically, this is impossible with fewer than $n$ labels, being that the success is…
An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal…
Self-similar solutions of the coherent diffusion equation are derived and measured. The set of real similarity solutions is generalized by the introduction of a nonuniform phase surface, based on the elegant Gaussian modes of optical…
This paper reports, by way of introduction, on the advances made by our group and the broader signal processing community on the concept of sample abundance; a phenomenon that naturally arises in one-bit and few-bit signal processing…
We present two experiments that achieve phase super-resolution at telecommunication wavelengths. One of the experiments is realized in the space domain and the other in the time domain. Both experiments show high visibilities and are…
This paper proposes a self-supervised objective for learning representations that localize objects under occlusion - a property known as object permanence. A central question is the choice of learning signal in cases of total occlusion.…
The probability of a random walker to return to its starting point in dimensions one and two is unity, a theorem first proven by G. Polya. The recurrence probability -- the probability to be found at the origin at a time t, is a power law…
In this letter, we show that a perfect lens can be employed to make multiple objects appear like only one in the far field, leading to a new concept of illusion optics. Numerical simulations are performed to verify the functionalities for…
The problem of signal recovery from its Fourier transform magnitude is of paramount importance in various fields of engineering and has been around for over 100 years. Due to the absence of phase information, some form of additional…
This paper considers the problem of sampling and reconstruction of a continuous-time sparse signal without assuming the knowledge of the sampling instants or the sampling rate. This topic has its roots in the problem of recovering multiple…
Phase retrieval problems involve solving linear equations, but with missing sign (or phase, for complex numbers) information. More than four decades after it was first proposed, the seminal error reduction algorithm of (Gerchberg and Saxton…
In this work we analyze the problem of phase retrieval from Fourier measurements with random diffraction patterns. To this end, we consider the recently introduced PhaseLift algorithm, which expresses the problem in the language of convex…
Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral…
Understanding and reconstructing occluded objects is a challenging problem, especially in open-world scenarios where categories and contexts are diverse and unpredictable. Traditional methods, however, are typically restricted to closed…
We propose and demonstrate a new phase retrieval method for imaging through random media. Although methods to recover the Fourier amplitude through random distortions are well established, recovery of the Fourier phase has been a more…
We present a novel diffractive imaging method that harnesses a low-resolution real-space image to guide the phase retrieval. A computational algorithm is developed to utilize such prior knowledge as a real-space constraint in the iterative…
We derive conditions under which random sequences of polarizations (two-point symmetrizations) converge almost surely to the symmetric decreasing rearrangement. The parameters for the polarizations are independent random variables whose…
Spectral dimensionality reduction algorithms are widely used in numerous domains, including for recognition, segmentation, tracking and visualization. However, despite their popularity, these algorithms suffer from a major limitation known…