Related papers: Norm retrieval and phase retrieval by projections
Many modern high-performing machine learning models such as GPT-3 primarily rely on scaling up models, e.g., transformer networks. Simultaneously, a parallel line of work aims to improve the model performance by augmenting an input instance…
This paper introduces the subgraph nomination inference task, in which example subgraphs of interest are used to query a network for similarly interesting subgraphs. This type of problem appears time and again in real world problems…
Frame design for phaseless reconstruction is now part of the broader problem of nonlinear reconstruction and is an emerging topic in harmonic analysis. The problem of phaseless reconstruction can be simply stated as follows. Given the…
Signal recovery from nonlinear measurements involves solving an iterative optimization problem. In this paper, we present a framework to optimize the sensing parameters to improve the quality of the signal recovered by the given iterative…
Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…
We generalize the Second Oversampling Theorem for wavelet frames and dual wavelet frames from the setting of integer dilations to real dilations. We also study the relationship between dilation matrix oversampling of semi-orthogonal…
This paper discusses predictive inference and feature selection for generalized linear models with scarce but high-dimensional data. We argue that in many cases one can benefit from a decision theoretically justified two-stage approach:…
We consider a phase retrieval problem, where we want to reconstruct a $n$-dimensional vector from its phaseless scalar products with $m$ sensing vectors, independently sampled from complex normal distributions. We show that, with a suitable…
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…
This paper discusses the connection between the phase retrieval problem and permutation invariant embeddings. We show that the real phase retrieval problem for $\mathbb{R}^d/O(1)$ is equivalent to Euclidean embeddings of the quotient space…
Phase retrieval aims to recover a signal from magnitude or power spectra measurements. It is often addressed by considering a minimization problem involving a quadratic cost function. We propose a different formulation based on Bregman…
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…
The average properties of the well-known Subset Sum Problem can be studied by the means of its randomised version, where we are given a target value $z$, random variables $X_1, \ldots, X_n$, and an error parameter $\varepsilon > 0$, and we…
Phase retrieval(PR) problem is a kind of ill-condition inverse problem which is arising in various of applications. Based on the Wirtinger flow(WF) method, a reweighted Wirtinger flow(RWF) method is proposed to deal with PR problem. RWF…
We consider the statistical inference problem of recovering an unknown perfect matching, hidden in a weighted random graph, by exploiting the information arising from the use of two different distributions for the weights on the edges…
This article gives a procedure to convert a frame which is not a tight frame into a Parseval frame for the same space, with the requirement that each element in the resulting Parseval frame can be explicitly written as a linear combination…
The standard approach to compressive sampling considers recovering an unknown deterministic signal with certain known structure, and designing the sub-sampling pattern and recovery algorithm based on the known structure. This approach…
Projective Norms are a class of tensor norms that map on the input and output spaces. These norms are useful for providing a measure of entanglement. Calculating the projective norms is an NP-hard problem, which creates challenges in…
Current endeavours in exoplanet characterisation rely on atmospheric retrieval to quantify crucial physical properties of remote exoplanets from observations. However, the scalability and efficiency of the technique are under strain with…
A general mathematical framework and recovery algorithm is presented for the holographic phase retrieval problem. In this problem, which arises in holographic coherent diffraction imaging, a "reference" portion of the signal to be recovered…