Related papers: Phase retrieval with rank $d$ measurements -- \emp…
In this paper, we investigate the sample size requirement for exact recovery of a high order tensor of low rank from a subset of its entries. We show that a gradient descent algorithm with initial value obtained from a spectral method can,…
This paper considers the phase retrieval problem in which measurements consist of only the magnitude of several linear measurements of the unknown, e.g., spectral components of a time sequence. We develop low-complexity algorithms with…
Phase reconstruction, which estimates phase from a given amplitude spectrogram, is an active research field in acoustical signal processing with many applications including audio synthesis. To take advantage of rich knowledge from data,…
We consider random walks evolving on two models of connected and undirected graphs and study the exact large deviations of a local dynamical observable. We prove, in the thermodynamic limit, that this observable undergoes a first-order…
Randomized Numerical Linear Algebra (RandNLA) uses randomness to develop improved algorithms for matrix problems that arise in scientific computing, data science, machine learning, etc. Determinantal Point Processes (DPPs), a seemingly…
Hypercomplex signal processing (HSP) offers powerful tools for analyzing and processing multidimensional signals by explicitly exploiting inter-dimensional correlations through Clifford algebra. In recent years, hypercomplex formulations of…
Dimensionality reduction (DR) algorithms compress high-dimensional data into a lower dimensional representation while preserving important features of the data. DR is a critical step in many analysis pipelines as it enables visualisation,…
Phase retrieval (PR) is an ill-conditioned inverse problem which can be found in various science and engineering applications. Assuming sparse priority over the signal of interest, recent algorithms have been developed to solve the phase…
The problem of recovering a signal from its phaseless Fourier transform measurements, called Fourier phase retrieval, arises in many applications in engineering and science. Fourier phase retrieval poses fundamental theoretical and…
The \textit{de facto} paradigm for applying dense retrieval (DR) to new tasks involves fine-tuning a pre-trained model for a specific task. However, this paradigm has two significant limitations: (1) It is difficult adapt the DR to a new…
Visual place recognition is a challenging task for autonomous driving and robotics, which is usually considered as an image retrieval problem. A commonly used two-stage strategy involves global retrieval followed by re-ranking using…
In recent years, data-driven reinforcement learning (RL), also known as offline RL, have gained significant attention. However, the role of data sampling techniques in offline RL has been overlooked despite its potential to enhance online…
The phase retrieval problem asks to recover a natural signal $y_0 \in \mathbb{R}^n$ from $m$ quadratic observations, where $m$ is to be minimized. As is common in many imaging problems, natural signals are considered sparse with respect to…
Many iterative procedures in stochastic optimization exhibit a transient phase followed by a stationary phase. During the transient phase the procedure converges towards a region of interest, and during the stationary phase the procedure…
Reliability-based topology optimization (RBTO) requires repeated estimation of small failure probabilities and their gradients, making conventional nested Monte Carlo approaches computationally prohibitive for large scale structural…
In this paper, we introduce a novel iterative algorithm for the problem of phase-retrieval where the measurements consist of only the magnitude of linear function of the unknown signal, and the noise in the measurements follow Poisson…
In recent years, the mathematical and algorithmic aspects of the phase retrieval problem have received considerable attention. Many papers in this area mention crystallography as a principal application. In crystallography, the signal to be…
In this research, we reveal the inborn but hitherto ignored properties of quantitative differential phase contrast (qDPC) imaging: the phase transfer function being an edge detection filter. Inspired by this, we highlighted the duality of…
This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal $x \in \mathbb{R}^p$ from noisy quadratic measurements $y_j = (a_j' x )^2 + \epsilon_j$, $j=1, \ldots, m$, with independent sub-exponential noise…
We study modeling and identification of stationary processes with a spectral density matrix of low rank. Equivalently, we consider processes having an innovation of reduced dimension for which Prediction Error Methods (PEM) algorithms are…