Publications related to Estimation of multiple phases from a single fringe pattern in digital holographic interferometry

The multivariate Serre conjecture ring

It is well-known that for any integral domain R, the Serre conjecture ring R(X), i.e., the localization of the univariate polynomial ring R[X] at monic polynomials, is a Bezout domain of Krull dimension

San Diego2023

Strictly Real Fundamental Theorem Of Algebra Using Polynomial Interlacing

Soham Basu

Without resorting to complex numbers or any advanced topological arguments, we show that any real polynomial of degree greater than two always has a real quadratic polynomial factor, which is equivalent to the fundamental theorem of algebra. The proof uses ...

CAMBRIDGE UNIV PRESS2021

Distributed Learning in Non-Convex Environments-Part II: Polynomial Escape From Saddle-Points

Ali H. Sayed, Stefan Vlaski

The diffusion strategy for distributed learning from streaming data employs local stochastic gradient updates along with exchange of iterates over neighborhoods. In Part I [3] of this work we established that agents cluster around a network centroid and pr ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications

Florian Karl Richter

We obtain new results pertaining to convergence and recurrence of multiple ergodic averages along functions from a Hardy field. Among other things, we confirm some of the conjectures posed by Frantzikinakis in [Fra10; Fra16] and obtain combinatorial applic ...

2020

Single and multiple recurrence along non-polynomial sequences

Florian Karl Richter

We establish new recurrence and multiple recurrence results for a rather large family of non-polynomial functions which contains tempered functions and (non-polynomial) functions from a Hardy field with polynomial growth. In particular, we show that, somew ...

2020

Local-polynomial-approximation-based phase unwrapping using state space analysis

Pramod Rastogi, Rishikesh Dilip Kulkarni

A new method of phase unwrapping is proposed for the absolute phase estimation based on the first-order polynomial phase approximation within a symmetric window generated around each pixel. The accurate estimation of polynomial coefficients is performed by ...

2017

Sampling at unknown locations, with an application in surface retrieval

Martin Vetterli, Benjamin Bejar Haro, Adam James Scholefield, Michalina Wanda Pacholska

We consider the problem of sampling at unknown locations. We prove that, in this setting, if we take arbitrarily many samples of a polynomial or real bandlimited signal, it is possible to find another function in the same class, arbitrarily far away from t ...

2017

Superresolved synthetic aperture microscope

Theo Lasser, Daniel Pawel Szlag, Tomas Lukes, Adrien Charles-François Raymond Descloux

Optical system comprising a synthetic aperture generating unit; said synthetic aperture generating unit being adapted for generating several apertures, which are correlated by interference for improving contrast and/or resolution based on the interference ...

2017

Spatial fringe analysis techniques for multiple phase and phase derivative estimation

Rishikesh Dilip Kulkarni

Analysis of fringe patterns for the accurate estimation of phase and phase derivatives is of crucial importance in optical interferometry as these quantities provide important information on the physical parameters under study. A wide range of applications ...

EPFL2016

Sampling and Reconstruction of Shapes with Algebraic Boundaries

Martin Vetterli, Arash Amini, Mitra Fatemi

We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of

\mathds{1}_{\{p\leq0\}}

to the image plane, where

\mathds{1}

denotes the indicator function and

p

is some r ...

2016

Estimation of multiple phases from a single fringe pattern in digital holographic interferometry

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The multivariate Serre conjecture ring

Strictly Real Fundamental Theorem Of Algebra Using Polynomial Interlacing

Distributed Learning in Non-Convex Environments-Part II: Polynomial Escape From Saddle-Points

Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications

Single and multiple recurrence along non-polynomial sequences

Local-polynomial-approximation-based phase unwrapping using state space analysis

Sampling at unknown locations, with an application in surface retrieval

Superresolved synthetic aperture microscope

Spatial fringe analysis techniques for multiple phase and phase derivative estimation

Sampling and Reconstruction of Shapes with Algebraic Boundaries

The multivariate Serre conjecture ring

Strictly Real Fundamental Theorem Of Algebra Using Polynomial Interlacing

Spatial fringe analysis techniques for multiple phase and phase derivative estimation

Distributed Learning in Non-Convex Environments-Part II: Polynomial Escape From Saddle-Points

Single and multiple recurrence along non-polynomial sequences

Sampling at unknown locations, with an application in surface retrieval

Multiple ergodic averages along functions from a Hardy field: convergence, recurrence and combinatorial applications

Local-polynomial-approximation-based phase unwrapping using state space analysis

Sampling and Reconstruction of Shapes with Algebraic Boundaries

Superresolved synthetic aperture microscope