Lecture

Fourier Filtering

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In course

BIO-695: Image Processing for Life Science

Registration details will be announced via email. It takes place yearly from Sept./October to December & intends to teach image processing with a strong emphasis of applications in life sciences. The idea is to enable the participants to solve image-proces ...

Description

This lecture introduces Fourier filtering, focusing on understanding the principles behind it rather than the mathematical details. It covers the concept of representing signals using sine waves, explores applications in biological images, and demonstrates how Fourier methods can be applied in Fiji software. The lecture explains how Fourier transforms can be used to enhance desired elements in an image while reducing unwanted components, showcasing practical examples such as removing background gradients and shadows in microscopy. It also demonstrates the process of creating filters in the Fourier domain to manipulate images and highlights the efficiency of Fast Fourier Transform (FFT) in digital image processing.

In MOOC

Image Processing and Analysis for Life Scientists

Nowadays, image-based methods are indispensable for life scientists. Light microscopy especially, has evolved from sketched out observations by eye, to high throughput multi-plane, multi-channel, multi-position and multimode acquisitions that easily produce thousands of information-rich images that must be quantified somehow to answer biological questions. This course will teach you core concepts from image acquisition to image filtering and segmentation, to help you tackle simple image analysis workflows

Instructors (4)

Nicolas René Chiaruttini

Olivier Burri

Expertise Development of bioimage analysis workflows and algorithms to extract quantitative data from microscopy imagesTools & Software: ImageJ/Fiji, CellProfiler, ilastik, Imaris, Arivis, Matlab, RStudio, IntelliJ, Eclipse, Jupyter NotebooksProgramming languages:Java, Groovy, JavaScript, TypeScript, PHP, Python, R, C, C , Matlab, Bash Expertise Development of bioimage analysis workflows and algorithms to extract quantitative data from microscopy imagesTools & Software: ImageJ/Fiji, CellProfiler, ilastik, I

Arne Seitz

04/1996-06/2000 Scientific co-worker at Philipps-University of Marburg, Dep. of Physical Chemistry 07/2000-10/2002 Post Doc at Max-Planck Unit for Structural Molecular Biology in Hamburg 11/2002-11/2005 Post Doc at European Molecular Biolohy Laboratory (EMBL), Cell Biology and Cell Biophysics Programme 11/2005-03/2009 Staff Scientist at Advanced Light Microscopy Facility, EMBL 04/2009- Head of Bioimaging and Optics platforme (BIOP), Ecole Polytechnique Fédérale de Lausanne (EPFL)

Romain Guiet

Expertise Development of BioImage Analysis workflows and algorithms to extract quantitative data from microscopy images.BioSample Preparation : in vitro cell, organoid, time-lapse, fixation, staining strategies, actin, mitochondria, fluorescent protein expressionBioImage Acquisition : Widefield, Confocal, Whole Slide Imaging, Super-resolution (SIM, STORM, STED), FRET, FRAP, FLIMBioImage Analysis: Colocalisation analysis, Deconvolution, Time-lapse , Whole Slide ImagingTools & Software: ImageJ/Fiji, QuPath, i

Official source

Quiz

Ontological neighbourhood

Information engineering

Signal processing: Fourier analysis

Related concepts (26)

Fourier analysis

In mathematics, Fourier analysis (ˈfʊrieɪ,_-iər) is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. The subject of Fourier analysis encompasses a vast spectrum of mathematics.

Fast Fourier transform

A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain (often time or space) to a representation in the frequency domain and vice versa. The DFT is obtained by decomposing a sequence of values into components of different frequencies. This operation is useful in many fields, but computing it directly from the definition is often too slow to be practical.

Discrete Fourier transform

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT (IDFT) is a Fourier series, using the DTFT samples as coefficients of complex sinusoids at the corresponding DTFT frequencies.

Discrete-time Fourier transform

In mathematics, the discrete-time Fourier transform (DTFT), also called the finite Fourier transform, is a form of Fourier analysis that is applicable to a sequence of values. The DTFT is often used to analyze samples of a continuous function. The term discrete-time refers to the fact that the transform operates on discrete data, often samples whose interval has units of time. From uniformly spaced samples it produces a function of frequency that is a periodic summation of the continuous Fourier transform of the original continuous function.

Non-uniform discrete Fourier transform

In applied mathematics, the nonuniform discrete Fourier transform (NUDFT or NDFT) of a signal is a type of Fourier transform, related to a discrete Fourier transform or discrete-time Fourier transform, but in which the input signal is not sampled at equally spaced points or frequencies (or both). It is a generalization of the shifted DFT. It has important applications in signal processing, magnetic resonance imaging, and the numerical solution of partial differential equations.

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