Deconvolution

deconvolutedeconvoluteddeconvolution problemdeconvolvedeconvolveddigital deconvolutionego-structure discoveryimage restorationzero phase
In mathematics, deconvolution is an algorithm-based process used to reverse the effects of convolution on recorded data.wikipedia
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Convolution

convolvedconvolvingconvolution kernel
In mathematics, deconvolution is an algorithm-based process used to reverse the effects of convolution on recorded data.
Computing the inverse of the convolution operation is known as deconvolution.

Wiener deconvolution

However, if we have at least some knowledge of the type of noise in the data (for example, white noise), we may be able to improve the estimate of ƒ through techniques such as Wiener deconvolution. The most common iterative algorithm for the purpose is the Richardson–Lucy deconvolution algorithm; the Wiener deconvolution (and approximations) are the most common non-iterative algorithms.
In mathematics, Wiener deconvolution is an application of the Wiener filter to the noise problems inherent in deconvolution.

Wiener filter

WienerWiener–Kolmogorov filterlinear discrete-time filters
The reflectivity may be recovered by designing and applying a Wiener filter that shapes the estimated wavelet to a Dirac delta function (i.e., a spike).
This filter is frequently used in the process of deconvolution; for this application, see Wiener deconvolution.

Reflection seismology

seismic reflectionseismic explorationseismic survey
The concept of deconvolution had an early application in reflection seismology.
There are three main processes in seismic data processing: deconvolution, common-midpoint (CMP) stacking and migration.

Blind deconvolution

This procedure is called blind deconvolution.
In electrical engineering and applied mathematics, blind deconvolution is deconvolution without explicit knowledge of the impulse response function used in the convolution.

Point spread function

PSFpoint-spread functionhere
The usual method is to assume that the optical path through the instrument is optically perfect, convolved with a point spread function (PSF), that is, a mathematical function that describes the distortion in terms of the pathway a theoretical point source of light (or other waves) takes through the instrument.
In microscope image processing and astronomy, knowing the PSF of the measuring device is very important for restoring the (original) object with deconvolution.

Hubble Space Telescope

HubbleHSTHubble Telescope
Early Hubble Space Telescope images were distorted by a flawed mirror and were sharpened by deconvolution.
The error was well characterized and stable, enabling astronomers to partially compensate for the defective mirror by using sophisticated image processing techniques such as deconvolution.

CLEAN (algorithm)

CLEANCLEAN algorithmHögbom CLEAN algorithm
A commonly used method is the CLEAN algorithm.
The CLEAN algorithm is a computational algorithm to perform a deconvolution on images created in radio astronomy.

Microscope image processing

microscopy
It is usually done in the digital domain by a software algorithm, as part of a suite of microscope image processing techniques.
This process is called deconvolution, and a variety of algorithms have been developed, some of great mathematical complexity.

Unsharp masking

unsharp masksharpeningimage sharpening
*Unsharp masking
For image processing, deconvolution is the process of approximately inverting the process that caused an image to be blurred.

Digital room correction

room correctionroom correction technologyroom optimization

Deblurring

image deblurringFocus recovery
By proper deconvolution of the point spread function K and the blurred image B, the blurred image B can be deblurred (unblur) and the sharp image S can be recovered.

Richardson–Lucy deconvolution

The most common iterative algorithm for the purpose is the Richardson–Lucy deconvolution algorithm; the Wiener deconvolution (and approximations) are the most common non-iterative algorithms.
* Deconvolution

Mathematics

mathematicalmathmathematician
In mathematics, deconvolution is an algorithm-based process used to reverse the effects of convolution on recorded data.

Algorithm

algorithmsalgorithm designcomputer algorithm
In mathematics, deconvolution is an algorithm-based process used to reverse the effects of convolution on recorded data. It is usually done in the digital domain by a software algorithm, as part of a suite of microscope image processing techniques.

Signal processing

signal analysissignalsignal processor
The concept of deconvolution is widely used in the techniques of signal processing and image processing.

Digital image processing

image processingimageprocessing
The concept of deconvolution is widely used in the techniques of signal processing and image processing.

Science

scientificsciencesscientific knowledge
Because these techniques are in turn widely used in many scientific and engineering disciplines, deconvolution finds many applications.

Engineering

engineerengineersengineered
Because these techniques are in turn widely used in many scientific and engineering disciplines, deconvolution finds many applications.

Transfer function

transfertransfer characteristicchannel transfer function
The function g might represent the transfer function of an instrument or a driving force that was applied to a physical system.

Statistics

statisticalstatistical analysisstatistician
This is most often done using methods of statistical estimation.

Estimation theory

parameter estimationestimationestimated
This is most often done using methods of statistical estimation.

Noise (electronics)

noiseelectronic noiseelectrical noise
In this case ε is noise that has entered our recorded signal.

Signal-to-noise ratio

signal to noise ratioSNRsignal-to-noise
The lower the signal-to-noise ratio, the worse our estimate of the deconvolved signal will be.

Inverse filter

That is the reason why inverse filtering the signal is usually not a good solution.