In mathematics,<unk>  is an algorithm-based process used to reverse the effects of convolution on recorded data. The concept of<unk>  is widely used in the techniques of signal processing and image processing.  Since these techniques are in turn widely used in many scientific and engineering disciplines,<unk>  finds many applications.
In general, the object of<unk>  is to find the solution of a convolution equation of the form:
Usually, 
h
{\displaystyle h}
 is some recorded signal, and 
f
{\displaystyle f}
 is some signal that we wish to recover, but has been convolved with some other signal 
g
{\displaystyle g}
 before we recorded it.  The function 
g
{\displaystyle g}
 might represent the transfer function of an instrument or a driving force that was applied to a physical system.  If we know 
g
{\displaystyle g}
, or at least know the form of 
g
{\displaystyle g}
, then we can perform deterministic<unk> .  However, if we do not know 
g
{\displaystyle g}
 in advance, then we need to estimate it.  This is most often done using methods of statistical estimation[citation needed].
In physical measurements, the situation is usually closer to
In this case 
ϵ
{\displaystyle \epsilon }
 is noise that has entered our recorded signal.  If we assume that a noisy signal or image is noiseless when we try to make a statistical estimate of 
g
{\displaystyle g}
, our estimate will be incorrect.  In turn, our estimate of 
f
{\displaystyle f}
 will also be incorrect.  The lower the signal-to-noise ratio, the poorer our estimate of the deconvolved signal will be. That is the reason why usually inverse filtering the signal is not a good solution. 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 
f
{\displaystyle f}
 through techniques such as Wiener<unk> .
The foundations for<unk>  and time-series analysis were largely laid by Norbert Wiener of the Massachusetts Institute of Technology in his book Extrapolation, Interpolation, and Smoothing of Stationary Time Series (1949).  The book was based on work Wiener had done during World War II but that had been classified at the time.  Some of the early attempts to apply these theories were in the fields of weather forecasting and economics.
Deconvolution
Transactivation
Mixture
Sublimation 
Amplification 
Mutualism
Induction 
Pronunciation