Hi, Alain,
How would you define Deconvolution? Anyone? I can't find a good definition on the web in regards to photography. The definitions I found are about algorithyms.
Many affronts to an image (such as imperfect focus) affect the "ideal" image as would a certain kind of filter, leading to the "injured" image.
If we run the injured image through a filter with the inverse response of the first "filter", it will nullify the effect of the original (and undesired) "filter" - restoring the original image.
The mathematical operation by which that is done is called
deconvolution.
That doesn't really define it, and in fact I won't really do that - its rather tricky.
But, for the masochists, I will try and give some insight into its significance through context.
Deconvolution
I will speak for a while about electrical signals, not images.
If we work in the "frequency domain", the effect of a filter (including an unintended one) on a signal is modeled mathematically this way:
We take the spectrum of the signal (the "plot" of the distribution of its power by frequency) and
multiply it by the frequency response of the filter. That means that for each frequency, we multiply the value of the spectrum at that frequency by the value of the filter response at that frequency. The result is the spectrum of the signal as affected by the filter - the "injured" signal if the filter is unintended.
To "back out" the effect of such a filter, we run the injured signal through a filter with the inverse response of the first filter. To model this mathematically, we take the spectrum of the (injured) signal and multiply it by the frequency response of the "inverse filter". But mathematically, this is the same as
dividing the injured signal's spectrum by the response of the original filter.
Now, if we work in the "time domain", we start with the
waveform of the original signal (not its spectrum) and
convolve it with the
time response (not frequency response) of the filter.
The process of convolution is quite tricky to define, and I won't really do that here. The important thing is that it we use it for the same thing when working in the time domain as we use
multiplication for in the frequency domain.
To remove the effect of the original filter, we can
deconvolve the injured signal by the time response of the original filter. That process is called
deconvolution.
We use it for the same thing when working in the time domain as we use
division for in the frequency domain.
Now back to photography
In photography, we are working in the "spatial domain", which is much like the time domain for electrical signals. When an ideal image is impacted by, for example, defocus blur (which is equivalent to the result of the application of a certain type of filter), the spatial variation of luminance is
convolved by the spread function of that "filter". The process is called
convolution.
To "back out" the impact of that undesirable "filter", we can take the injured image and
deconvolve it by the spread function of the "filter" (assuming we know that). That process is called
deconvolution.
Thus the name of that approach in removing (for example) the result of misfocus blur.
Best regards,
Doug