You have to invert the convolution kernel.
Regard the data and kernel (averaging scheme) as polynomials. Let N
be the number of data items. Then find the inverse of the kernel, a
polynomial which is the truncation of the power series of %kernel to
degree N.
This is the only complications. Here's the easy case of adding 2
sucessive terms.
ppr=: +//.@(*/)
kernel=:1 1
data=:?. 10 # 100
kernelinverse=:_1^i.#data
data
94 56 8 6 85 48 66 96 76 59
kernel ppr data
94 150 64 14 91 133 114 162 172 135 59
data-:(#data) {. kernelinverse ppr kernel ppr data
1
Best wishes,
John
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