This task is a straightforward generalization of [[Deconvolution/1D]] to higher dimensions. For example, the one dimensional case would be applicable to audio signals, whereas two dimensions would pertain to images. Define the discrete convolution in <math>\mathit d</math> dimensions of two functions

:<math>H,F:\mathbb{Z}^d\rightarrow\mathbb{R}</math>

taking <math>\mathit d</math>-tuples of integers to real numbers as the function

:<math>G:\mathbb{Z}^d\rightarrow\mathbb{R}</math>

also taking <math>\mathit d</math>-tuples of integers to reals and satisfying

:<math>G(n_0, \dots, n_{d-1})=\sum_{m_0=-\infty}^{\infty}\dots\sum_{m_{d-1}=-\infty}^{\infty}F(m_0, \dots, m_{d-1})H(n_0-m_0, \dots, n_{d-1}-m_{d-1})</math>

for all <math>\mathit d</math>-tuples of integers <math>(n_0, \dots, n_{d-1})\in\mathbb{Z}^d</math>. Assume
<math>\mathit F</math> and <math>\mathit H</math> (and therefore <math>\mathit G</math>) are non-zero over only a finite domain bounded by the origin, hence possible to represent as finite multi-dimensional arrays or nested lists <math>\mathit f</math>, <math>\mathit h</math>, and <math>\mathit g</math>.

For this task, implement a function (or method, procedure, subroutine, etc.) <code>deconv</code> to perform ''deconvolution'' (i.e., the ''inverse'' of convolution) by solving for <math>\mathit{h}</math> given <math>\mathit{f}</math> and <math>\mathit{g}</math>. (See [[Deconvolution/1D]] for details.)
* The function should work for <math>\mathit{g}</math> of arbitrary length in each dimension (i.e., not hard coded or constant) and <math>\mathit{f}</math> of any length up to that of <math>\mathit{g}</math> in the corresponding dimension.
* The <code>deconv</code> function will need to be parameterized by the dimension <math>\mathit d</math> unless the dimension can be inferred from the data structures representing <math>\mathit g</math> and <math>\mathit f</math>.
* There may be more equations than unknowns. If convenient, use a function from a [http://www.netlib.org/lapack/lug/node27.html library] that finds the best fitting solution to an overdetermined system of linear equations (as in the [[Multiple regression]] task).  Otherwise, prune the set of equations as needed and solve as in the [[Reduced row echelon form]] task.
* Debug your solution using [http://rosettacode.org/mw/index.php?title=Deconvolution/2D%2B/Test_data&action=raw this test data], of which a portion is shown below. Be sure to verify both that the deconvolution of <math>\mathit g</math> with <math>\mathit f</math> is <math>\mathit h</math> and that the deconvolution of <math>\mathit g</math> with <math>\mathit h</math> is <math>\mathit f</math>. Display the results in a human readable form for the three dimensional case ''only''.

dimension 1:
<pre>
h: [-8, 2, -9, -2, 9, -8, -2]
f: [ 6, -9, -7, -5]
g: [-48, 84, -16, 95, 125, -70, 7, 29, 54, 10]
</pre>
dimension 2:
<pre>
h: [
      [-8, 1, -7, -2, -9, 4],
      [4, 5, -5, 2, 7, -1],
      [-6, -3, -3, -6, 9, 5]]
f: [
      [-5, 2, -2, -6, -7],
      [9, 7, -6, 5, -7],
      [1, -1, 9, 2, -7],
      [5, 9, -9, 2, -5],
      [-8, 5, -2, 8, 5]]
g: [
      [40, -21, 53, 42, 105, 1, 87, 60, 39, -28],
      [-92, -64, 19, -167, -71, -47, 128, -109, 40, -21],
      [58, 85, -93, 37, 101, -14, 5, 37, -76, -56],
      [-90, -135, 60, -125, 68, 53, 223, 4, -36, -48],
      [78, 16, 7, -199, 156, -162, 29, 28, -103, -10],
      [-62, -89, 69, -61, 66, 193, -61, 71, -8, -30],
      [48, -6, 21, -9, -150, -22, -56, 32, 85, 25]]
</pre>
dimension 3:
<pre>
h: [
      [[-6, -8, -5, 9], [-7, 9, -6, -8], [2, -7, 9, 8]],
      [[7, 4, 4, -6], [9, 9, 4, -4], [-3, 7, -2, -3]]]
f: [
      [[-9, 5, -8], [3, 5, 1]],
      [[-1, -7, 2], [-5, -6, 6]],
      [[8, 5, 8],[-2, -6, -4]]]
g: [
      [
         [54, 42, 53, -42, 85, -72],
         [45, -170, 94, -36, 48, 73],
         [-39, 65, -112, -16, -78, -72],
         [6, -11, -6, 62, 49, 8]],
      [
         [-57, 49, -23, 52, -135, 66],
         [-23, 127, -58, -5, -118, 64],
         [87, -16, 121, 23, -41, -12],
         [-19, 29, 35, -148, -11, 45]],
      [
         [-55, -147, -146, -31, 55, 60],
         [-88, -45, -28, 46, -26, -144],
         [-12, -107, -34, 150, 249, 66],
         [11, -15, -34, 27, -78, -50]],
      [
         [56, 67, 108, 4, 2, -48],
         [58, 67, 89, 32, 32, -8],
         [-42, -31, -103, -30, -23, -8],
         [6, 4, -26, -10, 26, 12]]]
</pre>