the result of some other desired blur tensor b d operating on the physical process calling the desired result d i e d b d p we attempt to estimate d from m by multiplying m by a reconstruction tensor t i e d tm we have discovered that it is possible to solve this multidimensional problem to do so we have developed a way of constructing a reconstruction tensor for such problems moreover if the blur function has particular properties there is a practical way of solving the problem i e it is possible to construct a fast algorithm for solving the problem we have discovered and it can be shown that we can apply much of what is true about statistical operations on matrices to the multidimensional tensors that are defined as described herein that is everything generalizes to these multidimensional objects thus we construct t in such a way as to minimize the expected mean square error between the estimate of d and d itself to do so we construct a performance index j is the expected sum of squares of the reconstruction error a reconstruction tensor t that minimizes j will produce the smallest expected mean squared error of reconstruction hence we elect to solve the problem of minimizing j over t the gradient of j with respect to t will be 0 at a minimum or.