Dimension reduction via random projections.

Direct reconstruction.

Reconstruct with prior.

You can use random projections for dimension reduction.

Such reductions preserve a lot of basic structure and

geometric properties of the original data.

The sign flip,WHT random projection can be inverted by doing

a WHT and then the same sign flip again, allowing an

approximate reconstruction of the original data.

This can be improved by having some prior knowledge of

the original data, such as sparsity or smoothness.

In this case the original data is assumed to be invarient

under a 2d binomial smoothing filter.

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