Multidimensional associative memory neural network to recall nearest pattern from input [image matching example]

Summary form only given. We propose a multidimensional associative memory neural network (M-D AMNN) as a generalization of a 1D AMNN. The storage performance is greatly improved by a higher dimensional formulation in the product space of multiple real Hilbert spaces. The proposed M-D AMNN recalls the nearest pattern from the input, where such a formulation implies better error correction performance. This recalling scheme is essentially realized by convex projection techniques, for example, the Dykstra method and a projection method based on the fixed point theorem. Combined with a simple technique, named the pre-amplifying technique, the proposed M-D AMNN further improves the probability of successful recall. By applying it to the recovery of grayscale images, we demonstrate the effectiveness of the proposed AMNN over a multidimensional generalization of conventional 1D AMNN based on projections onto convex sets (POCS).