Signal Processing via Cross-Dimensional Projection

Abstract

Using projection between Euclidian spaces of different dimensions, the signal compression and decompression become straightforward. This encoding/decoding technique requires no preassigned measuring matrix as in compressed sensing. Moreover, in application there is no dimension or size restrictions. General formulas for encoding/decoding of any finite dimensional signals are provided. Their main properties are revealed. Particularly, it is shown that under the equivalence assumption the technique provides the best approximation with least square error.