Signal Processing via Cross-Dimensional Projection

TL;DR

This paper introduces a novel signal processing method using cross-dimensional projection that simplifies compression and decompression without needing preassigned matrices, applicable to signals of any size, and offers optimal approximation properties.

Contribution

It presents a new projection-based encoding/decoding technique that eliminates the need for preassigned measurement matrices and applies universally to finite-dimensional signals.

Findings

Provides general formulas for encoding and decoding signals.

Demonstrates the technique achieves the best approximation with least square error.

Applicable to signals of any dimension or size without restrictions.

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.