Hadamard Row-Wise Generation Algorithm

TL;DR

This paper presents an efficient on-demand Hadamard row generation algorithm that reduces memory and computational costs by constructing specific rows using Sylvester's recursive method and Kronecker products, suitable for imaging systems.

Contribution

The paper introduces a novel algorithm for generating individual Hadamard rows on demand, avoiding full matrix pre-computation and optimizing resource usage.

Findings

Reduces memory usage significantly

Enables fast on-demand row generation

Applicable to single-pixel imaging systems

Abstract

In this paper, we introduce an efficient algorithm for generating specific Hadamard rows, addressing the memory demands of pre-computing the entire matrix. Leveraging Sylvester's recursive construction, our method generates the required $i$-th row on demand, significantly reducing computational resources. The algorithm uses the Kronecker product to construct the desired row from the binary representation of the index, without creating the full matrix. This approach is particularly useful for single-pixel imaging systems that need only one row at a time.