Hadamard Row-Wise Generation Algorithm
This addresses a memory bottleneck for single-pixel imaging systems that require only one row at a time, though it is an incremental improvement on existing methods.
The paper tackles the memory-intensive problem of pre-computing entire Hadamard matrices by introducing an algorithm that generates specific rows on demand using Sylvester's recursive construction and the Kronecker product, reducing computational resources.
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.