无需存储完整矩阵，按需生成特定哈达玛行，节省内存。
Hadamard Row-Wise Generation Algorithm
- 基于二进制索引与克罗内克积，动态构造目标行
- 生成单行仅需常数时间与空间，不存储全矩阵
- 适用于单像素成像等只需逐行读取的系统
本文提出一种高效算法，用于按需生成特定的哈达玛行，解决预先计算整个矩阵带来的内存压力。利用西尔维斯特的递归构造方法，该算法通过索引的二进制表示，结合克罗内克积，直接构造所需第 i 行，无需构建完整矩阵。该方法显著降低计算资源消耗，特别适用于仅需逐行访问的单像素成像系统。
原文摘要 · Abstract (English)
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.
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