论文标题
通过$ K $ -SPARSE组件分析不确定的盲目识别：RANSAC驱动的正交子空间搜索
Underdetermined Blind Identification via $k$-Sparse Component Analysis: RANSAC-driven Orthogonal Subspace Search
论文作者
论文摘要
基于源矩阵的稀疏性：稀疏组件分析（SCA）和$ k $ -SCA的稀疏性存在两个主要的方法家族（UBI）。 SCA在每次瞬间都假设一个活动源，而$ k $ -sca允许$ k $代表的各种活动源。但是，现有的$ k $ -sca方法声称通过容纳$ k $ -sparse来源来解决UBI问题，主要依靠$ 1 $ -SPARSE的来源，从而限制了它们在具有较高噪音水平的现实情况下的有效性。 在本文中，我们为UBI提出了一种有效且计算较少的方法，特别关注活动源数量等于传感器数量减去一（$ k = M-1 $）时的具有挑战性的情况。我们的方法通过使用两步方案克服了局限性：（1）估计整个空间的正交补体子空间，以及（2）识别混合向量。我们提出了一种基于革兰氏 - schmidt过程和随机样品共识（RANSAC）方法的集成算法，以解决这两个步骤。使用模拟数据的实验结果表明，与现有算法相比，我们提出的方法的卓越有效性。
Two primary families of methods exist for underdetermined blind identification (UBI) based on the sparsity of the source matrix: sparse component analysis (SCA) and $k$-SCA. SCA assumes one active source at each time instant, while $k$-SCA allows for varying numbers of active sources represented by $k$. However, existing $k$-SCA methods, which claim to solve UBI problems by accommodating $k$-sparse sources, predominantly rely on $1$-sparse sources, limiting their effectiveness in real-world scenarios with high noise levels. In this paper, we propose an effective and computationally less complex approach for UBI, specifically focusing on the challenging case when the number of active sources is equal to the number of sensors minus one ($k=m-1$). Our approach overcomes limitations by using a two-step scenario: (1) estimating the orthogonal complement subspaces of the overall space and (2) identifying the mixing vectors. We present an integrated algorithm based on the Gram-Schmidt process and random sample consensus (RANSAC) method to solve both steps. Experimental results using simulated data demonstrate the superior effectiveness of our proposed method compared to existing algorithms.
