Generally, to apply the MUltiple SIgnal Classification (MUSIC) algorithm for the rapid imaging of small inhomogeneities, the complete elements of the multi-static response (MSR) matrix must be collected. However, in real-world applications such as microwave imaging or bistatic measurement configuration, diagonal elements of the MSR matrix are unknown. Nevertheless, it is possible to obtain imaging results using a traditional approach but theoretical reason of the applicability has not been investigated yet. In this paper, we establish mathematical structures of the imaging function of MUSIC from an MSR matrix without diagonal elements in both transverse magnetic (TM) and transverse electric (TE) polarizations. The established structures demonstrate why the shape of the location of small inhomogeneities can be retrieved via MUSIC without the diagonal elements of the MSR matrix. In addition, they reveal the intrinsic properties of imaging and the fundamental limitations. Results of numerical simulations are also provided to support the identified structures.

翻译：通常，为了应用多重信号分类（MUSIC）算法对小尺寸非均匀体进行快速成像，必须采集多静态响应（MSR）矩阵的完整元素。然而，在实际应用场景中（如微波成像或双基地测量配置），MSR矩阵的对角元素是未知的。尽管如此，仍可采用传统方法获得成像结果，但其适用性的理论依据至今尚未被深入研究。本文针对横向磁（TM）与横向电（TE）两种极化模式，建立了基于无对角元素MSR矩阵的MUSIC成像函数的数学结构。所建立的结构阐明了为何在缺失MSR矩阵对角元素的情况下，仍能通过MUSIC算法重构小尺寸非均匀体的位置形态。此外，这些结构还揭示了成像的内在特性及基本局限性。文中还给出了数值模拟结果以验证所识别的数学结构。