## 1 Introduction  
As a new paradigm first proposed in the mid-1990s, computational imaging transfers the burden of image formation from solely optical physics to both front-end measurements and post-detection processing, providing a desired imaging capability with reduced requirements in size, weight, power or cost [1]. A key feature of this paradigm is indirect measurements of probed objects, as opposed to direct ones in conventional approaches. Inspired by this feature, MCI illuminates the object with incoherent measurement modes, encoding spatial information into multiple measurements. Given the forward radiation model, the object is then retrieved from the echoes by post processing. Essentially, MCI transfers the complexity of microwave imaging systems from hardware to modelling and algorithms, thus enabling huge flexibility in modalities and avoiding the dependence on mechanical movements and antenna apertures that are densely populated with complex electronic components. In recent years, the emergence of electromagnetic metamaterials, which possesses unprecedented ability in the control of electromagnetic fields and thus greatly caters for the need of generating incoherent modes, has immensely promoted relevant research on MCI and made this paradigm one of the most popular topics in the field of microwave imaging [2; 3; 4; 5]. Mathematically, MCI solves a nonlinear Fredholm integral equation of the first kind, which belongs to a typical category of inverse problems [6]. In discrete form, the integral equation can be rewritten as a matrix equation in which the measurement modes in the measurements composes a measurement matrix. According to Reference [7], the integral (i.e., the measurement matrix) functions as a transformation from the space of the object, to the measurement space which is spanned by independent measurement modes. The imaging of the object, that is, the inverse of the transformation, naturally possesses nonlinear, ill-posed and instable characteristics, making it difficult to reconstruct from the echoes in the presence of noise [6; 8]. In order to ameliorate these ill conditions, it is crucial to enlarge the number of effective bases. In addition, some researchers demonstrated that the square of the spatial resolution is usually equal to the ratio of the image area to the number of independent modes [7]. The aim of enlarging the number of independent bases necessitates the minimization of the mutual coherences in the measurement matrix. Since the measurement modes are synthesized by antennas, the antenna optimization for the coherence minimization has become a research focus. According to Reference [9], in order to reduce the mutual coherences, an interesting option is to construct the modes as independent and identically distributed as random variables. Thus various antenna structures have been proposed for MCI by intuitively randomizing resonant cavity structures or element resonant properties, such as mode-mixing cavity [10], printed aperiodic cavity with irises distributed in a Fibonacci pattern [11], disordered cavity with dynamically tuneable impedance source [12] and printed metasurface with subwavelength metallic cylinders in the cavity [13]. These antennas have shown that the mutual coherences in the measurement matrix can be effectively reduced by introducing disorder and randomness in the antenna structures. However, these heuristic works do not give an explicit formulation of the coherences' formation, which burdens further theoretical analysis and optimization. For the antenna apertures assembled by elements with random resonant frequencies, it has been widely examined that the increase of the elements' quality factors leads to the decreases in both the coherences and radiation efficiency [14; 15]. However, this superficial phenomenon is still far from an explicit explanation of the mechanism underlying the generation of the coherences.