This paper presents a modal analysis that explores the spatially dominant coherent structures and their corresponding temporal dynamics in presence of missing data. This analysis is based on time-resolved particle image velocimetry (TR-PIV) applied to a wake-mixing layer flow [1]. A variant of the Gappy Proper Orthogonal Decomposition (POD) iterative algorithm is utilized to extract the leading coherent structures from the flow fields. Gappy POD algorithm, initially introduced in [2] and subsequently reviewed in [3, 4] has been implemented taking into account non uniformities of the recording areas and the different densities of the two phases. It is important to note that measurement locations originate from two separate PIV frames: one containing particles tracing the liquid phase, and the other the gaseous phase [5]. The Gappy POD algorithm iteratively reconstructs the flow fields by filling in the missing data, leading to the identification of dominant modes. The leading modes reveal a combination of flapping motion of the separation region and interfacial advection. The power spectral density analysis of the temporal coefficients indicates a dominant dimensionless frequency. This study provides valuable insights into the coherent structures of two-phase flow fields, enhancing our understanding of the complex interactions between gas and liquid phases in such systems. The methodology and findings have significant implications for the modeling and analysis of two-phase mixing layer, contributing to the advancement of the comprehension of this relevant class of industrial configurations.