The extraction of useful information and removal of redundant noise from data has become a major research topic in recent years. Data compression is necessary for all kinds of analysis, and the demand for efficient compression techniques has gained much attention. Digital image correlation (DIC) is a camera-based, optical measuring system, which has been widely applied in strain analysis because of the convenience of measuring displacement fields by simply selecting a region of interest. Currently, there is interest in applying such methods to engineering structures in dynamics. However, one of the major issues related to the integration of camera-based systems with dynamic measurement is the generation of huge amounts of data, typically extending to many thousands of data points, because of the requirements of high sampling rate, spatial resolution, and long duration of recording. In this study, the problem of data compression of displacement maps from 3D-DIC measurement is addressed. As a noncontact optical full-field measurement technique, 3D-DIC displacement measurement is becoming more widely applied to various kinds of dynamic issues. The research presented in this thesis attempts to apply the algorithms of sparse representation to deal with the huge amount of data acquired from 3D-DIC measurement. It aims to develop methods that have the capability of preserving nuances of displacement measurement and retaining the compactness of shape descriptor (SD) decomposition. Accordingly, two useful compression methods based upon the well-known K-SVD algorithm and compressed sensing (CS) method are developed for the purpose of a succinct and representative decomposition of displacement maps from 3D-DIC measurement. Firstly, a new algorithm is presented that addresses the need for efficiency in full-field data processing. By making use of the data itself and combining the concept of SD representation with Gram-Schmidt orthonormalisation (GSO), the number of basis functions used to represent the data can be reduced and a concise decomposition established. In both simulated and experimental cases, the compression ratios for data size and number of signals used in operational modal analysis are substantially diminished, thereby demonstrating the effectiveness of the proposed algorithm. A reduced number of new basis functions is determined for the representation of data under the condition that the reconstructed displacement map reproduces the raw measured data to within a chosen threshold of correlation coefficient. Secondly, the monitoring of an operating structure usually dealing with multiple set of data, which could pose an issue for transmission or storage and is particularly important when data acquisition is implemented with cameras, such as 3D-DIC system. Single images regularly extend to tens or even hundreds of thousands of data points and many thousands of images may be required for a single set of vibration tests. Such data must be handled efficiently for later remote reconstruction and analysis, typically OMA. It is this requirement that is addressed and solved by the integrated SD-CS method because CS alone is found to be prohibitively expensive for the processing of many thousands of camera images. Data reduction by a combination of SD decomposition and CS is applied to an industrial printed circuit board and reconstructed for OMA by l1 optimisation. This procedure is demonstrated on industrial DIC data from a partially observed printed circuit board and further significant compression, which is beyond the reduction effect provided by SD method alone, is achieved and OMA is carried out successfully on CS-recovered data. In summary, the basis-updating algorithm is a powerful tool for the adaptation of kernel functions to the data set collected by 3D-DIC displacement measurement system. The algorithm is capable of finding a representative set of shape descriptors for displacement maps from an initial basis. On the other hand, the integration of CS theory and SD method offers a new way to extract the core information from the measured data. This post-processing technique not only improves the compression ratio but also provides the possibility of structural health monitoring.