In acoustic reconstruction, the frequency range is fundamentally determined by the size of the array and the microphone density. A solution to achieve large array and/or high microphone density is to scan the object of interest by moving sequentially a small prototype array (sequential measurements). In comparison with a large array and/or high microphone density array that can acquire simultaneously all the information of the spectral matrix (including both the auto-spectral and cross-spectral parts), sequential measurements can only acquire a block diagonal spectral matrix that comprises auto-spectra of each measurement, while the cross-spectra between sequential measurement remain unknown due to the missing phase relationships between consecutive array positions. Nevertheless, this unknown cross-spectral parts are significant for a- coustic reconstruction. Thus, the problem is formulated as a spectral matrix completion problem, i.e. how to reconstruct a complete matrix by incomplete measurements? This typically requires a number of fixed refer- ences in classic methods (Conditioned Spectral Analysis, Principal Component Analysis). In this work, the case of sequential measurements without reference is dealt with, boiling down the spectral matrix completion problem to rank minimization and spatial basis projection. Subsequently, a cyclic projection(CP) algorithm is proposed in this work to find an optimal solution in the intersection between three predefined sets