In our previous work, a two-phase multiobjective 1 sparse unmixing approach (Tp-MoSU) has been proposed, which 2 settled the regularization parameter issues of the regularization 3 unmixing methods. However, Tp-MoSU has limited performance 4 in identifying the real endmembers from the highly noisy data in 5 the first phase and cannot effectively exploit the spatial-contextual 6 information in the second phase because of the similarity measure 7 it used. To settle these two problems, a composite spectral 8 similarity (CSS) measure is firstly constructed by fusing the 9 spectral correlation angle (SCA) and the Euclidean distance. 10 It is used instead of the Frobenius norm (F -norm) to measure 11 the unmixing residuals in the first phase because it considers 12 both the shape and amplitude discrepancy between two spectra 13 simultaneously. Then, the L2,∞ norm is used instead of the l2 14 norm to measure the unmixing residuals in the second phase, 15 and the initialization, recombination, mutation and local search 16 strategies are also elaborately redesigned to help reduce this 17 new objective, based on which the unmixing tasks of all pixels 18 in a hyperspectral image can be completed at once. Therefore, this new measure facilitates the estimation of the abundances 20 as a whole, and thus the spatial-contextual information can be 21 better exploited to improve the estimated abundances. Besides, 22 the time efficiency for abundance estimation is also greatly 23 improved. Experimental results demonstrate that the proposed 24 method (termed as Tp-MoSU+) outperforms Tp-MoSU in both of the two phases under heavy noise, and outperforms the tested 26 regularization algorithms in estimating the abundances. 27 Index Terms-Multiobjective sparse unmixing, highly noisy 28 data, composite spectral similarity measure, L2,∞ norm, spatial-29 contextual information, time efficiency. 30 I. INTRODUCTION 31 Hyperspectral imaging is currently able to acquire tens to 32 hundreds of contiguous spectral bands which provide much 33 more information about a scene than the spaced spectral bands 34 obtained by multispectral imaging, not to mention the RGB 35 image which contains only three bands [1]. This attribute 36 facilitates the identification and classification of objects [2, 3], 37 and the analysis of potential substances in hyperspectral scene 38 via the spectroscopic technique. Thus, hyperspectral image has 39 been widely used in the environmental monitoring [4], mineral 40