In this paper we propose a new iterative thresholding algorithm for distributed compressed sensing (CS) based on a set of local cost functions referred as HALS-CS algorithm (compare with). This algorithm allows reconstructing all sources simultaneously by processing row by row of the compressed signals. Moreover, with an adaptive nonlinearly decreasing thresholding strategy, we are able to reconstruct almost perfectly sources for ill-conditioned and ill-posed problems, for example in difficult cases when the number of compressed samples is lower than four times of the number of nonzero coefficients in the signals. The extensive experimental results confirm the validity and high performance of the developed algorithm.