In support of applications involving multiview sources in distributed object recognition using lightweight cameras, we propose a new method for the distributed coding of sparse sources as visual descriptor histograms extracted from multiview images. The problem is challenging due to the computational and energy constraints at each camera as well as the limitations regarding inter-camera communication. Our approach addresses these challenges by exploiting the sparsity of the visual descriptor histograms as well as their intra- and inter-camera correlations. Our method couples distributed source coding of the sparse sources with a new joint recovery algorithm that incorporates multiple side information signals, where prior knowledge (low quality) of all the sparse sources is initially sent to exploit their correlations. Experimental evaluation using the histograms of shift-invariant feature transform (SIFT) descriptors extracted from multiview images shows that our method leads to bit-rate saving of up to 43% compared to the state-of-the-art distributed compressed sensing method with independent encoding of the sources.