This paper introduces the vector sparse matrix transform (vector SMT), a new decorrelating transform suitable for performing distributed processing of high-dimensional signals in sensor networks. We assume that each sensor in the network encodes its measurements into vector outputs instead of scalar ones. The proposed transform decorrelates a sequence of pairs of vector outputs, until these vectors are decorrelated. In our experiments, we simulate distributed anomaly detection by a network of cameras, monitoring a spatial region. Each camera records an image of the monitored environment from its particular viewpoint and outputs a vector encoding the image. Our results, with both artificial and real data, show that the proposed vector SMT transform effectively decorrelates image measurements from the multiple cameras in the network while maintaining low overall communication energy consumption. Since it enables joint processing of the multiple vector outputs, our method provides significant improvements to anomaly detection accuracy when compared with the baseline case when the images are processed independently.