One-bit distributed compressed sensing with partial gaussian circulant matrices

One-bit distributed compressed sensing has been widely used in multi-node networks and many other fields. Conventional approaches often employ random Gaussian measurement matrices, but these unstructured matrices demand significant memory and computational resources. To address this limitation, we propose the use of structured partial Gaussian circulant matrices. This kind of matrix facilitates faster matrix operations and permits low storage, making it more practical. To the best of our knowledge, we are the first to theoretically prove that these matrices satisfy the \(\ell _1/\ell _{2,1}\)-RIP in one-bit distributed compressed sensing. We prove that the required number of measurements under partial Gaussian circulant measurements enjoys the same order with that of Gaussian, which, however, is more computational efficient. Furthermore, numerical experiments confirm that partial Gaussian circulant matrices and random Gaussian matrices exhibit comparable reconstruction performance. Additionally, partial Gaussian circulant matrices spend less recovery time, offering higher computational efficiency.