In this work we propose a fronthaul compression scheme for distributed MIMO systems with multi-antenna receivers, in which, prior to signal quantisation, dimension reduction is performed at each receiver by matched filtering the received signal with a subset of the local user channel vectors. By choosing these matched filter vectors based on global channel information, a high proportion of the potential capacity may be captured by a small number of signal components, which can then be compressed efficiently using local signal compression. We outline a greedy algorithm for selecting the matched filtering vectors for each receiver, and a local transform coding approach for quantising them, giving expressions for the resulting system sum and user capacities. We then show that the scheme is easily modified to account for imperfect CSI at the receivers. Numerical results show that with a low signal dimension the scheme is able to operate very close to the cut-set bound in the fronthaul-limited regime, and demonstrates significant improvements in rate-capacity trade-off versus local compression at all operating points, particularly at high SNR.