Multisensor array processing of noisy measurements has received considerable attention in many areas of signal processing. The optimal processing techniques developed so far usually assume that the signal and noise processes are at least wide sense stationary, yet a need exists for efficient, effective methods for processing nonstationary signals. Although wavelets have proven to be useful tools in dealing with certain nonstationary signals, the way in which wavelets are to be used in the multisensor setting is still an open question. Based on the structure for optimal linear estimation of nonstationary multisensor data and statistical models of spatial signal coherence, we propose a multisensor denoising algorithm that fully exploits, in a statistically optimal fashion, the additional information afforded by multisensor measurements. Under certain conditions, we show that the proposed estimator can be realized efficiently and robustly in a completely blind fashion, employing only wavelet and discrete Fourier transforms while entailing only a small loss in performance.