Optimal estimation of a two-dimensional (2-D) multichannel signal ideally decorrelates the data in both channel and space and weights the resulting coefficients according to their SNR. Many scenarios exist where the required second-order signal and noise statistics are not known in which the decorrelation is difficult or expensive to calculate. An asymptotically optimal estimation scheme proposed here uses a 2-D discrete wavelet transform to approximately decorrelate the signal in space and the discrete Fourier transform to decorrelate between channels. The coefficient weighting is replaced with a wavelet-domain thresholding operation to result in an efficient estimation scheme for both stationary and nonstationary signals. In contrast to optimal estimation, this new scheme does not require second-order signal statistics, making it well suited to many applications. In addition to providing vastly improved visual quality, the new estimator typically yields signal-to-noise ratio gains 12 dB or higher for hyperspectral imagery and functional magnetic resonance images.

In this paper, we present a new wavelet-based estimator for 2-D multichannel signals. Estimation of a 2-D multichannel signal relies on the ability to decorrelate the signal in both space and channel. The new estimator we present uses a 2-D discrete wavelet transform to approximately decorrelate the signal in space, allowing for efficient estimation of both stationary and nonstationary signals. When channel correlation is unknown, but depends only on channel separation, the DFT may be utilized to decorrelate the channel efficiently. In contrast to the optimal estimation scheme, our new estimator does not require second-order signal statistics, making it well suited to many applications. In addition to providing vastly improved visual quality, the new estimator typically yields signal-to-noise ratio gains of over 12 dB.