Subspace partition weighted sum filters for image deconvolution

The previously proposed partition-based weighted sum (PWS) filters combine Vector Quantization (VQ) and linear finite impulse response (FIR) Wiener filter concepts. By partitioning the observation space and applying a tuned Wiener filter to each partition, the PWS is spatially adaptive and has been shown to perform well in noise reduction applications. In this paper, we propose the subspace PWS (SPWS) filter and evaluate the efficacy of the SPWS filter applied to the image deconvolution problem. In the SPWS filter, we project the observation vectors into a subspace using principal component analysis (PCA) for partitioning. This subspace projection can dramatically reduce the computational burden associated with the large window size PWS filters that are needed for effective image deconvolution. In some cases, performance is also enhanced due to improved partitioning.