Transform domain image restoration methods: review, comparison, and interpretation

Two families of transform domain signal restoration (denoising and deblurring) and enhancement methods well suited to processing non-stationary signals are reviewed and comprehensively compared in their different modifications in terms of their signal restoration capability and computational complexity: sliding window transform domain (SWTD) filters and wavelet (WL) based algorithms. SWTD filters work in sliding window in the domain of an orthogonal transform and, in each position of the window, nonlinearly transform window transform coefficients to generate an estimate of the central pixel of the window. As a transform, DCT has been found to be one of the most efficient in most applications. WL methods act globally and apply element-wise nonlinear transformation similar to those used in SWTD methods to the wavelet transform coefficients to generate an estimate of the output signal. The paper provides results of extensive experimental comparisons of image restoration capabilities of the methods and demonstrates that they can naturally be interpreted in a unified way as different implementations of signal sub-band decomposition with uniform (in SWTD filters) or logarithmic (for WL-methods) arrangement of signal sub-bands and element-wise processing decomposed components. As a bridge, a hybrid wavelet/sliding window processing that combines advantages of both methods is described.