This paper deals with the design of interpolating wavelets based on a variety of Lagrange functions, combined with novel signal processing techniques for digital imaging. Halfband Lagrange wavelets, B-spline Lagrange wavelets and Gaussian Lagrange (Lagrange distributed approximating functional (DAF)) wavelets are presented as specific examples of the generalized Lagrange wavelets. Our approach combines the perceptually dependent visual group normalization (VGN) technique and a softer logic masking (SLM) method. These are utilized to rescale the wavelet coefficients, remove perceptual redundancy and obtain good visual performance for digital image processing.

New wavelet techniques are designed to improve the perceptual quality of images/signal, enhance and detect the detail features in the region of interest (ROI). Distributed approximating functionals (DAFs) are used to construct a new class of smooth wavelets, which enable better signal processing performance. This paper is focused on improvements in DAF wavelet signal processing. The combined perceptual techniques (such as regularization, visual group normalization and contrast nonlinear enhancement) produce natural high-quality images based on the human vision system. The underlying technologies significantly facilitate the creation of generic signal processing and computer-aided diagnostic (CAD) systems.

New wavelet techniques are employed to improve the perceptual quality of images, and to enhance and detect the detail features in the region of interest (ROI). Distributed approximating functionals (DAFs) are used to construct a new class of interpolating wavelets, which enable better image processing performance. This paper is focused on previous improvements in DAF wavelet image processing. The combined perceptual techniques (such as visual group normalization and contrast nonlinear enhancement) produce natural high-quality images adapted to the human vision system. The underlying technologies significantly facilitate the creation of generic image processing and computer-aided diagnostic (CAD) systems.

The alpha-trimmed mean (ATM) filter is introduced and a median-weighted ATM (MWATM) filter is proposed to detect and remove impulse noise from corrupted images by combining them with a modified iterative switching scheme. It is shown that although the ATM filter may not perform better than the median filter in impulse noise removal, it is a better impulse detector. The MWATM filter is generated by set the weight of the median value in the ATM filter as a filtering parameter instead of one. Simulations show that the optimum weight of the median value does not equal to one in general. We also noticed that the iterative switching scheme used by Zhang and Wang (see Optical Engineering, vol.37, p.1275-82, 1998) is not optimized. A modified version of it is therefore proposed.

We present a novel polynomial functional neural networks using distributed approximating functional (DAF) wavelets (infinitely smooth filters in both time and frequency regimes), for signal estimation and surface fitting. The remarkable advantage of these polynomial nets is that the functional space smoothness is identical to the state space smoothness (consisting of the weighting vectors). The constrained cost energy function using optimal regularization programming endows the networks with a natural time-varying filtering feature. Theoretical analysis and an application show that the approach is extremely stable and efficient for signal processing and curve/surface fitting.