RESUMO
Multiwavelets are a new addition to the body of wavelet theory. Realizable as matrix-valued filterbanks leading to wavelet bases, multiwavelets offer simultaneous orthogonality, symmetry, and short support, which is not possible with scalar two-channel wavelet systems. After reviewing this theory, we examine the use of multiwavelets in a filterbank setting for discrete-time signal and image processing. Multiwavelets differ from scalar wavelet systems in requiring two or more input streams to the multiwavelet filterbank. We describe two methods (repeated row and approximation/deapproximation) for obtaining such a vector input stream from a one-dimensional (1-D) signal. Algorithms for symmetric extension of signals at boundaries are then developed, and naturally integrated with approximation-based preprocessing. We describe an additional algorithm for multiwavelet processing of two-dimensional (2-D) signals, two rows at a time, and develop a new family of multiwavelets (the constrained pairs) that is well-suited to this approach. This suite of novel techniques is then applied to two basic signal processing problems, denoising via wavelet-shrinkage, and data compression. After developing the approach via model problems in one dimension, we apply multiwavelet processing to images, frequently obtaining performance superior to the comparable scalar wavelet transform.
RESUMO
Uniform quantization of wavelet coefficients introduces perceptually disturbing artifacts by decreasing the visual smoothness. In this paper, the local Holder regularity is used to quantify these changes in visual smoothness. A modified uniform quantization scheme that constrains local regularity reduction is proposed. The quantizer modification is applicable to any uniform quantization scheme and requires no additional side information to be transmitted to the decoder, unlike standard deadzone quantizers. The reconstructed images show a noticeable perceptual improvement as well as an increased PSNR relative to uniform quantization.