Adaptive noise cancellation and image restoration with multivariable lattice filters

This dissertation applies multivariable (multiexperiment and multichannel) least-square and gradient lattice filters in image restoration and adaptive noise cancellation (ANC). A new two-dimensional method of adaptive filtering for restoration of images based on a least-square lattice filter was used to filter and enhance the noisy gray or color images. Implementations of the adaptive noise filtering and image enhancement are considered. The results show that noise reduction has been achieved even at high input signal-to-noise ratio (SNR). Edge detection issue is also discussed. When noisy images are recovered, the edges are simultaneously figured out under the image enhancement scheme. In ANC, a new ANC algorithm was developed to reduce acoustical random noise. The ANC method implemented is described and the experimental results are demonstrated. Furthermore, a new multivariable gradient lattice algorithm for AR and FIR models is also proposed. Adaptive step sizes of this algorithm are derived according to past residual errors. Also, a transpose lattice based on the gradient lattice is developed for the multivariable ANC. Finally, the implementation and comparison of the multivariable ANC by using these lattice filters to achieve the global control are discussed.