An error-correcting code is said to be locally decodable if a randomized algorithm can recover any single bit of a message by reading only a small number of symbols of a possibly corrupted encoding of the message. Katz and Trevisan (On the efficiency of local decoding procedures for error correcting codes, STOC 2000, 80–86) showed that any such code C : {0, 1}n → Σ with a decoding algorithm tha...

In this thesis, nonlinear locally adaptive techniques of noise removal and restoration are considered for image processing applications in mixed noise environments. These techniques are designed and tested for radar, ultrasound, and gray-level test images. The image observation models take into account the influence of fluctuating (additive and multiplicative) and impulsive noise as well as blu...

This thesis contains a presentation and an analysis of adaptive filtering strategies for multidimensional data. The size, shape and orientation of the filter are signal controlled and thus adapted locally to each neighbourhood according to a predefined model. The filter is constructed as a linear weighting of fixed oriented bandpass filters having the same shape but different orientations. The ...

We present a novel local image registration method based on adaptive filtering techniques. The proposed method utilizes an adaptive filter to track smoothly, locally varying changes in the motion field between the images. Image pixels are traversed following a scanning order established by Hilbert curves to preserve the contiguity in the 2-D image plane. We have performed experiments using both...

This paper presents a new variable step-size normalized subband adaptive filter (VSS-NSAF) algorithm. The proposed algorithm uses the prior knowledge of the system impulse response statistics and the optimal step-size vector is obtained by minimizing the mean-square deviation(MSD). In comparison with NSAF, the VSS-NSAF algorithm has faster convergence speed and lower MSD. To reduce the computa...