The purpose is to study qualitative and quantitative rates of image compression by using different Haar wavelet banks. The experimental results of adaptive compression are provided. The paper deals with specific examples of orthogonal Haar bases generated by multiresolution analysis. Bases consist of three piecewise constant wavelet functions with a support $[0,1] \times [0,1] $.

In our previous work, we showed empirically that independent (Haar) wavelet models were parsimonious, computationally efficient and accurate in modeling heterogeneous network traffic measured by both auto-covariance functions and buffer loss rate. We also proved analytically that such models were capable of capturing any decay rate of auto-covariance functions at large lags. But the simplicity ...

Noiselets are a family of functions completely uncompressible using Haar wavelet analysis. The resultant perfect incoherence to the Haar transform, coupled with the existence of a fast transform has resulted in their interest and use as a sampling basis in compressive sampling. We derive a recursive construction of noiselet matrices and give a short matrix-based proof of the incoherence.

A probabilistic equivalence checking method is developed based on the use of partial Haar spectral diagrams (HSDs). Partial HSDs are deened and used to represent a subset of Haar spectral coeecients for two Boolean functions. The resulting coeecients are then used to compute and to iteratively reene the probability that two functions are equivalent. This problem has applications in both logic s...

Modified sign Haar transform with sign Walsh-like structure is introduced in this article. This nonlinear transform converts binary/ternary vectors into digital spectral domain and is invertible. Recursive definitions for the calculation of this transform have been developed. The properties of logic functions and variables in the spectral domain of the modified sign Haar transform are presented.

This study deals with the 3D recovering of magnetic susceptibility model by incorporating the sparsity-based constraints in the inversion algorithm. For this purpose, the area under prospect was divided into a large number of rectangular prisms in a mesh with unknown susceptibilities. Tikhonov cost functions with two sparsity functions were used to recover the smooth parts as well as the sharp ...

Noiselets are a family of functions completely uncompressible using Haar wavelet analysis. The resultant perfect incoherence to the Haar transform, coupled with the existence of a fast transform has resulted in their interest and use as a sampling basis in compressive sampling. We derive a recursive construction of noiselet matrices and give a short matrix-based proof of the incoherence.