When studying “random” operators it is essential to be able to integrate over the Haar measure, both analytically and algorithmically. Unitary t-designs provide a method to simplify integrating polynomials of degree less than t over U(d). In particular, by replacing averages over the Haar measure by averages over a finite set, they allow applications in algorithms. We provide three equivalent d...

The efficient and discriminating feature extraction is a significant problem in pattern recognition and computer vision. This paper presents a novel Discriminating Haar (D-Haar) features for eye detection. The DHaar feature extraction starts with a Principal Component Analysis (PCA) followed by a whitening transformation on the Haar feature space. A discriminant analysis is then performed on th...

This chapter shows that combining Haar-Hilbert and Log-Gabor improves iris recognition performance leading to a less ambiguous biometric decision landscape in which the overlap between the experimental intraand interclass score distributions diminishes or even vanishes. Haar-Hilbert, Log-Gabor and combined Haar-Hilbert and Log-Gabor encoders are tested here both for single and dual iris approac...

We study nonlinear approximation in Lp(R) (0 < p < ∞, d > 1) from (a) n-term rational functions, and (b) piecewise polynomials generated by different anisotropic dyadic partitions of Rd. To characterize the rates of each such piecewise polynomial approximation we introduce a family of smoothness spaces (B-spaces) which can be viewed as an anisotropic variation of Besov spaces. We use the B-spac...

In this paper a new method of image data compression for medical images has been proposed to achieve high PSNR (Peak Signal to Noise Ratio). Image compression using Set Partitioning In Hierarchical Trees (SPIHT) transform is being compared with the other well known wavelets like Discrete Cosine Transform (DCT), Discrete Wavelet Transform (DWT), Dual Tree Complex Wavelet Transform (DTCWT) and Em...

In this work, we present a novel way of computing the continuous Haar, Fourier and cosine series coefficients of rectilinear polygons. We derive algorithms to compute the inner products with the continuous basis functions directly from the vertices of the polygons. We show that the overall computational complexity of those algorithms is lower than that of the traditional corresponding discrete ...

In certain imaging applications, the captured images are corrupted by Poisson noise. For such images, Poisson unbiased risk estimate (PURE) has been proposed as an unbiased estimator of the mean square error between the original and estimated images. By minimizing PURE, noise can be reduced. PURE was originally defined in the Haar wavelet domain. Since the wavelet functions are isotropic in eve...

Orthogonal and Symmetric Haar Wavelets on the Sphere Christian Lessig Master of Science Graduate Department of Computer Science University of Toronto 2007 The efficient representation of signals defined over spherical domains has many applications. We derive a new spherical Haar wavelet basis (SOHO) that is both orthogonal and symmetric, rebutting previous work that presumed the nonexistence of...

Many important problems in engineering and science are well-modeled by Poisson processes. In many applications it is of great interest to accurately estimate the intensities underlying observed Poisson data. In particular, this work is motivated by photon-limited imaging problems. This paper studies a new Bayesian approach to Poisson intensity estimation based on the Haar wavelet transform. It ...

Orthogonal and Symmetric Haar Wavelets on the Sphere Christian Lessig Master of Science Graduate Department of Computer Science University of Toronto 2007 The efficient representation of signals defined over spherical domains has many applications. We derive a new spherical Haar wavelet basis (SOHO) that is both orthogonal and symmetric, rebutting previous work that presumed the nonexistence of...