Wavelets are a powerful tool for planar image processing. The resulting algorithms are straightforward, fast, and efficient. With the recently developed spherical wavelets this framework can be transposed to spherical textures. We describe a class of processing operators which are diagonal in the wavelet basis and which can be used for smoothing and enhancement. Since the wavelets (filters) are...

High Angular Resolution Diffusion Imaging (HARDI) demands a higher amount of data measurements compared to Diffusion Tensor Imaging (DTI), restricting its use in practice. We propose to represent the probabilistic Orientation Distribution Function (ODF) in the frame of Spherical Wavelets (SW), where it is highly sparse. From a reduced subset of measurements (nearly four times less than the stan...

We discuss Spherical Needlets and their properties. Needlets are a form of spherical wavelets which do not rely on any kind of tangent plane approximation and enjoy good localization properties in both pixel and harmonic space; moreover needlets coefficients are asymptotically uncorrelated at any fixed angular distance, which makes their use in statistical procedures very promising. In view of ...

This paper presents a novel wavelet-based denoising and compression statistical model for 3D hippocampus shapes. Shapes are encoded using spherical wavelets and the objective is to remove noisy coefficients while keeping significant shape information. To do so, we develop a non-linear wavelet shrinkage model based on a data-driven Bayesian framework. We threshold wavelet coefficients by locally...

We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially decaying tails. We show that, for random fields on the sphere, the needlet coefficients are asymptotically uncorrelated for any fixed angular distance. This pro...

This paper deals with Szegö type limits for multiplication operators on L(R) with respect to Haar orthonormal basis. Similar studies have been carried out by Morrison for multiplication operators Tf using Walsh System and Legendre polynomials [14]. Unlike the Walsh and Fourier basis functions, the Haar basis functions are local in nature. It is observed that Szegö type limit exist for a class o...

Our concern is with the construction of a frame in L 2 (S) consisting of smooth functions based on kernels of spherical harmonics. The corresponding decomposition and reconstruction algorithms utilize discrete spherical Fourier transforms. Numerical examples connrm the theoretical expectations. x1. Introduction Traditionally, wavelets were tailored to problems on the Euclidean space IR d. Howev...

In this paper we establish a multiscale approximation for random fields on the sphere using spherical needlets — a class of spherical wavelets. We prove that the semidiscrete needlet decomposition converges in mean and pointwise senses for weakly isotropic random fields on Sd, d ≥ 2. For numerical implementation, we construct a fully discrete needlet approximation of a smooth 2-weakly isotropic...