Tomographic reconstruction using nonseparable wavelets

Tomographic Reconstruction of the Ionospheric Electron Density in term of Wavelets

Ionospheric tomography is a method to investigate the ionospheric electron density in two or three dimensions. In this study, the function-based tomographic technique has been used for regional reconstruction of a 3D tomographic model of the ionospheric electron density using the GPS measurements of the Iranian Permanent GPS Network. Two-dimensional Haar wavelets and empirical orthogonal functi...

Construction of Compactly Supported Nonseparable Orthogonal Wavelets of L^2(R^n)

Construction of a class of trivariate nonseparable compactly supported wavelets with special dilation matrix

We present a method for  the construction of compactlysupported $left (begin{array}{lll}1 & 0 & -1\1 & 1 & 0 \1 &  0 & 1\end{array}right )$-wavelets  under a mild condition. Wavelets inherit thesymmetry of the corresponding scaling function and satisfies thevanishing moment condition originating in the symbols of the scalingfunction. As an application, an  example is  provided.

Projectable Multivariate Wavelets: Separable vs Nonseparable

Tensor product (separable) multivariate (bi)orthogonal wavelets have been widely used in many applications. On the other hand, non-tensor product (nonseparable) wavelets have been extensively argued in the literature to have many advantages over separable wavelets, for example, more freedom in design of nonseparable wavelets (such design is typically much more complicated and di±cult than the a...

Reconstruction of dynamic PET data using spatio-temporal wavelet l(1) regularization.

Tomographic reconstruction from PET data is an ill-posed problem that requires regularization. Recently, Daubechies et al. [1] proposed an l (1) regularization of the wavelet coefficients that can be optimized using iterative thresholding schemes. In this paper, we extend this approach for the reconstruction of dynamic (spatio-temporal) PET data. Instead of using classical wavelets in the tempo...