Nonseparable wavelet-based cone-beam reconstruction in 3-d rotational angiography

Abstract

In this paper, we propose a new wavelet-based reconstruction method suited to three-dimensional (3-D) cone-beam (CB) tomography. It is derived from the Feldkamp algorithm and is valid for the same geometrical conditions. The demonstration is done in the framework of nonseparable wavelets and requires ideally radial wavelets. The proposed inversion formula yields to a filtered backprojection algorithm but the filtering step is implemented using quincunx wavelet filters. The proposed algorithm reconstructs slice by slice both the wavelet and approximation coefficients of the 3-D image directly from the CB projection data. The validity of this multiresolution approach is demonstrated on simulations from both mathematical phantoms and 3-D rotational angiography clinical data. The same quality is achieved compared with the standard Feldkamp algorithm, but in addition, the multiresolution decomposition allows to apply directly image processing techniques in the wavelet domain during the inversion process. As an example, a fast low-resolution reconstruction of the 3-D arterial vessels with the progressive addition of details in a region of interest is demonstrated. Other promising applications are the improvement of image quality by denoising techniques and also the reduction of computing time using the space localization of wavelets.

Symmetric Multivariate Wavelets

“…Another successful application of nonseparable wavelets in 3D rotational angiography is given in Ref. 5.…”

Real inline X-ray 3D CT with short cycle times for light metal casting inspection in production

“…(21r)-1 I-1'Re x . Due to the inversion formula (2), V x solves the equation 'R*V x == ex and is therefore the reconstruction kernel of the approximate inverse of the Radon transform. We conclude This inversion formula is of filtered backprojection type.…”

“…RESULTS (2) We have used a multiresolution analysis with quincunx decimation, i.e. the dilation matrix was defined.…”

“…MULTIRESOLUTION ANALYSIS Since wavelet analysis has become a powerful tool for signal and image processing, the multiresolution approach provides a solution for many practical applications. In X-ray computerized tomography algorithms for multiresolution 2D parallel beam, 20 fan-beam, and 3D cone-beam (Feldkamptype) reconstruction using tensor or quincunx wavelets were introduced in [1], [2], [3]. These reconstruction formulas are based on the strong relationship between the continuous wavelet transform and the Radon transform as mentioned in [4].…”

A survey of medical applications of 3D image analysis and computer graphics

“…In a special issue of IEEE Transactions on Medical Imaging devoted to wavelets (March 2003), applications to a large number of problems, such as brain function image analysis [30][31][32], noise elimination [33][34][35][36][37], cone-beam CT image reconstruction [38], mammography [39,40], dynamic contour models [41], and medical image compression [42][43][44], were reviewed.…”