# Tomographic reconstruction using nonseparable wavelets

@article{Bonnet2000TomographicRU, title={Tomographic reconstruction using nonseparable wavelets}, author={St{\'e}phane Bonnet and Françoise Peyrin and Francis Turjman and R{\'e}my Prost}, journal={IEEE transactions on image processing : a publication of the IEEE Signal Processing Society}, year={2000}, volume={9 8}, pages={ 1445-50 } }

In this paper, the use of nonseparable wavelets for tomographic reconstruction is investigated. Local tomography is also presented. The algorithm computes both the quincunx approximation and detail coefficients of a function from its projections. Simulation results showed that nonseparable wavelets provide a reconstruction improvement versus separable wavelets.

## 30 Citations

### FBP and the interior problem in 2D tomography

- Mathematics2011 IEEE Nuclear Science Symposium Conference Record
- 2011

We consider the Filtered Back Projection reconstruction method in the case of interior data in Computerized Tomography. In this framework we prove that the difference between the FBP reconstruction…

### Nonseparable wavelet-based cone-beam reconstruction in 3-D rotational angiography

- PhysicsIEEE Transactions on Medical Imaging
- 2003

A fast low-resolution reconstruction of the 3-D arterial vessels with the progressive addition of details in a region of interest is demonstrated and the improvement of image quality by denoising techniques and also the reduction of computing time using the space localization of wavelets.

### Multiresolution reconstruction in fan-beam tomography

- Mathematics2000 IEEE Nuclear Science Symposium. Conference Record (Cat. No.00CH37149)
- 2000

Simulations on mathematical phantoms show that wavelet decomposition is acceptable for small beam angles but deteriorates at high angles, and an approximate reconstruction formula based on a near-radial quincunx multiresolution scheme is proposed.

### A wavelet algorithm for zoom-in tomography

- Mathematics2010 IEEE International Symposium on Biomedical Imaging: From Nano to Macro
- 2010

The proposed algorithm for combining the two data sets using the discrete wavelet transform and the Haar wavelet is compared to a previously reported method that involves padding of the high resolution data with a supersampled version of the low resolution data, and to zero padding and edge extension, using synthetic data sets.

### Filtered backprojection method and the interior problem in 2D tomography

- Mathematics
- 2009

We address here the interior problem in local tomography, by means of Filtered Back Projection (FBP). This algorithm, traditionally used in the context of complete data, is usually not considered as…

### Multiresolution local tomography in dental radiology using wavelets

- Mathematics2007 29th Annual International Conference of the IEEE Engineering in Medicine and Biology Society
- 2007

The proposed wavelet-based multiresolution method is used to reduce the number of unknowns in the reconstruction problem by abandoning fine-scale wavelets outside the region of interest (ROI).

### Practical error estimation in zoom-in and truncated tomography reconstructions.

- MathematicsThe Review of scientific instruments
- 2007

This article uses existing theoretical results to estimate the error present in truncated and zoom-in tomographic reconstructions and proposes a practical method for estimating the error in Zoom-in and truncated tomographies.

### Bayesian multiresolution method for local tomography in dental x-ray imaging

- MathematicsPhysics in medicine and biology
- 2007

Compared to traditional voxel-based models, this multiresolution approach allows significant reduction of degrees of freedom without loss of accuracy inside the ROI, as shown by 2D examples using simulated and in vitro local tomography data.

### Region‐of‐interest tomography using filtered backprojection: assessing the practical limits

- MathematicsJournal of microscopy
- 2011

It is found that for a wide range of objects the effect of truncation on feature detection is negligible and that excellent images can be reconstructed if the number of projections is calculated not on the basis of the numbers of pixels on the camera, but on thenumber of pixels that would be required to scan the whole sample at the chosen pixel resolution.

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