Bandlimited and Haar filtered back-projection reconstructions

Guédon, Jean-Pierre; Bizais, Y.

doi:10.1109/42.310874

Cited by 28 publications

(20 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the FBP literature [18], the customary rule is to use four-times over-sampling on the sinogram and twice as many angles as the size of the image along one dimension. Our experiments refines this rule and suggests similar rules for higher approximation orders.…”

Section: E Fbp: Angular Resolution Versus Sinogram Sampling Stepmentioning

confidence: 99%

“…Even though the standard implementation uses a rather rudimentary discretization-at least by modern standards, it has not been much improved over the years, except for the aspect of filter design [17]. One noteworthy exception is the work of Guédon et al who derived an optimal reconstruction filter based on a piecewise-constant model of the image [18]. Some wavelet approaches can also be viewed as multi-scale variations on FBP [19]- [21].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Discretization of the radon transform and of its inverse by spline convolutions

Horbelt

Liebling

Unser

2002

IEEE Trans. Med. Imaging

View full text Add to dashboard Cite

Abstract-We present an explicit formula for B-spline convolution kernels; these are defined as the convolution of several B-splines of variable widths and degrees . We apply our results to derive spline-convolution-based algorithms for two closely related problems: the computation of the Radon transform and of its inverse. First, we present an efficient discrete implementation of the Radon transform that is optimal in the least-squares sense. We then consider the reverse problem and introduce a new spline-convolution version of the filtered back-projection algorithm for tomographic reconstruction. In both cases, our explicit kernel formula allows for the use of high-degree splines; these offer better approximation performance than the conventional lower-degree formulations (e.g., piecewise constant or piecewise linear models). We present multiple experiments to validate our approach and to find the parameters that give the best tradeoff between image quality and computational complexity. In particular, we find that it can be computationally more efficient to increase the approximation degree than to increase the sampling rate.Index Terms-B-spline convolution kernel, computer tomography, filtered back-projection, Radon transform.

show abstract

Section: E Fbp: Angular Resolution Versus Sinogram Sampling Stepmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Discretization of the radon transform and of its inverse by spline convolutions

Horbelt

Liebling

Unser

2002

IEEE Trans. Med. Imaging

View full text Add to dashboard Cite

show abstract

“…This correspondance has been applied for the continuous and discrete Radon transforms defined into spline spaces leading to new filtered backprojection algorithms [7,8].…”

Section: Related Workmentioning

confidence: 99%

How to Obtain a Lattice Basis from a Discrete Projected Space

Normand

Servières

Guédon

2005

Discrete Geometry for Computer Imagery

View full text Add to dashboard Cite

Abstract. Euclidean spaces of dimension n are characterized in discrete spaces by the choice of lattices. The goal of this paper is to provide a simple algorithm finding a lattice onto subspaces of lower dimensions onto which these discrete spaces are projected. This first obtained by depicting a tile in a space of dimension n -1 when starting from an hypercubic grid in dimension n. Iterating this process across dimensions gives the final result. Abstract. Euclidean spaces of dimension n are characterized in discrete spaces by the choice of lattices. The goal of this paper is to provide a simple algorithm finding a lattice onto subspaces of lower dimensions onto which these discrete spaces are projected. This first obtained by depicting a tile in a space of dimension n − 1 when starting from an hypercubic grid in dimension n. Iterating this process across dimensions gives the final result.

show abstract

“…Guédon et al [1] have shown that the standard FBP could be improved by using an explicit piecewise constant model of the image with basis functions that are B-splines of degree n = 0. Here, we will use our B-spline convolution kernels to extend the approach to higher-order splines.…”

Section: Spline-based Radon Transform and Filtered Back-projectionmentioning

confidence: 99%

“…B-splines basis functions are well suited for this kind of computation [7]. In particular, they have been applied to the problems of image resizing [2], [4], [8] and to tomographic reconstruction by filtered back-projection [1], [3]. The main difficulty of the above-mentioned algorithms is that they involve the computation of inner products (or continuously-defined convolutions) of B-splines of different widths.…”

Section: Introductionmentioning

confidence: 99%

Spline kernels for continuous-space image processing

Horbelt

Munoz

Blu

et al.

2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100)

View full text Add to dashboard Cite

We present an explicit formula for spline kernels; these are defined as the convolution of several B-splines of variable widths hi and degrees ni. The spline kernels are useful for continuous signal processing algorithms that involve Bspline inner-products or the convolution of several spline basis functions. We apply our results to the derivation of spline-based algorithms for two classes of problems. The first is the resizing of images with arbitrary scaling factors. The second is the computation of the Radon transform and of its inverse; in particular, we present a new spline-based version of the filtered backprojection algorithm for tomographic reconstruction. In both cases, our explicit kernel formula allows for the use of high-degree splines; these offer better approximation performance than the conventional lower-order formulations (e.g., piecewise constant or piecewise linear models).

show abstract

Bandlimited and Haar filtered back-projection reconstructions

Cited by 28 publications

References 25 publications

Discretization of the radon transform and of its inverse by spline convolutions

Discretization of the radon transform and of its inverse by spline convolutions

How to Obtain a Lattice Basis from a Discrete Projected Space

Spline kernels for continuous-space image processing

Contact Info

Product

Resources

About