Sari Peltonen

Gap-Filling for the High-Resolution PET Sinograms With a Dedicated DCT-Domain Filter

High-resolution positron emission tomography (PET) scanners have brought many improvements to the nuclear medicine imaging field. However, the mechanical limitations in the construction of the scanners introduced gaps between the detectors, and accordingly, to the acquired projection data. When the methods requiring full-sinogram dataset, e.g., filtered backprojection (FBP) are applied, the missing parts degrade the reconstructed images. In this study, we aim to compensate the sinograms for the missing parts, i.e., gaps. For the gap filling, we propose an iterative discrete-cosine transform (DCT) domain method with two versions: (1) with basic DCT domain filter and (2) with dedicated and gap-dependent DCT domain filter. For the testing of the methods, 2-D FBP reconstructions were applied to the gap-filled sinograms. The proposed DCT domain gap-filling method with two different filters was compared to the constrained Fourier space (CFS) method. For the quantitative analysis, we used numerical phantoms at eight different Poisson noise levels with 100 realizations. Mean-square error, bias, and variance evaluations were performed over the selected regions of interest. Only the dedicated gap-dependent DCT domain filter showed quantitative improvement in all regions, at each noise level. We also assessed the methods visually with a [11C] raclopride human brain study reconstructed by 2-D FBP after gap filling. The visual comparisons of the methods showed that the gap filling with both DCT domain filters performed better than the CFS method. The proposed technique can be used for the sinograms, not only with limited range of projections as in the high-resolution research tomograph (ECAT HRRT) PET scanner, but also with detector failure artifacts.

Nonlinear filter design: methodologies and challenges

Linear filtering techniques have serious limitations in dealing with signals that have been created or processed by a system exhibiting some degree of nonlinearity, or, in general, situations where the relevance of information cannot be specified in the frequency domain. In image processing, many of these characteristics are often present, and it is no wonder that image processing is the field where nonlinear filtering techniques have first shown clear superiority over linear filters. Since nonlinear filters are all of those filters that are not linear, there is a large variety of different filters in use, and no common theory can exist. This makes filter design challenging, and optimization is meaningful only after restricting the class. It can be done in several conceptually different ways and, in this paper, we consider these techniques and the optimization methods that go together with the particular restriction. We review polynomial and rational filter classes and the optimization of stack filters under structural constraints and statistical constraints.

Interpolation for the gap-filling of the HRRT PET sinograms by using the slices in the direction of the radial samples

The ECAT High Resolution Research Tomograph (HRRT) (CTI PET Systems, Knoxville, TN, USA) is the state-of-the-art positron emission tomography (PET) scanner in the nuclear medicine imaging field. The gantry of the HRRT PET scanner has detector-free regions. These regions between the detector blocks introduce missing parts to the acquired PET data. Without the estimation of the missing parts of the sinogram data, the methods which require full sinogram dataset give undesired results. Previously, we proposed the iterative discrete cosine transform (DCT) domain gap-filling method which gave better quantitative and visual results than the previously published gap-filling methods. The gap-filling methods published so far estimate the missing parts only on the transaxial slices while they are ignoring the information from the neighboring transaxial slices. In this study, we propose a non-iterative gap-filling method for the compensation of the HRRT PET sinogram data by using the slices in the direction of radial samples. We compared the results of this new method with the results of the improved version of the DCT domain gap-filling approach. We used 3D numerical phantom sinogram at eight different Poisson noise levels for checking the regional quantitative results. For visual assessment, we employed a [11C]-raclopride human brain study. After the missing parts were estimated, we applied 2D filtered backprojection which obligates full sinogram dataset. The results showed that the non-iterative interpolation by using the slices in the direction of radial samples gave similar results as the DCT domain data estimation method. Its simplicity and the short processing time over the DCT domain gap-filling method are the notable advantageous properties of this non-iterative gap-filling approach.

Compensation of missing wedge effects with sequential statistical reconstruction in electron tomography.

Electron tomography (ET) of biological samples is used to study the organization and the structure of the whole cell and subcellular complexes in great detail. However, projections cannot be acquired over full tilt angle range with biological samples in electron microscopy. ET image reconstruction can be considered an ill-posed problem because of this missing information. This results in artifacts, seen as the loss of three-dimensional (3D) resolution in the reconstructed images. The goal of this study was to achieve isotropic resolution with a statistical reconstruction method, sequential maximum a posteriori expectation maximization (sMAP-EM), using no prior morphological knowledge about the specimen. The missing wedge effects on sMAP-EM were examined with a synthetic cell phantom to assess the effects of noise. An experimental dataset of a multivesicular body was evaluated with a number of gold particles. An ellipsoid fitting based method was developed to realize the quantitative measures elongation and contrast in an automated, objective, and reliable way. The method statistically evaluates the sub-volumes containing gold particles randomly located in various parts of the whole volume, thus giving information about the robustness of the volume reconstruction. The quantitative results were also compared with reconstructions made with widely-used weighted backprojection and simultaneous iterative reconstruction technique methods. The results showed that the proposed sMAP-EM method significantly suppresses the effects of the missing information producing isotropic resolution. Furthermore, this method improves the contrast ratio, enhancing the applicability of further automatic and semi-automatic analysis. These improvements in ET reconstruction by sMAP-EM enable analysis of subcellular structures with higher three-dimensional resolution and contrast than conventional methods.

Output distributional influence function

When a filter is being selected for an application, it is often essential to know that the behavior of the filter does not change significantly if there are small deviations from the initial assumptions. This robustness of a filter is traditionally explored by means of the influence function (IF) and change-of-variance function (CVF). However, as these are asymptotic measures, there is uncertainty of the applicability of the obtained results to the finite-length filters used in the real-world filtering applications. We present a new method called the output distributional influence function (ODIF) that examines the robustness of the finite-length filters. The method gives most extensive information about the robustness for filters with a known output distribution function. As examples, the ODIFs for the distribution function, density function, expectation, and variance are given for the well-known mean and median filters and are interpreted in detail.

New Sinogram Filter Design Utilizing Sinusoidal Trajectories

Stackgram filtering has recently been found to be very promising way of positron emission tomography (PET) data filtering providing quantitatively better results than common radial sinogram domain filtering. Stackgrams allow separate processing of each sinusoidal trajectory signal but the practical use of stackgrams is restricted by their large size. In this paper we introduce new angular sinogram domain filters approximating the stackgram filters. The structure of these filters gives new insight into the area of sinogram filtering. The filtering results of the proposed sinogram filters are shown to be very close to the results obtained by corresponding stackgram filters and quantitatively better than results obtained by common radial sinogram filtering.

Data estimation for the ECAT HRRT sinograms by utilizing the DCT domain

The ECAT High Resolution Research Tomograph (HRRT) (CTI PET Systems, Knoxville, TN, USA) is a milestone positron emission tomography scanner in nuclear medicine imaging field. The gantry port of the HRRT is constructed by eight detector panels each of which is separated by 17 mm gaps from its neighboring detector panels. The existence of the gaps results in the missing parts in the acquired projection data. Consequently, the quantification of the reconstructed images is degraded if a method which requires complete dataset, such as Fourier rebinning or filtered backprojection (FBP), is applied without estimation of the missing data.

Robustness of nonlinear filters for image processing

In this paper we study robustness of nonlinear filters for image processing by using a recently introduced method called output distributional influence function (ODIF). Unlike the traditionally used asymptotic methods, such as the influence function and the change-of-variance function, the ODIF provides information about the robustness of finite length filters used in image processing. The ODIF is not only a good theoretical analysis tool but it can also be used in real filtering situations for selecting filters behaving as desired in the presence of contamination. The applicability of the ODIF to the real image processing tasks is validated by experiments on images. We present the ODIFs for stack and L-filters which include many of the filters useful in the image processing applications. The usefulness of the ODIF in the analysis of the robustness of different filters is demonstrated in several illustrative examples by using the ODIFs for the expectation and variance.

PET sinogram denoising by block-matching and 3D filtering

We consider the denoising of noisy positron emission tomography (PET) sinograms by sparse 3D transform domain collaborative filtering. The filtering operation is realized by block-matching and 3D (BM3D) filtering algorithm that groups similar 2D sinogram fragments into 3D groups and filters each group by collaborative filtering. This filtering jointly filters the similar blocks in the transform domain and offers a way for efficient denoising while preserving essential information of each sinogram fragment. The obtained results are compared with conventional radial filtering and stackgram filtering that utilizes an intermediate stage between sinogram and image domains, called stackgram domain. Both quantitative and qualitative comparisons show that the proposed approach to filter the sinogram with BM3D filter outperforms the other filtering methods.

Low count PET sinogram denoising

Poisson noise is characteristic of count accumulation in positron emission tomography (PET) sinograms. We consider the denoising of low count PET sinograms by the following filters: block-matching and 3D (BM3D) filter, radial filter and stackgram filter. We also study the effect of first stabilizing the sinogram noise variance with Anscombe transformation, denoising the sinogram by the three methods and finally using exact unbiased inverse transformation to get back to the original sinogram domain. Quantitative results show that for the entire image the BM3D filter outperforms the other methods, but more careful region of interest (ROI) based analysis reveals that for the ROls in the central area of the image radial filtering with arithmetic mean filter gives the best quantitative results. Anscombe transformation has beneficial effect on BM3D filtering results. For the other filters its effect is negligible.