Anja Borsdorf

Wavelet Based Noise Reduction in CT-Images Using Correlation Analysis

The projection data measured in computed tomography (CT) and, consequently, the slices reconstructed from these data are noisy. We present a new wavelet based structure-preserving method for noise reduction in CT-images that can be used in combination with different reconstruction methods. The approach is based on the assumption that data can be decomposed into information and temporally uncorrelated noise. In CT two spatially identical images can be generated by reconstructions from disjoint subsets of projections: using the latest generation dual source CT-scanners one image can be reconstructed from the projections acquired at the first, the other image from the projections acquired at the second detector. For standard CT-scanners the two images can be generated by splitting up the set of projections into even and odd numbered projections. The resulting images show the same information but differ with respect to image noise. The analysis of correlations between the wavelet representations of the input images allows separating information from noise down to a certain signal-to-noise level. Wavelet coefficients with small correlation are suppressed, while those with high correlations are assumed to represent structures and are preserved. The final noise-suppressed image is reconstructed from the averaged and weighted wavelet coefficients of the input images. The proposed method is robust, of low complexity and adapts itself to the noise in the images. The quantitative and qualitative evaluation based on phantom as well as real clinical data showed, that high noise reduction rates of around 40% can be achieved without noticeable loss of image resolution.

Wavelet denoising of multiframe optical coherence tomography data

We introduce a novel speckle noise reduction algorithm for OCT images. Contrary to present approaches, the algorithm does not rely on simple averaging of multiple image frames or denoising on the final averaged image. Instead it uses wavelet decompositions of the single frames for a local noise and structure estimation. Based on this analysis, the wavelet detail coefficients are weighted, averaged and reconstructed. At a signal-to-noise gain at about 100% we observe only a minor sharpness decrease, as measured by a full-width-half-maximum reduction of 10.5%. While a similar signal-to-noise gain would require averaging of 29 frames, we achieve this result using only 8 frames as input to the algorithm. A possible application of the proposed algorithm is preprocessing in retinal structure segmentation algorithms, to allow a better differentiation between real tissue information and unwanted speckle noise.

Wavelet based noise reduction by identification of correlations

In this paper we present a novel wavelet based method for edge preserving noise reduction. In contrast to most common methods, the algorithm introduced here does not work on single input data. It takes two or more spatially identical images, which are both impaired by noise. Assuming the statistical independence of noise in the different images, correlation computations can be used in order to preserve structures while reducing noise. Different methods for correlation analysis have been investigated, on the one hand based directly on the original input images and on the other hand taking into account the wavelet representation of the input data. The presented approach proves to be suited for the application in computed tomography, where high noise reduction rates of approximately 50% can be achieved without loss of structure information.

Analytic noise-propagation in indirect fan-beam FBP reconstruction

Precise knowledge of the local image noise is an essential ingredient to efficient application of post-processing methods such as wavelet or diffusion filtering to computed tomography (CT) images. The non-stationary, object dependent nature of noise in CT images is a direct result from the noise present in the projection data. Since quantum and electronics noise are the dominating noise sources, comparably simple models can be used for direct noise estimates in the individual projections. In this article, we describe the analytic propagation of these noise estimates through fan-beam filtered backprojection (FBP) reconstruction. Contrary to earlier publications in this field, we include the correlations within the parallel projections resulting from the rebinning, the convolution, and the backprojection processes. The method has been validated against Monte-Carlo results and good accuracy with an average relative error below 3.6% was acchieved for arbitrary objects and over the full range of commonly used convolution kernels and field-of-view settings.

Analytic noise propagation for anisotropic denoising of CT images

In X-ray Computed Tomography (CT) the measured projections and consequently the reconstructed CT images are subject to quantum and electronics noise. While noise in the projections can be well described and estimated with a corresponding physics model, the distribution of noise in the reconstructed CT images is not directly evident. Due to attenuation variations along different directions, the nature of noise in CT images is non-stationary and directed. This complicates the direct application of standard post-processing methods like bilateral filtering. In this article we describe a possibility to compute precise orientation dependent noise estimates for every pixel position. This is done by analytic propagation of projection noise estimates through indirect fan-beam filtered backprojection reconstruction. The resulting orientation dependent image noise estimates are subsequently used in adaptive bilateral filters. Taking into account the non-stationary and non-isotropic nature of noise in CT images, an average improvement in SNR of about 60% is achieved compared to linear filtering at the same resolution.

Local orientation-dependent noise propagation for anisotropic denoising of CT-images

In X-ray Computed Tomography (CT) the measured projections and consequently the reconstructed CT images are subject to quantum and electronics noise. While noise in the projections can be well described and estimated with a corresponding physics model, the distribution of noise in the reconstructed CT images is not directly evident. Due to attenuation variations along different directions, the nature of noise in CT images is non-stationary and non-isotropic. This complicates the direct application of standard post-processing methods like bilateral filtering. In this article we describe a possibility to compute precise orientation dependent noise estimates for every pixel position. This is done by analytic propagation of projection noise estimates through indirect fan-beam filtered backprojection reconstruction. The resulting orientation dependent image noise estimates are subsequently used in adaptive bilateral filters. Taking into account the non-stationary and non-isotropic nature of noise in CT images, a reduction in image noise of about 55% compared to 39% of the standard approach is achieved with much less variability over different image regions.

Multiple CT-reconstructions for locally adaptive anisotropic wavelet denoising

Objective: The signal-to-noise ratio in computed tomography (CT) data should be improved by using adaptive noise estimation for level-dependent threshold determination in the wavelet domain.Method: The projection data measured in CT and, thus, the slices reconstructed from these data are noisy. For a reliable diagnosis and subsequent image processing, like segmentation, the ratio between relevant tissue contrasts and the noise amplitude must be sufficiently large. By separate reconstructions from disjoint subsets of projections, e.g. even and odd numbered projections, two CT volumes can be computed, which only differ with respect to noise. We show that these images allow a position and orientation adaptive noise estimation for level-dependent threshold determination in the wavelet domain. The computed thresholds are applied to the averaged wavelet coefficients of the input data.Results: The final result contains data from the complete set of projections, but shows approximately 50% improvement in signal-to-noise ratio.Conclusions: The proposed noise reduction method adapts itself to the noise power in the images and allows for the reduction of spatially varying and oriented noise.

Edge-Preserving Denoising for Segmentation in CT-images

In the clinical environment the segmentation of organs is an increasingly important application and used, for example, to restrict the perfusion analysis to a certain organ. In order to automate the time-consuming segmentation process denoising techniques are required, which can simultaneously remove the locally varying and oriented noise in computed tomography (CT) images and preserve edges of relevant structures. We analyze the suitability of different edge-preserving noise reduction methods to be used as a pre-processing step for Geodesic Active Contours (GAC) segmentation. Two popular methods, bilateral filtering and anisotropic diffusion, are compared to a wavelet-based approach, which is adjusted to the CT-specific noise characteristics. We show that robust segmentation results for different organs at varying noise levels can only be achieved using the wavelet-based denoising. Furthermore, the optimal selection of parameters for the bilateral filter and the anisotropic diffusion is highly dependent on the dataset and the segmentation task.

Separate CT-reconstruction for 3D wavelet based noise reduction using correlation analysis

The projection data measured in computed tomography (CT) and, consequently, the volumes reconstructed from these data contain noise. For a reliable diagnosis and subsequent image processing, like segmentation, the ratio between relevant tissue contrasts and the noise amplitude must be sufficiently large. We propose a novel 3D wavelet based method for structure- preserving noise reduction in CT. By separate reconstructions from disjoint subsets of projections, two volumes can be computed, which only differ with respect to noise. Two disjoint subsets of projections can be directly acquired using a dual- source CT-scanner. Otherwise, the two volumes can be generated by reconstructing even and odd numbered projections separately. Correlation analysis between the approximation coefficients of the two input datasets, combined with an orientation and position dependent noise estimation are used for differentiating between structure and noise at each level of the wavelet decomposition. The proposed method adapts itself to the locally varying noise power and allows an anisotropic denoising. The quantitative and qualitative evaluation on phantom and clinical data showed that noise reduction rates up to 60% can be achieved without noticeable loss of resolution.