Lesion detection in dynamic FDG-PET using matched subspace detection

Adaptive Brain Activity Detection in Structured Interference and Partially Homogeneous Locally Correlated Disturbance

OBJECTIVE

In this paper, we aim to address the problem of subspace detection in the presence of locally-correlated complex Gaussian noise and interference. For applications like brain activity detection using functional magnetic resonance imaging (fMRI) data where the noise is possibly locally correlated, using the sample covariance estimator is not a suitable choice due to significant dependency of its accuracy on the number of observations.

METHODS

In this study, we take advantage of an assumed banded structure in the covariance matrix to model the local dependence in the noise and propose a new covariance estimation approach. In particular, we use the idea of fac-torizing the joint likelihood function into a few conditional likelihood terms and maximizing each term independently of the others. This process leads to an explicit estimator for banded covariance matrices which requires fewer observations to achieve the same accuracy as the sample covari-ance. This estimate is then fed into an adaptive matched filter, two-step Rao and two-step Wald tests for detection.

RESULTS

Simulation results reveal the superiority of the proposed methods over well known classical detectors. Finally, the proposed methods are applied to functional magnetic resonance imaging (fMRI) data to localize neural activities in the brain.

CONCLUSION

The proposed method can offer better activation maps in terms of accuracy and spatial smoothness.

SIGNIFICANCE

The proposed methods can be seen as alternatives for standard detection approaches which are not perfectly aligned with the properties of fMRI data.

Kernel graph filtering-A new method for dynamic sinogram denoising

Low count PET (positron emission tomography) imaging is often desirable in clinical diagnosis and biomedical research, but its images are generally very noisy, due to the very weak signals in the sinograms used in image reconstruction. To address this issue, this paper presents a novel kernel graph filtering method for dynamic PET sinogram denoising. This method is derived from treating the dynamic sinograms as the signals on a graph, and learning the graph adaptively from the kernel principal components of the sinograms to construct a lowpass kernel graph spectrum filter. The kernel graph filter thus obtained is then used to filter the original sinogram time frames to obtain the denoised sinograms for PET image reconstruction. Extensive tests and comparisons on the simulated and real life in-vivo dynamic PET datasets show that the proposed method outperforms the existing methods in sinogram denoising and image enhancement of dynamic PET at all count levels, especially at low count, with a great potential in real life applications of dynamic PET imaging.

Relative Patlak plot for dynamic PET parametric imaging without the need for early-time input function

The Patlak graphical method is widely used in parametric imaging for modeling irreversible radiotracer kinetics in dynamic PET. The net influx rate of radiotracer can be determined from the slope of the Patlak plot. The implementation of the standard Patlak method requires the knowledge of full-time input function from the injection time until the scan end time, which presents a challenge for use in the clinic. This paper proposes a new relative Patlak plot method that does not require early-time input function and therefore can be more efficient for parametric imaging. Theoretical analysis proves that the effect of early-time input function is a constant scaling factor on the Patlak slope estimation. Thus, the parametric image of the slope of the relative Patlak plot is related to the parametric image of standard Patlak slope by a global scaling factor. This theoretical finding has been further demonstrated by computer simulation and real patient data. The study indicates that parametric imaging of the relative Patlak slope can be used as a substitute of parametric imaging of standard Patlak slope for tasks that do not require absolute quantification, such as lesion detection and tumor volume segmentation.

Theoretical Analysis of Penalized Maximum-Likelihood Patlak Parametric Image Reconstruction in Dynamic PET for Lesion Detection

Detecting cancerous lesions is a major clinical application of emission tomography. In a previous work, we studied penalized maximum-likelihood (PML) image reconstruction for lesion detection in static PET. Here we extend our theoretical analysis of static PET reconstruction to dynamic PET. We study both the conventional indirect reconstruction and direct reconstruction for Patlak parametric image estimation. In indirect reconstruction, Patlak parametric images are generated by first reconstructing a sequence of dynamic PET images, and then performing Patlak analysis on the time activity curves (TACs) pixel-by-pixel. In direct reconstruction, Patlak parametric images are estimated directly from raw sinogram data by incorporating the Patlak model into the image reconstruction procedure. PML reconstruction is used in both the indirect and direct reconstruction methods. We use a channelized Hotelling observer (CHO) to assess lesion detectability in Patlak parametric images. Simplified expressions for evaluating the lesion detectability have been derived and applied to the selection of the regularization parameter value to maximize detection performance. The proposed method is validated using computer-based Monte Carlo simulations. Good agreements between the theoretical predictions and the Monte Carlo results are observed. Both theoretical predictions and Monte Carlo simulation results show the benefit of the indirect and direct methods under optimized regularization parameters in dynamic PET reconstruction for lesion detection, when compared with the conventional static PET reconstruction.

Matched signal detection on graphs: theory and application to brain network classification

We develop a matched signal detection (MSD) theory for signals with an intrinsic structure described by a weighted graph. Hypothesis tests are formulated under different signal models. In the simplest scenario, we assume that the signal is deterministic with noise in a subspace spanned by a subset of eigenvectors of the graph Laplacian. The conventional matched subspace detection can be easily extended to this case. Furthermore, we study signals with certain level of smoothness. The test turns out to be a weighted energy detector, when the noise variance is negligible. More generally, we presume that the signal follows a prior distribution, which could be learnt from training data. The test statistic is then the difference of signal variations on associated graph structures, if an Ising model is adopted. Effectiveness of the MSD on graph is evaluated both by simulation and real data. We apply it to the network classification problem of Alzheimer's disease (AD) particularly. The preliminary results demonstrate that our approach is able to exploit the sub-manifold structure of the data, and therefore achieve a better performance than the traditional principle component analysis (PCA).

Non-local means denoising of dynamic PET images

Objective

Dynamic positron emission tomography (PET), which reveals information about both the spatial distribution and temporal kinetics of a radiotracer, enables quantitative interpretation of PET data. Model-based interpretation of dynamic PET images by means of parametric fitting, however, is often a challenging task due to high levels of noise, thus necessitating a denoising step. The objective of this paper is to develop and characterize a denoising framework for dynamic PET based on non-local means (NLM).

Theory

NLM denoising computes weighted averages of voxel intensities assigning larger weights to voxels that are similar to a given voxel in terms of their local neighborhoods or patches. We introduce three key modifications to tailor the original NLM framework to dynamic PET. Firstly, we derive similarities from less noisy later time points in a typical PET acquisition to denoise the entire time series. Secondly, we use spatiotemporal patches for robust similarity computation. Finally, we use a spatially varying smoothing parameter based on a local variance approximation over each spatiotemporal patch.

Methods

To assess the performance of our denoising technique, we performed a realistic simulation on a dynamic digital phantom based on the Digimouse atlas. For experimental validation, we denoised PET images from a mouse study and a hepatocellular carcinoma patient study. We compared the performance of NLM denoising with four other denoising approaches – Gaussian filtering, PCA, HYPR, and conventional NLM based on spatial patches.

Results

The simulation study revealed significant improvement in bias-variance performance achieved using our NLM technique relative to all the other methods. The experimental data analysis revealed that our technique leads to clear improvement in contrast-to-noise ratio in Patlak parametric images generated from denoised preclinical and clinical dynamic images, indicating its ability to preserve image contrast and high intensity details while lowering the background noise variance.

Patient-adaptive lesion metabolism analysis by dynamic PET images

Dynamic PET imaging provides important spatial-temporal information for metabolism analysis of organs and tissues, and generates a great reference for clinical diagnosis and pharmacokinetic analysis. Due to poor statistical properties of the measurement data in low count dynamic PET acquisition and disturbances from surrounding tissues, identifying small lesions inside the human body is still a challenging issue. The uncertainties in estimating the arterial input function will also limit the accuracy and reliability of the metabolism analysis of lesions. Furthermore, the sizes of the patients and the motions during PET acquisition will yield mismatch against general purpose reconstruction system matrix, this will also affect the quantitative accuracy of metabolism analyses of lesions. In this paper, we present a dynamic PET metabolism analysis framework by defining a patient adaptive system matrix to improve the lesion metabolism analysis. Both patient size information and potential small lesions are incorporated by simulations of phantoms of different sizes and individual point source responses. The new framework improves the quantitative accuracy of lesion metabolism analysis, and makes the lesion identification more precisely. The requirement of accurate input functions is also reduced. Experiments are conducted on Monte Carlo simulated data set for quantitative analysis and validation, and on real patient scans for assessment of clinical potential.

Controlling familywise error rate for matched subspace detection in dynamic FDG PET

Detection of small lesions in fluorodeoxyglucose (FDG) positron emission tomography (PET) is limited by image resolution and low signal to noise ratio. We have previously described a matched subspace detection method that uses the time activity curve to distinguish tumors from background in dynamic FDG PET. Applying this algorithm on a voxel by voxel basis throughout the dynamic image produces a test statistic image or "map" which on thresholding indicates the potential locations of secondary or metastatic tumors. In this paper, we describe a thresholding method that controls familywise error rate (FWER) for the matched subspace detection statistical map. The method involves three steps. First, the PET image is segmented into several homogeneous regions. Then, the statistical map is normalized to a zero mean unit variance Gaussian random field. Finally, the images are thresholded at a fixed FWER by estimating their spatial smoothness and applying a random field theory maximum statistic approach. We evaluate this thresholding method using digital phantoms generated from clinical dynamic images. We also present an application of the proposed approach to clinical PET data from a breast cancer patient with metastatic disease.