The increasing application of deep learning in medical imaging has prompted the need for developing analysis tools to understand, evaluate, and enhance neural networks and their outcomes. However, image quality assessment of learning-based methods remains challenging due to their nonlinear and data-dependent nature. In this study, we introduce an analysis method for learning-based CT denoising algorithms based on the Jacobian matrix, which characterizes the response of the network to perturbations around its input. We trained a classic denoising network architecture using the normal dose images as label but using progressively lower dose images as input. For each network, the Jacobian matrices for an example input image were evaluated over 50 noise realizations in terms of their width and anisotropy. We further performed null space analysis of the Jacobians to investigate the preserved and null components of input perturbations. The variability in the network outputs and Jacobian matrices was found to increase with a reduction in dose levels. Such behavior, however, is only observed around edges in the anatomy. The width of the Jacobian matrix also increased as the dose decreased, suggesting an increase in the strength of the smoothing effect. The anisotropy of the Jacobian was more pronounced about the edges, indicating edge enhancement in the denoising process. The null space analysis showed a reduction in the preserved features of an input perturbation as the dose decreased, indicating greater misrepresentation of anatomical structures. The analysis proposed in this work aids in understanding and interpreting the denoising behavior of neural networks and can potentially serve as a means to regulate and optimize network performance.
Non-circular orbits in cone-beam CT (CBCT) imaging are increasingly being studied for potential benefits in field-of-view, dose reduction, improved image quality, minimal interference in guided procedures, metal artifact reduction, and more. While modern imaging systems such as robotic C-arms are enabling more freedom in potential orbit designs, practical implementation on such clinical systems remains challenging due to obstacles in critical stages of the workflow, including orbit realization, geometric calibration, and reconstruction. In this work, we build upon previous successes in clinical implementation and address key challenges in the geometric calibration stage with a novel calibration method. The resulting workflow eliminates the need for prior patient scans or dedicated calibration phantoms, and can be conducted in clinically relevant processing times.
KEYWORDS: Neural networks, Denoising, Computed tomography, Complex systems, Algorithm development, Medical imaging, Visualization, Spherical lenses, Space operations, Signal to noise ratio
The rapid development of deep-learning methods in medical imaging has called for an analysis method suitable for non-linear and data-dependent algorithms. In this work, we investigate a local linearity analysis where a complex neural network can be represented as piecewise linear systems. We recognize that a large number of neural networks consists of alternating linear layers and rectified linear unit (ReLU) activations, and are therefore strictly piecewise linear. We investigated the extent of these locally linear regions by gradually adding perturbations to an operating point. For this work, we explored perturbations based on image features of interest, including lesion contrast, background, and additive noise. We then developed strategies to extend these strictly locally linear regions to include neighboring linear regions with similar gradients. Using these approximately linear regions, we applied singular value decomposition (SVD) analysis to each local linear system to investigate and explain the overall nonlinear and data-dependent behaviors of neural networks. The analysis was applied to an example CT denoising algorithm trained on thorax CT scans. We observed that the strictly local linear regions are highly sensitive to small signal perturbations. Over a range of lesion contrast from 0.007 to 0.04 mm−1, there is a total of 33992 linear regions. The Jacobians are also shift-variant. However, the Jacobians of neighboring linear regions are very similar. By combining linear regions with similar Jacobians, we narrowed down the number of approximately linear regions to four over lesion contrast from 0.001 to 0.08 mm−1. The SVD analysis to different linear regions revealed denoising behavior that is highly dependent on the background intensity. Analysis further identified greater amount of noise reduction in uniform regions compared to lesion edges. In summary, the local linearity analysis framework we proposed has the potential for us to better characterize and interpret the non-linear and data-dependent behaviors of neural networks.
The proliferation of deep learning image processing calls for a quantitative image quality assessment framework that is suitable for nonlinear, data-dependent algorithms. In this work, we propose a method to systematically evaluate the system and noise responses such that the nonlinear transfer properties can be mapped out. The method involves sampling of lesion perturbations as a function of size, contrast, as well as clinically relevant features such as shape and texture that may be important for diagnosis. We embed the perturbations in backgrounds of varying attenuation levels, noise magnitude and correlation that are associated with different patient anatomies and imaging protocols. The range of system and noise response are further used to evaluate performance for clinical tasks such as signal detection and classification. We performed the assessment for an example CNN-denoising algorithm for low does lung CT screening. The system response of the CNN-denoising algorithm exhibits highly nonlinear behavior where both contrast and higher order lesion features such as spiculated boundaries are not reliably represented for lesions perturbations with small size and low contrast. The noise properties are potentially highly nonstationary, and should be assumed to be the same between the signal-present and signal-absent images. Furthermore, we observer a high degree dependency of both system and noise response on the background attenuation levels. Inputs around zeros are effectively imposed a non-negativity constraint; transfer properties for higher background levels are highly variable. For a detection task, CNN-denoised images improved detectability index by 16-18% compared to low dose CT inputs. For classification task between spiculated and smooth lesions, CNN-denoised images result in a much larger improvement up to 50%. The performance assessment framework propose in this work can systematically map out the nonlinear transfer functions for deep learning algorithms and can potentially enable robust deployment of such algorithms in medical imaging applications.
Recent years have seen the increasing application of deep learning methods in medical imaging formation, processing, and analysis. These methods take advantage of the flexibility of nonlinear neural network models to encode information and features in ways that can outperform conventional approaches. However, because of the nonlinear nature of this processing, images formed by neural networks have properties that are highly datadependent and difficult to analyze. In particular, the generalizability and robustness of these approaches can be difficult to ascertain. In this work, we analyze a class of neural networks that use only piece-wise linear activation functions. This class of networks can be represented by locally linear systems where the linear properties are highly data-dependent - allowing, for example, estimation of noise in image output via standard propagation methods. We propose a nonlinearity index metric that quantifies the fidelity of a local linear approximation of trained models based on specific input data. We applied this analysis to three example CT denoising CNNs to analytically predict the noise properties in the output images. We found that the proposed nonlinearity metric highly correlates with the accuracy of noise predictions. The analysis proposed in this work provides theoretical understanding of the nonlinear behavior of neural networks and enables performance prediction and quantitation under certain conditions.
Printed phantoms hold great potential as a tool for examining task-based image quality of x-ray imaging systems. Their ability to produce complex shapes rendered in materials with adjustable attenuation coefficients allows a new level of flexibility in the design of tasks for the evaluation of physical imaging systems. We investigate performance in a fine “boundary discrimination” task in which fine features at the margin of a clearly visible “lesion” are used to classify the lesion as malignant or benign. These tasks are appealing because of their relevance to clinical tasks, and because they typically emphasize higher spatial frequencies relative to more common lesion detection tasks. A 3D printed phantom containing cylindrical shells of varying thickness was used to generate lesions profiles that differed in their edge profiles. This was intended to approximate lesions with indistinct margins that are clinically associated with malignancy. Wall thickness in the phantom ranged from 0.4mm to 0.8mm, which allows for task difficulty to be varied by choosing different thicknesses to represent malignant and benign lesions. The phantom was immersed in a tub filled with water and potassium phosphate to approximate the attenuating background, and imaged repeatedly on a benchtop cone-beam CT scanner. After preparing the image data (reconstruction, ROI Selection, sub-pixel registration), we find that the mean frequency of the lesion profile is 0.11 cyc/mm. The mean frequency of the lesion-difference profile, representative of the discrimination task, is approximately 6 times larger. Model observers show appropriate dose performance in these tasks as well.
CT reconstruction requires an accurate physical model. Mismatches between model and data represent unmodeled biases and can induce artifacts and systematic quantitation errors. Bias effects are dependent on bias structure and data processing (e.g. model-based iterative reconstruction versus filtered-backprojection). In this work, we illustrate this sensitivity and develop a strategy to estimate unmodeled biases for situations where the underlying source is unknown or difficult to estimate directly. We develop a CNN framework for projection-domain de-biasing using a ResUNet architecture and spatial-frequency loss function. We demonstrate a reduction in reconstruction errors across bias conditions and reconstruction methods.
Assessment of computed tomography (CT) images can be complex due to a number of dependencies that affect system performance. In particular, it is well-known that noise in CT is object-dependent. Such objectdependence can be more pronounced and extend to resolution and image textures with the increasing adoption of model-based reconstruction and processing with machine learning methods. Moreover, such processing is often inherently nonlinear complicating assessments with simple measures of spatial resolution, etc. Similarly, recent advances in CT system design have attempted to improve fine resolution details – e.g., with newer detectors, smaller focal spots, etc. Recognizing these trends, there is a greater need for imaging assessment that are considering specific features of interest that can be placed within an anthropomorphic phantom for realistic emulation and evaluation. In this work, we devise a methodology for 3D-printing phantom inserts using procedural texture generation for evaluation of performance of high-resolution CT systems. Accurate representations of texture have previously been a hindrance to adoption of processing methods like model-based reconstruction, and texture serves as an important diagnostic feature (e.g. heterogeneity of lesions is a marker for malignancy). We consider the ability of different systems to reproduce various textures (as a function of the intrinsic feature sizes of the texture), comparing microCT, cone-beam CT, and diagnostic CT using normal- and high-resolution modes. We expect that this general methodology will provide a pathway for repeatable and robust assessments of different imaging systems and processing methods.
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