A Feasibility Study of Extracting Tissue Textures From a Previous Full-Dose CT Database as Prior Knowledge for Bayesian Reconstruction of Current Low-Dose CT Images

Texture-preserving low dose CT image denoising using Pearson divergence

Objective.The mean squared error (MSE), also known asL2loss, has been widely used as a loss function to optimize image denoising models due to its strong performance as a mean estimator of the Gaussian noise model. Recently, various low-dose computed tomography (LDCT) image denoising methods using deep learning combined with the MSE loss have been developed; however, this approach has been observed to suffer from the regression-to-the-mean problem, leading to over-smoothed edges and degradation of texture in the image.Approach.To overcome this issue, we propose a stochastic function in the loss function to improve the texture of the denoised CT images, rather than relying on complicated networks or feature space losses. The proposed loss function includes the MSE loss to learn the mean distribution and the Pearson divergence loss to learn feature textures. Specifically, the Pearson divergence loss is computed in an image space to measure the distance between two intensity measures of denoised low-dose and normal-dose CT images. The evaluation of the proposed model employs a novel approach of multi-metric quantitative analysis utilizing relative texture feature distance.Results.Our experimental results show that the proposed Pearson divergence loss leads to a significant improvement in texture compared to the conventional MSE loss and generative adversarial network (GAN), both qualitatively and quantitatively.Significance.Achieving consistent texture preservation in LDCT is a challenge in conventional GAN-type methods due to adversarial aspects aimed at minimizing noise while preserving texture. By incorporating the Pearson regularizer in the loss function, we can easily achieve a balance between two conflicting properties. Consistent high-quality CT images can significantly help clinicians in diagnoses and supporting researchers in the development of AI-diagnostic models.

Machine Learned Texture Prior From Full-Dose CT Database via Multi-Modality Feature Selection for Bayesian Reconstruction of Low-Dose CT

In our earlier study, we proposed a regional Markov random field type tissue-specific texture prior from previous full-dose computed tomography (FdCT) scan for current low-dose CT (LdCT) imaging, which showed clinical benefits through task-based evaluation. Nevertheless, two assumptions were made for early study. One assumption is that the center pixel has a linear relationship with its nearby neighbors and the other is previous FdCT scans of the same subject are available. To eliminate the two assumptions, we proposed a database assisted end-to-end LdCT reconstruction framework which includes a deep learning texture prior model and a multi-modality feature based candidate selection model. A convolutional neural network-based texture prior is proposed to eliminate the linear relationship assumption. And for scenarios in which the concerned subject has no previous FdCT scans, we propose to select one proper prior candidate from the FdCT database using multi-modality features. Features from three modalities are used including the subjects' physiological factors, the CT scan protocol, and a novel feature named Lung Mark which is deliberately proposed to reflect the z-axial property of human anatomy. Moreover, a majority vote strategy is designed to overcome the noise effect from LdCT scans. Experimental results showed the effectiveness of Lung Mark. The selection model has accuracy of 84% testing on 1,470 images from 49 subjects. The learned texture prior from FdCT database provided reconstruction comparable to the subjects having corresponding FdCT. This study demonstrated the feasibility of bringing clinically relevant textures from available FdCT database to perform Bayesian reconstruction of any current LdCT scan.

A total variation prior unrolling approach for computed tomography reconstruction

BACKGROUND

With the rapid development of deep learning technology, deep neural networks can effectively enhance the performance of computed tomography (CT) reconstructions. One kind of commonly used method to construct CT reconstruction networks is to unroll the conventional iterative reconstruction (IR) methods to convolutional neural networks (CNNs). However, most unrolling methods primarily unroll the fidelity term of IR methods to CNNs, without unrolling the prior terms. The prior terms are always directly replaced by neural networks.

PURPOSE

In conventional IR methods, the prior terms play a vital role in improving the visual quality of reconstructed images. Unrolling the hand-crafted prior terms to CNNs may provide a more specialized unrolling approach to further improve the performance of CT reconstruction. In this work, a primal-dual network (PD-Net) was proposed by unrolling both the data fidelity term and the total variation (TV) prior term, which effectively preserves the image edges and textures in the reconstructed images.

METHODS

By further deriving the Chambolle-Pock (CP) algorithm instance for CT reconstruction, we discovered that the TV prior updates the reconstructed images with its divergences in each iteration of the solution process. Based on this discovery, CNNs were applied to yield the divergences of the feature maps for the reconstructed image generated in each iteration. Additionally, a loss function was applied to the predicted divergences of the reconstructed image to guarantee that the CNNs' results were the divergences of the corresponding feature maps in the iteration. In this manner, the proposed CNNs seem to play the same roles in the PD-Net as the TV prior in the IR methods. Thus, the TV prior in the CP algorithm instance can be directly unrolled to CNNs.

RESULTS

The datasets from the Low-Dose CT Image and Projection Data and the Piglet dataset were employed to assess the effectiveness of our proposed PD-Net. Compared with conventional CT reconstruction methods, our proposed method effectively preserves the structural and textural information in reference to ground truth.

CONCLUSIONS

The experimental results show that our proposed PD-Net framework is feasible for the implementation of CT reconstruction tasks. Owing to the promising results yielded by our proposed neural network, this study is intended to inspire further development of unrolling approaches by enabling the direct unrolling of hand-crafted prior terms to CNNs.

A Joint-Parameter Estimation and Bayesian Reconstruction Approach to Low-Dose CT

Most penalized maximum likelihood methods for tomographic image reconstruction based on Bayes' law include a freely adjustable hyperparameter to balance the data fidelity term and the prior/penalty term for a specific noise-resolution tradeoff. The hyperparameter is determined empirically via a trial-and-error fashion in many applications, which then selects the optimal result from multiple iterative reconstructions. These penalized methods are not only time-consuming by their iterative nature, but also require manual adjustment. This study aims to investigate a theory-based strategy for Bayesian image reconstruction without a freely adjustable hyperparameter, to substantially save time and computational resources. The Bayesian image reconstruction problem is formulated by two probability density functions (PDFs), one for the data fidelity term and the other for the prior term. When formulating these PDFs, we introduce two parameters. While these two parameters ensure the PDFs completely describe the data and prior terms, they cannot be determined by the acquired data; thus, they are called complete but unobservable parameters. Estimating these two parameters becomes possible under the conditional expectation and maximization for the image reconstruction, given the acquired data and the PDFs. This leads to an iterative algorithm, which jointly estimates the two parameters and computes the to-be reconstructed image by maximizing a posteriori probability, denoted as joint-parameter-Bayes. In addition to the theoretical formulation, comprehensive simulation experiments are performed to analyze the stopping criterion of the iterative joint-parameter-Bayes method. Finally, given the data, an optimal reconstruction is obtained without any freely adjustable hyperparameter by satisfying the PDF condition for both the data likelihood and the prior probability, and by satisfying the stopping criterion. Moreover, the stability of joint-parameter-Bayes is investigated through factors such as initialization, the PDF specification, and renormalization in an iterative manner. Both phantom simulation and clinical patient data results show that joint-parameter-Bayes can provide comparable reconstructed image quality compared to the conventional methods, but with much less reconstruction time. To see the response of the algorithm to different types of noise, three common noise models are introduced to the simulation data, including white Gaussian noise to post-log sinogram data, Poisson-like signal-dependent noise to post-log sinogram data and Poisson noise to the pre-log transmission data. The experimental outcomes of the white Gaussian noise reveal that the two parameters estimated by the joint-parameter-Bayes method agree well with simulations. It is observed that the parameter introduced to satisfy the prior's PDF is more sensitive to stopping the iteration process for all three noise models. A stability investigation showed that the initial image by filtered back projection is very robust. Clinical patient data demonstrated the effectiveness of the proposed joint-parameter-Bayes and stopping criterion.

Deep learning tomographic reconstruction through hierarchical decomposition of domain transforms

Deep learning (DL) has shown unprecedented performance for many image analysis and image enhancement tasks. Yet, solving large-scale inverse problems like tomographic reconstruction remains challenging for DL. These problems involve non-local and space-variant integral transforms between the input and output domains, for which no efficient neural network models are readily available. A prior attempt to solve tomographic reconstruction problems with supervised learning relied on a brute-force fully connected network and only allowed reconstruction with a 128⁴ system matrix size. This cannot practically scale to realistic data sizes such as 512⁴ and 512⁶ for three-dimensional datasets. Here we present a novel framework to solve such problems with DL by casting the original problem as a continuum of intermediate representations between the input and output domains. The original problem is broken down into a sequence of simpler transformations that can be well mapped onto an efficient hierarchical network architecture, with exponentially fewer parameters than a fully connected network would need. We applied the approach to computed tomography (CT) image reconstruction for a 512⁴ system matrix size. This work introduces a new kind of data-driven DL solver for full-size CT reconstruction without relying on the structure of direct (analytical) or iterative (numerical) inversion techniques. This work presents a feasibility demonstration of full-scale learnt reconstruction, whereas more developments will be needed to demonstrate superiority relative to traditional reconstruction approaches. The proposed approach is also extendable to other imaging problems such as emission and magnetic resonance reconstruction. More broadly, hierarchical DL opens the door to a new class of solvers for general inverse problems, which could potentially lead to improved signal-to-noise ratio, spatial resolution and computational efficiency in various areas.

Prior-image-based CT reconstruction using attenuation-mismatched priors

Prior-image-based reconstruction (PIBR) methods are powerful tools for reducing radiation doses and improving the image quality of low-dose computed tomography (CT). Apart from anatomical changes, prior and current images can also have different attenuations because they originated from different scanners or from the same scanner but with different x-ray beam qualities (e.g., kVp settings, beam filters) during data acquisition. In such scenarios, with attenuation-mismatched priors, PIBR is challenging. In this work, we investigate a specific PIBR method, called statistical image reconstruction, using normal-dose image-induced nonlocal means regularization (SIR-ndiNLM), to address PIBR with such attenuation-mismatched priors and achieve quantitative low-dose CT imaging. We propose two corrective schemes for the original SIR-ndiNLM method, (1) a global histogram-matching approach and (2) a local attenuation correction approach, to account for the attenuation differences between the prior and current images in PIBR. We validate the efficacy of the proposed schemes using images acquired from dual-energy CT scanners to simulate attenuation mismatches. Meanwhile, we utilize different CT slices to simulate anatomical mismatches or changes between the prior and the current low-dose image. We observe that the original SIR-ndiNLM introduces artifacts to the reconstruction when an attenuation-mismatched prior is used. Furthermore, we find that a larger attenuation mismatch between the prior and current images results in more severe artifacts in the SIR-ndiNLM reconstruction. Our two proposed corrective schemes enable SIR-ndiNLM to effectively handle the attenuation mismatch and anatomical changes between the two images and successfully eliminate the artifacts. We demonstrate that the proposed techniques permit SIR-ndiNLM to leverage the attenuation-mismatched prior and achieve quantitative low-dose CT reconstruction from both low-flux and sparse-view data acquisitions. This work permits robust and reliable PIBR for CT data acquired using different beam settings.

Spectral CT Reconstruction via Low-Rank Representation and Region-Specific Texture Preserving Markov Random Field Regularization

Photon-counting spectral computed tomography (CT) is capable of material characterization and can improve diagnostic performance over traditional clinical CT. However, it suffers from photon count starving for each individual energy channel which may cause severe artifacts in the reconstructed images. Furthermore, since the images in different energy channels describe the same object, there are high correlations among different channels. To make full use of the inter-channel correlations and minimize the count starving effect while maintaining clinically meaningful texture information, this paper combines a region-specific texture model with a low-rank correlation descriptor as an a priori regularization to explore a superior texture preserving Bayesian reconstruction of spectral CT. Specifically, the inter-channel correlations are characterized by the low-rank representation, and the inner-channel regional textures are modeled by a texture preserving Markov random field. In other words, this paper integrates the spectral and spatial information into a unified Bayesian reconstruction framework. The widely-used Split-Bregman algorithm is employed to minimize the objective function because of the non-differentiable property of the low-rank representation. To evaluate the tissue texture preserving performance of the proposed method for each channel, three references are built for comparison: one is the traditional CT image from energy integration detection. The second one is spectral images from dual-energy CT. The third one is individual channels images from custom-made photon-counting spectral CT. As expected, the proposed method produced promising results in terms of not only preserving texture features but also suppressing image noise in each channel, comparing to existing methods of total variation (TV), low-rank TV and tensor dictionary learning, by both visual inspection and quantitative indexes of root mean square error, peak signal to noise ratio, structural similarity and feature similarity.

Characterization of tissue-specific pre-log Bayesian CT reconstruction by texture-dose relationship

PURPOSE

Tissue textures have been recognized as biomarkers for various clinical tasks. In computed tomography (CT) image reconstruction, it is important but challenging to preserve the texture when lowering x-ray exposure from full- toward low-/ultra-low dose level. Therefore, this paper aims to explore the texture-dose relationship within one tissue-specific pre-log Bayesian CT reconstruction algorithm.

METHODS

To enhance the texture in ultra-low dose CT (ULdCT) reconstruction, this paper presents a Bayesian type algorithm. A shifted Poisson model is adapted to describe the statistical properties of pre-log data, and a tissue-specific Markov random field prior (MRFt) is used to incorporate tissue texture from previous full-dose CT, thus called SP-MRFt algorithm. Utilizing the SP-MRFt algorithm, we investigated tissue texture degradation as a function of x-ray dose levels from full dose (100 mAs/120 kVp) to ultralow dose (1 mAs/120 kVp) by using quantitative texture-based evaluation metrics.

RESULTS

Experimental results show the SP-MRFt algorithm outperforms conventional filtered back projection (FBP) and post-log domain penalized weighted least square MRFt (PWLS-MRFt) in terms of noise suppression and texture preservation. Comparable results are also obtained with shifted Poisson model with 7 × 7 Huber MRF weights (SP-Huber7). The investigation on texture-dose relationship shows that the quantified texture measures drop monotonically as dose level decreases, and interestingly a turning point is observed on the texture-dose response curve.

CONCLUSIONS

This important observation implies that there exists a minimum dose level, at which a given CT scanner (hardware configuration and image reconstruction software) can achieve without compromising clinical tasks. Moreover, the experiment results show that the variance of electronic noise has higher impact than the mean to the texture-dose relationship.

Radon Inversion via Deep Learning

The Radon transform is widely used in physical and life sciences, and one of its major applications is in medical X-ray computed tomography (CT), which is significantly important in disease screening and diagnosis. In this paper, we propose a novel reconstruction framework for Radon inversion with deep learning (DL) techniques. For simplicity, the proposed framework is denoted as iRadonMAP, i.e., inverse Radon transform approximation. Specifically, we construct an interpretable neural network that contains three dedicated components. The first component is a fully connected filtering (FCF) layer along the rotation angle direction in the sinogram domain, and the second one is a sinusoidal back-projection (SBP) layer, which back-projects the filtered sinogram data into the spatial domain. Next, a common network structure is added to further improve the overall performance. iRadonMAP is first pretrained on a large number of generic images from the ImageNet database and then fine-tuned with clinical patient data. The experimental results demonstrate the feasibility of the proposed iRadonMAP framework for Radon inversion.

Constructing a tissue-specific texture prior by machine learning from previous full-dose scan for Bayesian reconstruction of current ultralow-dose CT images

Purpose: Bayesian theory provides a sound framework for ultralow-dose computed tomography (ULdCT) image reconstruction with two terms for modeling the data statistical property and incorporating a priori knowledge for the image that is to be reconstructed. We investigate the feasibility of using a machine learning (ML) strategy, particularly the convolutional neural network (CNN), to construct a tissue-specific texture prior from previous full-dose computed tomography. Approach: Our study constructs four tissue-specific texture priors, corresponding with lung, bone, fat, and muscle, and integrates the prior with the prelog shift Poisson (SP) data property for Bayesian reconstruction of ULdCT images. The Bayesian reconstruction was implemented by an algorithm called SP-CNN-T and compared with our previous Markov random field (MRF)-based tissue-specific texture prior algorithm called SP-MRF-T. Results: In addition to conventional quantitative measures, mean squared error and peak signal-to-noise ratio, structure similarity index, feature similarity, and texture Haralick features were used to measure the performance difference between SP-CNN-T and SP-MRF-T algorithms in terms of the structure and tissue texture preservation, demonstrating the feasibility and the potential of the investigated ML approach. Conclusions: Both training performance and image reconstruction results showed the feasibility of constructing CNN texture prior model and the potential of improving the structure preservation of the nodule comparing to our previous regional tissue-specific MRF texture prior model.

A Task-dependent Investigation on Dose and Texture in CT Image Reconstruction

Localizing and characterizing clinically-significant lung nodules, a potential precursor to lung cancer, at the lowest achievable radiation dose is demanded to minimize the stochastic radiation effects from x-ray computed tomography (CT). A minimal dose level is heavily dependent on the image reconstruction algorithms and clinical task, in which the tissue texture always plays an important role. This study aims to investigate the dependence through a task-based evaluation at multiple dose levels and variable textures in reconstructions with prospective patient studies. 133 patients with a suspicious pulmonary nodule scheduled for biopsy were recruited and the data was acquired at120kVp with three different dose levels of 100, 40 and 20mAs. Three reconstruction algorithms were implemented: analytical filtered back-projection (FBP) with optimal noise filtering; statistical Markov random field (MRF) model with optimal Huber weighting (MRF-H) for piecewise smooth reconstruction; and tissue-specific texture model (MRF-T) for texture preserved statistical reconstruction. Experienced thoracic radiologists reviewed and scored all images at random, blind to the CT dose and reconstruction algorithms. The radiologists identified the nodules in each image including the 133 biopsy target nodules and 66 other non-target nodules. For target nodule characterization, only MRF-T at 40mAs showed no statistically significant difference from FBP at 100mAs. For localizing both the target nodules and the non-target nodules, some as small as 3mm, MRF-T at 40 and 20mAs levels showed no statistically significant difference from FBP at 100mAs, respectively. MRF-H and FBP at 40 and 20mAs levels performed statistically differently from FBP at 100mAs. This investigation concluded that (1) the textures in the MRF-T reconstructions improves both the tasks of localizing and characterizing nodules at low dose CT and (2) the task of characterizing nodules is more challenging than the task of localizing nodules and needs more dose or enhanced textures from reconstruction.

Energy enhanced tissue texture in spectral computed tomography for lesion classification

Tissue texture reflects the spatial distribution of contrasts of image voxel gray levels, i.e., the tissue heterogeneity, and has been recognized as important biomarkers in various clinical tasks. Spectral computed tomography (CT) is believed to be able to enrich tissue texture by providing different voxel contrast images using different X-ray energies. Therefore, this paper aims to address two related issues for clinical usage of spectral CT, especially the photon counting CT (PCCT): (1) texture enhancement by spectral CT image reconstruction, and (2) spectral energy enriched tissue texture for improved lesion classification. For issue (1), we recently proposed a tissue-specific texture prior in addition to low rank prior for the individual energy-channel low-count image reconstruction problems in PCCT under the Bayesian theory. Reconstruction results showed the proposed method outperforms existing methods of total variation (TV), low-rank TV and tensor dictionary learning in terms of not only preserving texture features but also suppressing image noise. For issue (2), this paper will investigate three models to incorporate the enriched texture by PCCT in accordance with three types of inputs: one is the spectral images, another is the co-occurrence matrices (CMs) extracted from the spectral images, and the third one is the Haralick features (HF) extracted from the CMs. Studies were performed on simulated photon counting data by introducing attenuation-energy response curve to the traditional CT images from energy integration detectors. Classification results showed the spectral CT enriched texture model can improve the area under the receiver operating characteristic curve (AUC) score by 7.3%, 0.42% and 3.0% for the spectral images, CMs and HFs respectively on the five-energy spectral data over the original single energy data only. The CM- and HF-inputs can achieve the best AUC of 0.934 and 0.927. This texture themed study shows the insight that incorporating clinical important prior information, e.g., tissue texture in this paper, into the medical imaging, such as the upstream image reconstruction, the downstream diagnosis, and so on, can benefit the clinical tasks.

A Feasibility Study of Extracting Tissue Textures From a Previous Full-Dose CT Database as Prior Knowledge for Bayesian Reconstruction of Current Low-Dose CT Images

Markov random field (MRF) has been widely used to incorporate a priori knowledge as penalty or regularizer to preserve edge sharpness while smoothing the region enclosed by the edge for pieces-wise smooth image reconstruction. In our earlier study, we proposed a type of MRF reconstruction method for low-dose CT (LdCT) scans using tissue-specific textures extracted from the same patient's previous full-dose CT (FdCT) scans as prior knowledge. It showed advantages in clinical applications. This paper aims to remove the constraint of using previous data of the same patient. We investigated the feasibility of extracting the tissue-specific MRF textures from an FdCT database to reconstruct a LdCT image of another patient. This feasibility study was carried out by experiments designed as follows. We constructed a tissue-specific MRF-texture database from 3990 FdCT scan slices of 133 patients who were scheduled for lung nodule biopsy. Each patient had one FdCT scan (120 kVp/100 mAs) and one LdCT scan (120 kVp/20 mAs) prior to biopsy procedure. When reconstructing the LdCT image of one patient among the 133 patients, we ranked the closeness of the MRF-textures from the other 132 patients saved in the database and used them as the a prior knowledge. Then, we evaluated the reconstructed image quality using Haralick texture measures. For any patient within our database, we found more than eighteen patients' FdCT MRF texures can be used without noticeably changing the Haralick texture measures on the lung nodules (to be biopsied). These experimental outcomes indicate it is promising that a sizable FdCT texture database could be used to enhance Bayesian reconstructions of any incoming LdCT scans.