Comparison of Regularization Methods in Fluorescence Molecular Tomography

Simultaneous reconstruction of 3D fluorescence distribution and object surface using structured light illumination and dual-camera detection

Fluorescence molecular tomography (FMT) serves as a noninvasive modality for visualizing volumetric fluorescence distribution within biological tissues, thereby proving to be an invaluable imaging tool for preclinical animal studies. The conventional FMT relies upon a point-by-point raster scan strategy, enhancing the dataset for subsequent reconstruction but concurrently elongating the data acquisition process. The resultant diminished temporal resolution has persistently posed a bottleneck, constraining its utility in dynamic imaging studies. We introduce a novel system capable of simultaneous FMT and surface extraction, which is attributed to the implementation of a rapid line scanning approach and dual-camera detection. The system performance was characterized through phantom experiments, while the influence of scanning line density on reconstruction outcomes has been systematically investigated via both simulation and experiments. In a proof-of-concept study, our approach successfully captures a moving fluorescence bolus in three dimensions with an elevated frame rate of approximately 2.5 seconds per frame, employing an optimized scan interval of 5 mm. The notable enhancement in the spatio-temporal resolution of FMT holds the potential to broaden its applications in dynamic imaging tasks, such as surgical navigation.

Superfast Scan of Focused X-Ray Luminescence Computed Tomography Imaging

X-ray luminescence computed tomography (XLCT) is a hybrid molecular imaging modality having the high spatial resolution of x-ray imaging and high measurement sensitivity of optical imaging. Narrow x-ray beam based XLCT imaging has shown promise for high spatial resolution imaging of luminescent targets in deep tissues, but the slow acquisition speed limits its applications. In this work, we have introduced a superfast XLCT scan scheme based on the photon counter detector and a fly-scanning method. The new scan scheme is compared with three other scan methods. We have also designed and built a single-pixel x-ray detector to detect object boundaries automatically. With the detector, we can perform the parallel beam CT imaging with the XLCT imaging simultaneously. We have built the prototype XLCT imaging system to verify the proposed scan scheme. A phantom embedded with a set of four side-by-side cylindrical targets was scanned. With the proposed superfast scan scheme, we have achieved 43 seconds per transverse scan, which is 28.6 times faster than before with slightly better XLCT image quality. The superfast scan allows us to perform 3D pencil beam XLCT imaging in the future.

Super-Fast Three-Dimensional Focused X-ray Luminescence Computed Tomography with a Gated Photon Counter

X-ray luminescence computed tomography (XLCT) is a hybrid molecular imaging modality combining the merits of both x-ray imaging (high spatial resolution) and optical imaging (high sensitivity to tracer nanophosphors). Narrow x-ray beam based XLCT imaging has shown promise for high spatial resolution imaging, but the slow acquisition speed limits its applications for in vivo imaging. We introduced a continuous scanning scheme to replace the selective excitation scheme to improve imaging speed in a previous study. Under the continuous scanning scheme, the main factor that limits the scanning speed is the data acquisition time at each interval position. In this work, we have used a gated photon counter (SR400, Stanford Research Systems) to replace the high-speed oscilloscope (MDO3104, Tektronix) to acquire measurement data. The gated photon counter only counts the photon peaks in each measurement interval, while the oscilloscope records the entire waveform including both background noise data and photon peak data. The photon counter records much less data without losing any relevant information, which makes it ideal for super-fast three-dimensional (3D) imaging. We have built prototype XLCT imaging systems of both types and performed both single target and multiple target phantom experiments in 3D. The results have verified the feasibility of our proposed photon counter based system and good 3D imaging capabilities of XLCT within a reasonable time, yielding a 14 times faster scanning time compared with the oscilloscope based XLCT system. Now, the total scan time is reduced to 27 seconds per transverse section.

Contrast agents for x-ray luminescence computed tomography

Imaging probes are an important consideration for any type of contrast agent-based imaging method. X-ray luminescence imaging (XLI) and x-ray luminescence computed tomography (XLCT) are both contrast agent-based imaging methods that employ x-ray excitable scintillating imaging probes that emit light to be measured for optical imaging. In this work, we compared the performance of several select imaging probes, both commercial and self-synthesized, for application in XLI/XLCT imaging. Commercially available cadmium telluride quantum dots (CdTe QDs) and europium-doped gadolinium oxysulfide (GOS:Eu) microphosphor as well as synthesized NaGdF4 nanophosphors doped with either europium or terbium were compared through their x-ray luminescence emission spectra, luminescence intensity, and also by performing XLCT scans using phantoms embedded with each of the imaging probes. Each imaging probe displayed a unique emission spectrum that was ideal for deep-tissue optical imaging. In terms of luminescence intensity, due to the large particle size, GOS:Eu had the brightest emission, followed by NaGdF4:Tb, NaGdF4:Eu, and finally the CdTe QDs. Lastly, XLCT scans showed that each imaging probe could be reconstructed with good shape and location accuracy.

X-ray luminescence imaging for small animals

X-ray luminescence imaging emerged for about a decade and combines both the high spatial resolution of x-ray imaging with the high measurement sensitivity of optical imaging, which could result in a great molecular imaging tool for small animals. So far, there are two types of x-ray luminescence computed tomography (XLCT) imaging. One uses a pencil beam x-ray for high spatial resolution at a cost of longer measurement time. The other uses cone beam x-ray to cover the whole mouse to obtain XLCT images at a very short time but with a compromised spatial resolution. Here we review these two methods in this paper and highlight the synthesized nanophosphors by different research groups. We are building a focused x-ray luminescence tomography (FXLT) imaging system, developing a machine-learning based FXLT reconstruction algorithm, and synthesizing nanophosphors with different emission wavelengths. In this paper, we will report our current progress from these three aspects. Briefly, we mount all main components, including the focused x-ray tube, the fiber detector, and the x-ray tube and x-ray detector for a microCT system, on a rotary which is a heavy-duty ring track. A microCT scan will be performed before FXLT scan. For a FXLT scan, we will have four PMTs to measure four fiber detectors at two different wavelengths simultaneously for each linear scan position. We expect the spatial resolution of the FXLT imaging will be around 100 micrometers and a limit of detection of approximately 2 μg/mL (for Gd2O2S:Eu).

Fluorescence Molecular Tomography Based on Group Sparsity Priori for Morphological Reconstruction of Glioma

OBJECTIVE

Fluorescence molecular tomography (FMT) is an important tool for life science, which can noninvasive real-time three-dimensional (3-D) visualization for fluorescence source location. FMT is widely used in tumor research due to its high-sensitive and low cost. However, the reconstruction of FMT is difficult. Although the reconstruction methods of FMT have developed rapidly in recent years, the morphological reconstruction of FMT is still a challenge problem. Thus, the purpose of this study is to realize the morphological reconstruction performance of FMT in glioma research.

METHODS

In this study, group sparsity was used as a new priori information for FMT. Besides sparsity, group sparsity also takes the group structure of the fluorescent sources, which can maintain the morphological information of the sources. Fused LASSO method (FLM) was proved it can efficiently model the group sparsity prior. Thus, we utilize FLM to reconstruct the morphological information of glioma. Furthermore, to reduce the influence of the high scattering of skull, we modified the FLM for improving the accuracy of morphological reconstruction.

RESULTS

Glioma numerical simulation model and in vivo glioma model were established to evaluate the performance of morphological reconstruction of the proposed method. The results demonstrated that the proposed method was efficient to reconstruct the morphological information of glioma.

CONCLUSION

Group sparsity priori can effectively improve the morphological accuracy of FMT reconstruction.

SIGNIFICANCE

Group sparsity can maintain the morphological information of fluorescent sources effectively, which has great application potential in FMT. The group sparsity based methods can realize the morphological reconstruction, which is of great practical significance in tumor research.

Half Thresholding Pursuit Algorithm for Fluorescence Molecular Tomography

OBJECTIVE

Fluorescence Molecular Tomography (FMT) is a promising optical tool for small animal imaging. The l_1/2-norm regularization has attracted attention in the field of FMT due to its ability in enhancing sparsity of solution and coping with the high ill-posedness of the inverse problem. However, efficient algorithm for solving the nonconvex regularized model deserve to explore.

METHOD

A Half Thresholding Pursuit Algorithm (HTPA) combined with parameter optimization is proposed in this paper to efficiently solve the nonconvex optimization model. Specifically, the half thresholding iteration method is utilized to solve l_1/2-norm model, pursuit strategy is used to accelerate the process of iteration, and the parameter optimization scheme is designed to obtain robust parameter.

RESULTS

Analysis and assessment on simulated and experimental data demonstrate that the proposed HTPA performs better in location accuracy and reconstructed fluorescent yield in less time cost, compared with the state-of-the-art reconstruction algorithms.

CONCLUSION

The proposed HTPA combined with the parameter optimization scheme is an efficient and robust reconstruction approach to FMT.

Synchronization-based clustering algorithm for reconstruction of multiple reconstructed targets in fluorescence molecular tomography

Fluorescence molecular tomography (FMT) is an important in vivo molecular imaging technique and has been widely studied in preclinical research. Many methods perform well in the reconstruction of a single fluorescent target but may fail in reconstructing multiple targets because of the severe ill-posedness of the FMT inverse problem. In this paper the original synchronization-inspired clustering algorithm (OSC) is introduced into FMT for resolving multiple targets from the reconstruction result. Based on OSC, a synchronization-based clustering algorithm for FMT (SC-FMT) is developed to further improve location accuracy. Both algorithms utilize the minimum spanning tree to automatically identify the number of the reconstructed targets without prior information and human intervention. A serial of numerical simulation results demonstrates that SC-FMT and OSC can resolve multiple targets robustly and automatically, which also shows the potential of the proposed postprocessing algorithms in FMT reconstruction.

An iterative weighted method based on YALL1 for cone-beam X-ray luminescence optical tomography imaging: A phantom experimental study

Cone-beam X-ray luminescence optical tomography (CB-XLOT) plays an important role in in vivo small animal imaging study, which can non-invasively image the three-dimensional (3-D) distribution of x-ray-excitable nanophosphors deeply embedded in imaged object. However, CB-XLOT suffers from a low spatial resolution due to the ill-posed nature of optical reconstruction. To alleviate the ill-posedness of reconstruction and improve the imaging performance of XLOT, in this paper, we propose an iterative weighted L₁ minimization method which is achieved by incorporating YALL1 (Your algorithm for L₁ norm problems). The physical phantom experiment was conducted to evaluate the performance of the proposed method, where a custom-made cone-beam XLOT system was used as the imaging platform. The experimental results indicate that by applying the proposed iterative weighted strategy to YALL1 method, the reconstruction performance of XLOT can be improved when compared with the conventional YALL1 method.

Anatomical image-guided fluorescence molecular tomography reconstruction using kernel method

Fluorescence molecular tomography (FMT) is an important in vivo imaging modality to visualize physiological and pathological processes in small animals. However, FMT reconstruction is ill-posed and ill-conditioned due to strong optical scattering in deep tissues, which results in poor spatial resolution. It is well known that FMT image quality can be improved substantially by applying the structural guidance in the FMT reconstruction. An approach to introducing anatomical information into the FMT reconstruction is presented using the kernel method. In contrast to conventional methods that incorporate anatomical information with a Laplacian-type regularization matrix, the proposed method introduces the anatomical guidance into the projection model of FMT. The primary advantage of the proposed method is that it does not require segmentation of targets in the anatomical images. Numerical simulations and phantom experiments have been performed to demonstrate the proposed approach’s feasibility. Numerical simulation results indicate that the proposed kernel method can separate two FMT targets with an edge-to-edge distance of 1 mm and is robust to false-positive guidance and inhomogeneity in the anatomical image. For the phantom experiments with two FMT targets, the kernel method has reconstructed both targets successfully, which further validates the proposed kernel method.

Sensitivity study of x-ray luminescence computed tomography

X-ray luminescence computed tomography (XLCT) is a hybrid molecular imaging modality that combines the merits of both x-ray imaging (high resolution) and optical imaging (high sensitivity). In this study, we have evaluated the sensitivity of XLCT with phantom experiments by scanning targets of different phosphor concentrations at different depths. We found that XLCT is capable of imaging targets of very low concentrations (27.6 μM or 0.01 mg/mL) at significant depths, such as 21 mm. Our results demonstrate that there is little variation in the reconstructed target size with a maximum target size error of 4.35% for different imaging depths for XLCT. We have, we believe for the first time, compared the sensitivity of XLCT with that of traditional computed tomography (CT) for phosphor targets. We found that XLCT's use of x-ray-induced photons provides much higher measurement sensitivity and contrast compared to CT, which provides image contrast solely based on x-ray attenuation.

Laplacian manifold regularization method for fluorescence molecular tomography

Sparse regularization methods have been widely used in fluorescence molecular tomography (FMT) for stable three-dimensional reconstruction. Generally, ? 1 -regularization-based methods allow for utilizing the sparsity nature of the target distribution. However, in addition to sparsity, the spatial structure information should be exploited as well. A joint ? 1 and Laplacian manifold regularization model is proposed to improve the reconstruction performance, and two algorithms (with and without Barzilai–Borwein strategy) are presented to solve the regularization model. Numerical studies and in vivo experiment demonstrate that the proposed Gradient projection-resolved Laplacian manifold regularization method for the joint model performed better than the comparative algorithm for ? 1 minimization method in both spatial aggregation and location accuracy.

An Inversion Scheme for Hybrid Fluorescence Molecular Tomography Using a Fuzzy Inference System

The imaging performance of fluorescence molecular tomography (FMT) improves when information from the underlying anatomy is incorporated into the inversion scheme, in the form of priors. The requirement for incorporation of priors has recently driven the development of hybrid FMT systems coupled to other modalities, such as X-ray CT and MRI. A critical methodological aspect in this modality relates to the particular method selected to incorporate prior information obtained from the anatomical imaging modality into the FMT inversion. We propose herein a new approach for utilizing prior information, which preferentially minimizes residual errors associated with measurements that better describe the anatomical segments considered. This preferential minimization was realized using a weighted least square (WLS) approach, where the weights were optimized using a Mamdani-type fuzzy inference system. The method of priors introduced herein was deployed as a two-step structured regularization approach and was verified with experimental measurements from phantoms as well as ex vivo and in vivo animal studies. The results demonstrate accurate performance and minimization of reconstruction bias, without requiring user input for setting the regularization parameters. As such, the proposed method offers significant progress in incorporation of anatomical priors in FMT and, as a result, in realization of the full potential of hybrid FMT.

Reconstruction algorithm for fluorescence molecular tomography using sorted L-one penalized estimation

Fluorescence molecular tomography (FMT) has been a promising imaging tool that provides convenience for accurate localization and quantitative analysis of the fluorescent probe. In this study, we present a reconstruction method combining sorted L-one penalized estimation with an iterative-shrinking permissible region strategy to reconstruct fluorescence targets. Both numerical simulation experiments on a three-dimensional digital mouse model and physical experiments on a cubic phantom were carried out to validate the accuracy, effectiveness, and robustness of the proposed method. The results indicate that the proposed method can produce better location and satisfactory fluorescent yield with computational efficiency, which makes it a practical and promising reconstruction method for FMT.

Improved sparse reconstruction for fluorescence molecular tomography with L1/2 regularization

Fluorescence molecular tomography (FMT) is a promising imaging technique that allows in vivo visualization of molecular-level events associated with disease progression and treatment response. Accurate and efficient 3D reconstruction algorithms will facilitate the wide-use of FMT in preclinical research. Here, we utilize L1/2-norm regularization for improving FMT reconstruction. To efficiently solve the nonconvex L1/2-norm penalized problem, we transform it into a weighted L1-norm minimization problem and employ a homotopy-based iterative reweighting algorithm to recover small fluorescent targets. Both simulations on heterogeneous mouse model and in vivo experiments demonstrated that the proposed L1/2-norm method outperformed the comparative L1-norm reconstruction methods in terms of location accuracy, spatial resolution and quantitation of fluorescent yield. Furthermore, simulation analysis showed the robustness of the proposed method, under different levels of measurement noise and number of excitation sources.

Nonuniform update for sparse target recovery in fluorescence molecular tomography accelerated by ordered subsets

Fluorescence molecular tomography (FMT) is a promising imaging modality and has been actively studied in the past two decades since it can locate the specific tumor position three-dimensionally in small animals. However, it remains a challenging task to obtain fast, robust and accurate reconstruction of fluorescent probe distribution in small animals due to the large computational burden, the noisy measurement and the ill-posed nature of the inverse problem. In this paper we propose a nonuniform preconditioning method in combination with L (1) regularization and ordered subsets technique (NUMOS) to take care of the different updating needs at different pixels, to enhance sparsity and suppress noise, and to further boost convergence of approximate solutions for fluorescence molecular tomography. Using both simulated data and phantom experiment, we found that the proposed nonuniform updating method outperforms its popular uniform counterpart by obtaining a more localized, less noisy, more accurate image. The computational cost was greatly reduced as well. The ordered subset (OS) technique provided additional 5 times and 3 times speed enhancements for simulation and phantom experiments, respectively, without degrading image qualities. When compared with the popular L (1) algorithms such as iterative soft-thresholding algorithm (ISTA) and Fast iterative soft-thresholding algorithm (FISTA) algorithms, NUMOS also outperforms them by obtaining a better image in much shorter period of time.