Compressed-sensing-inspired reconstruction algorithms in low-dose computed tomography: A review

BACKGROUND

Optimization of the dose the patient receives during scanning is an important problem in modern medical X-ray computed tomography (CT). One of the basic ways to its solution is to reduce the number of views. Compressed sensing theory helped promote the development of a new class of effective reconstruction algorithms for limited data CT. These compressed-sensing-inspired (CSI) algorithms optimize the Lp (0 ≤ p ≤ 1) norm of images and can accurately reconstruct CT tomograms from a very few views. The paper presents a review of the CSI algorithms and discusses prospects for their further use in commercial low-dose CT.

METHODS

Many literature references with the CSI algorithms have been were searched. To structure the material collected the author gives a classification framework within which he describes Lp regularization methods, the basic CSI algorithms that are used most often in few-view CT, and some of their derivatives. Lots of examples are provided to illustrate the use of the CSI algorithms in few-view and low-dose CT.

RESULTS

A list of the CSI algorithms is compiled from the literature search. For better demonstrativeness they are summarized in a table. The inference is done that already today some of the algorithms are capable of reconstruction from 20 to 30 views with acceptable quality and dose reduction by a factor of 10.

DISCUSSION

In conclusion the author discusses how soon the CSI reconstruction algorithms can be introduced in the practice of medical diagnosis and used in commercial CT scanners.

Spatial Sensitivity to Absorption Changes for Various Near-Infrared Spectroscopy Methods: A Compendium Review

This compendium review focuses on the spatial distribution of sensitivity to localized absorption changes in optically diffuse media, particularly for measurements relevant to near-infrared spectroscopy. The three temporal domains, continuous-wave, frequency-domain, and time-domain, each obtain different optical data-types whose changes may be related to effective homogeneous changes in the absorption coefficient. Sensitivity is the relationship between a localized perturbation and the recovered effective homogeneous absorption change. Therefore, spatial sensitivity maps representing the perturbation location can be generated for the numerous optical data-types in the three temporal domains. The review first presents a history of the past 30 years of work investigating this sensitivity in optically diffuse media. These works are experimental and theoretical, presenting 1-, 2-, and 3-dimensional sensitivity maps for different near-infrared spectroscopy methods, domains, and data-types. Following this history, we present a compendium of sensitivity maps organized by temporal domain and then data-type. This compendium provides a valuable tool to compare the spatial sensitivity of various measurement methods and parameters in one document. Methods for one to generate these maps are provided in the appendix, including code. This historical review and comprehensive sensitivity map compendium provides a single source researchers may use to visualize, investigate, compare, and generate sensitivity to localized absorption change maps.

Fluorescence molecular tomography for quantum yield and lifetime

Fluorescence molecular tomography (FMT) is a promising modality for noninvasive imaging of internal fluorescence agents in biological tissues, especially in small animal models, with applications in diagnosis, therapy, and drug design. In this paper, we present a fluorescent reconstruction algorithm that combines time-resolved fluorescence imaging data with photon-counting microcomputed tomography (PCMCT) images to estimate the quantum yield and lifetime of fluorescent markers in a mouse model. By incorporating PCMCT images, a permissible region of interest of fluorescence yield and lifetime can be roughly estimated as prior knowledge, reducing the number of unknown variables in the inverse problem and improving the image reconstruction stability. Our numerical experiments demonstrate the accuracy and stability of the proposed reconstruction method in the presence of data noise, achieving a reconstruction error of 0.02 ns for the fluorescence lifetime and an average relative error of 18% for quantum yield reconstruction.

Multi-Energy and Fast-Convergence Iterative Reconstruction Algorithm for Organic Material Identification Using X-ray Computed Tomography

In order to significantly reduce the computing time while, at the same time, keeping the accuracy and precision when determining the local values of the density and effective atomic number necessary for identifying various organic material, including explosives and narcotics, a specialized multi-stage procedure based on a multi-energy computed tomography investigation within the 20-160 keV domain was elaborated. It consisted of a compensation for beam hardening and other non-linear effects that affect the energy dependency of the linear attenuation coefficient (LAC) in the chosen energy domain, followed by a 3D fast reconstruction algorithm capable of reconstructing the local LAC values for 64 energy values from 19.8 to 158.4 keV, and, finally, the creation of a set of algorithms permitting the simultaneous determination of the density and effective atomic number of the investigated materials. This enabled determining both the density and effective atomic number of complex objects in approximately 24 s, with an accuracy and precision of less than 3%, which is a significantly better performance with respect to the reported literature values.

Reconstruction of fluorophore absorption and fluorescence lifetime using early photon mesoscopic fluorescence molecular tomography: a phantom study

SIGNIFICANCE

Fluorescence molecular lifetime tomography (FMLT) plays an increasingly important role in experimental oncology. The article presents and experimentally verifies an original method of mesoscopic time domain FMLT, based on an asymptotic approximation to the fluorescence source function, which is valid for early arriving photons.

AIM

The aim was to justify the efficiency of the method by experimental scanning and reconstruction of a phantom with a fluorophore. The experimental facility included the TCSPC system, the pulsed supercontinuum Fianium laser, and a three-channel fiber probe. Phantom scanning was done in mesoscopic regime for three-dimensional (3D) reflectance geometry.

APPROACH

The sensitivity functions were simulated with a Monte Carlo method. A compressed-sensing-like reconstruction algorithm was used to solve the inverse problem for the fluorescence parameter distribution function, which included the fluorophore absorption coefficient and fluorescence lifetime distributions. The distributions were separated directly in the time domain with the QR-factorization least square method.

RESULTS

3D tomograms of fluorescence parameters were obtained and analyzed using two strategies for the formation of measurement data arrays and sensitivity matrices. An algorithm is developed for the flexible choice of optimal strategy in view of attaining better reconstruction quality. Variants on how to improve the method are proposed, specifically, through stepped extraction and further use of a posteriori information about the object.

CONCLUSIONS

Even if measurement data are limited, the proposed method is capable of giving adequate reconstructions but their quality depends on available a priori (or a posteriori) information. Further research aims to improve the method by implementing the variants proposed.

Monte Carlo simulation of sensitivity functions for few-view computed tomography of strongly absorbing media

The paper describes a sensitivity function calculation method for few-view X-ray computed tomography of strongly absorbing objects. It is based on a probabilistic interpretation of energy transport through the object from a source to a detector. A PRIZMA code package is used to track photons. The code is developed at FSUE “RFNC–VNIITF named after Academ. E. I. Zababakhin” and implements a stochastic Monte Carlo method. The value of the sensitivity function in a discrete cell of the reconstruction region is assumed to be directly proportional to the fraction of photon trajectories which cross the cell from all those recorded by the detector. The method’s efficiency is validated through a numerical experiment on the reconstruction of a section of a spherical heavy-metal phantom with an air cavity and a density difference of 25 Ṫhe proposed method is shown to outperform the method based on projection approximation in case of reconstruction from 9 views.

Early-photon reflectance fluorescence molecular tomography for small animal imaging: Mathematical model and numerical experiment

The paper presents an original approach to time-domain reflectance fluorescence molecular tomography (FMT) of small animals. It is based on the use of early arriving photons and state-of-the-art compressed-sensing-like reconstruction algorithms and aims to improve the spatial resolution of fluorescent images. We deduce the fundamental equation that models the imaging operator and derive analytical representations for the sensitivity functions which are responsible for the reconstruction of the fluorophore absorption coefficient. The idea of fluorescence lifetime tomography with our approach is also discussed. We conduct a numerical experiment on 3D reconstruction of box phantoms with spherical fluorescent inclusions of small diameters. For modeling measurement data and constructing the sensitivity matrix we assume a virtual fluorescence tomograph with a scanning fiber probe that illuminates and collects light in reflectance geometry. It provides for large source-receiver separations which correspond to the macroscopic regime. Two compressed-sensing-like reconstruction algorithms are used to solve the inverse problem. These are the algebraic reconstruction technique with total variation regularization and our modification of the fast iterative shrinkage-thresholding algorithm. Results of our numerical experiment show that our approach is capable of achieving as good spatial resolution as 0.2 mm and even better at depths to 9 mm inclusive.

Accelerated Stimulated Raman Projection Tomography by Sparse Reconstruction From Sparse-View Data

OBJECTIVE

Stimulated Raman projection tomography (SRPT), a recently developed label-free volumetric chemical imaging technology, has been reported to quantitatively reconstruct the distribution of chemicals in a three-dimensional (3D) complex system. The current image reconstruction scheme used in SRPT is based on a filtered back projection (FBP) algorithm that requires at least 180 angular-dependent projections to rebuild a reasonable SRPT image, resulting in a long total acquisition time. This is a big limitation for longitudinal studies on live systems.

METHODS

We present a sparse-view data-based sparse reconstruction scheme, in which sparsely sampled projections at 180 degrees were used to reconstruct the volumetric information. In the scheme, the simultaneous algebra reconstruction technique (SART), combined with total variation regularization, was used for iterative reconstruction. To better describe the projection process, a pixel vertex driven model (PVDM) was developed to act as projectors, whose performance was compared with those of the distance driven model (DDM).

RESULTS

We evaluated our scheme with numerical simulations and validated it for SRPT by mapping lipid contents in adipose cells. Simulation results showed that the PVDM performed better than the DDM in the case of using sparse-view data. Our scheme could maintain the quality of the reconstructed images even when the projection number was reduced to 15. The cell-based experimental results demonstrated that the proposed scheme can improve the imaging speed of the current FBP-based SRPT scheme by a factor of 9-12 without sacrificing discernible imaging details.

CONCLUSION

Our proposed scheme significantly reduces the total acquisition time required for SRPT at a speed of one order of magnitude faster than the currently used scheme. This significant improvement in imaging speed would potentially promote the applicability of SRPT for imaging living organisms.

Multimodal imaging combining time-domain near-infrared optical tomography and continuous-wave fluorescence molecular tomography

Fluorescence molecular tomography (FMT) emerges as a powerful non-invasive imaging tool with the ability to resolve fluorescence signals from sources located deep in living tissues. Yet, the accuracy of FMT reconstruction depends on the deviation of the assumed optical properties from the actual values. In this work, we improved the accuracy of the initial optical properties required for FMT using a new-generation time-domain (TD) near-infrared optical tomography (NIROT) system, which effectively decouples scattering and absorption coefficients. We proposed a multimodal paradigm combining TD-NIROT and continuous-wave (CW) FMT. Both numerical simulation and experiments were performed on a heterogeneous phantom containing a fluorescent inclusion. The results demonstrate significant improvement in the FMT reconstruction by taking the NIROT-derived optical properties as prior information. The multimodal method is attractive for preclinical studies and tumor diagnostics since both functional and molecular information can be obtained.

Joint image reconstruction and segmentation: Comparison of two algorithms for few-view tomography

Two algorithms of few-view tomography are compared, specifically, the iterative Potts minimization algorithm (IPMA) and the algebraic reconstruction technique with TV-regularization and adaptive segmentation (ART-TVS). Both aim to reconstruct piecewise-constant structures, use the compressed sensing theory, and combine image reconstruction and segmentation procedures. Using a numerical experiment, it is shown that either algorithm can exactly reconstruct the Shepp-Logan phantom from as small as 7 views with noise characteristic of the medical applications of X-ray tomography. However, if an object has a complicated high-frequency structure (QR-code), the minimal number of views required for its exact reconstruction increases to 17–21 for ART-TVS and to 32–34 for IPMA. The ART-TVS algorithm developed by the authors is shown to outperform IPMA in reconstruction accuracy and speed and in resistance to abnormally high noise as well. ART-TVS holds good potential for further improvement.

Sparse-view tomography via displacement function interpolation

Sparse-view tomography has many applications such as in low-dose computed tomography (CT). Using under-sampled data, a perfect image is not expected. The goal of this paper is to obtain a tomographic image that is better than the naïve filtered backprojection (FBP) reconstruction that uses linear interpolation to complete the measurements. This paper proposes a method to estimate the un-measured projections by displacement function interpolation. Displacement function estimation is a non-linear procedure and the linear interpolation is performed on the displacement function (instead of, on the sinogram itself). As a result, the estimated measurements are not the linear transformation of the measured data. The proposed method is compared with the linear interpolation methods, and the proposed method shows superior performance.

Time-Domain Near-Infrared Spectroscopy and Imaging: A Review

This article reviews the past and current statuses of time-domain near-infrared spectroscopy (TD-NIRS) and imaging. Although time-domain technology is not yet widely employed due to its drawbacks of being cumbersome, bulky, and very expensive compared to commercial continuous wave (CW) and frequency-domain (FD) fNIRS systems, TD-NIRS has great advantages over CW and FD systems because time-resolved data measured by TD systems contain the richest information about optical properties inside measured objects. This article focuses on reviewing the theoretical background, advanced theories and methods, instruments, and studies on clinical applications for TD-NIRS including some clinical studies which used TD-NIRS systems. Major events in the development of TD-NIRS and imaging are identified and summarized in chronological tables and figures. Finally, prospects for TD-NIRS in the near future are briefly described.

Optoacoustic Breast Imaging: Imaging-Pathology Correlation of Optoacoustic Features in Benign and Malignant Breast Masses

OBJECTIVE

Optoacoustic ultrasound breast imaging is a fused anatomic and functional modality that shows morphologic features, as well as hemoglobin amount and relative oxygenation within and around breast masses. The purpose of this study is to investigate the positive predictive value (PPV) of optoacoustic ultrasound features in benign and malignant masses.

SUBJECTS AND METHODS

In this study, 92 masses assessed as BI-RADS category 3, 4, or 5 in 94 subjects were imaged with optoacoustic ultrasound. Each mass was scored by seven blinded independent readers according to three internal features in the tumor interior and two external features in its boundary zone and periphery. Mean and median optoacoustic ultrasound scores were compared with histologic findings for biopsied masses and nonbiopsied BI-RADS category 3 masses, which were considered benign if they were stable at 12-month follow-up. Statistical significance was analyzed using a two-sided Wilcoxon rank sum test with a 0.05 significance level.

RESULTS

Mean and median optoacoustic ultrasound scores for all individual internal and external features, as well as summed scores, were higher for malignant masses than for benign masses (p < 0.0001). High external scores, indicating increased hemoglobin and deoxygenation and abnormal vessel morphologic features in the tumor boundary zone and periphery, better distinguished benign from malignant masses than did high internal scores reflecting increased hemoglobin and deoxygenation within the tumor interior.

CONCLUSION

High optoacoustic ultrasound scores, particularly those based on external features in the boundary zone and periphery of breast masses, have high PPVs for malignancy and, conversely, low optoacoustic ultrasound scores have low PPV for malignancy. The functional component of optoacoustic ultrasound may help to overcome some of the limitations of morphologic overlap in the distinction of benign and malignant masses.

Volumetric chemical imaging by stimulated Raman projection microscopy and tomography

Volumetric imaging allows global understanding of three-dimensional (3D) complex systems. Light-sheet fluorescence microscopy and optical projection tomography have been reported to image 3D volumes with high resolutions and at high speeds. Such methods, however, usually rely on fluorescent labels for chemical targeting, which could perturb the biological functionality in living systems. We demonstrate Bessel-beam-based stimulated Raman projection (SRP) microscopy and tomography for label-free volumetric chemical imaging. Our SRP microscope enables fast quantitation of chemicals in a 3D volume through a two-dimensional lateral scan. Furthermore, combining SRP and sample rotation, we demonstrate the SRP tomography that can reconstruct the 3D distribution of chemical compositions with optical spatial resolution at a higher speed than the Gaussian-beam-based stimulated Raman scattering sectioning imaging can. We explore the potential of our SRP technology by mapping polymer particles in 3D volumes and lipid droplets in adipose cells.

Recent advances have enabled high-speed three-dimensional optical imaging through the use of fluorescent markers. Here, Chen et al. integrate stimulated Raman imaging into those methods, enabling the label-free and chemically specific volumetric imaging of complex samples.

Depth discrimination in diffuse optical transmission imaging by planar scanning off-axis fibers: initial applications to optical mammography

We present a method for depth discrimination in parallel-plate, transmission mode, diffuse optical imaging. The method is based on scanning a set of detector pairs, where the two detectors in each pair are separated by a distance δDi along direction δ D i within the x-y scanning plane. A given optical inhomogeneity appears shifted by αi δ D i (with 0≤ αi ≤1) in the images collected with the two detection fibers of the i-th pair. Such a spatial shift can be translated into a measurement of the depth z of the inhomogeneity, and the depth measurements based on each detector pair are combined into a specially designed weighted average. This depth assessment is demonstrated on tissue-like phantoms for simple inhomogeneities such as straight rods in single-rod or multiple-rod configurations, and for more complex curved structures which mimic blood vessels in the female breast. In these phantom tests, the method has recovered the depth of single inhomogeneities in the central position of the phantom to within 4 mm of their actual value, and within 7 mm for more superficial inhomogeneities, where the thickness of the phantom was 65 mm. The application of this method to more complex images, such as optical mammograms, requires a robust approach to identify corresponding structures in the images collected with the two detectors of a given pair. To this aim, we propose an approach based on the inner product of the skeleton images collected with the two detectors of each pair, and we present an application of this approach to optical in vivo images of the female breast. This depth discrimination method can enhance the spatial information content of 2D projection images of the breast by assessing the depth of detected structures, and by allowing for 3D localization of breast tumors.

Spatial Resolution Analysis for Few-Views Discrete Tomography Based on MART-AP Algorithm

We study a new MART-AP algorithm of few-views discrete tomography. Its efficiency for high-frequency structure reproduction is investigated in a numerical experiment where we reconstruct a 2D model for the estimation of the spatial resolution limit. We estimate the modulation transfer function of the reconstruction algorithm and compare it with the modulation transfer function of projection distortions. Our results show that MART-AP weakly influences the contrast of spatial structures being reproduced and can be used for high-resolution reconstruction when only a few projections are registered.

Perturbation-resilient block-iterative projection methods with application to image reconstruction from projections

A block-iterative projection algorithm for solving the consistent convex feasibility problem in a finite-dimensional Euclidean space that is resilient to bounded and summable perturbations (in the sense that convergence to a feasible point is retained even if such perturbations are introduced in each iterative step of the algorithm) is proposed. This resilience can be used to steer the iterative process towards a feasible point that is superior in the sense of some functional on the points in the Euclidean space having a small value. The potential usefulness of this is illustrated in image reconstruction from projections, using both total variation and negative entropy as the functional.

Fluorescence diffuse tomography for detection of red fluorescent protein expressed tumors in small animals

A fluorescence diffuse tomography (FDT) setup for monitoring tumor growth in small animals has been created. In this setup an animal is scanned in the transilluminative configuration by a single source and detector pair. To remove stray light in the detection system, we used a combination of interferometric and absorption filters. To reduce the scanning time, an experimental animal was scanned using the following algorithm: (1) large-step scanning to obtain a general view of the animal (source and detector move synchronously); (2) selection of the fluorescing region; and (3) small-step scanning of the selected region and different relative shifts between the source and detector to obtain sufficient information for 3D reconstruction. We created a reconstruction algorithm based on the Holder norm to estimate the fluorophore distribution. This algorithm converges to the solution with a minimum number of fluorescing zones. The use of tumor cell lines transfected with fluorescent proteins allowed us to conduct intravital monitoring studies. Cell lines of human melanomas Mel-P, Mel-Ibr, Mel-Kor, and human embryonic kidney HEK293 Phoenix were transfected with DsRed-Express and Turbo-RFP genes. The emission of red fluorescent proteins (RFPs) in the long-wave optical range permits detection of deep-seated tumors. In vivo experiments were conducted immediately after subcutaneous injection of fluorescing cells into small animals.