Versatile regularisation toolkit for iterative image reconstruction with proximal splitting algorithms

This paper presents a novel method for segmentation and change detection of multispectral images using proximal splitting-based clustering and multiclass support vector machine (MSVM). Initially, the multitemporal satellite images are preprocessed and then textures are extracted using Difference of Offset Gaussian filter. In general, the traditional clustering method uses Euclidean distance as a prime factor for segmentation process. For multitextured images such as remotely sensed images, this metric provides inconsistent output. To achieve better segmented results, proximal splitting algorithm has been proposed. This method has been considered as a solution for iterative minimization problem, which is required to find exact changes between the multitemporal images. The MSVM is chosen to group the segmented clusters into a fixed number of classes, since the clusters obtained from the proximal splitting algorithm are not independent with each other. Then, the classified images are subjected to image differencing method to detect the changes. Experimentation is performed with two real data sets of Landsat7 images, which illustrates that the mean of difference in area obtained by the proposed method is reduced by an average of 35.24% compared to the conventional system. The validity index obtained for data set 1 using proposed algorithm is lower than the existing methods.

X-ray computed tomography (CT) imaging plays an essential role in disease diagnosis due to its noninvasive, painless mode and superior penetration depth. However, the resolution of the soft tissue ...

Noninvasive imaging in the evaluation of a wide variety of cardiovascular diseases has gained an increasing role in the diagnostic strategy in current cardiology practice [1][2][3][4].This holds in particular for patients with myocardial ischaemia due to coronary artery disease (CAD) [5][6][7].Of the present imaging modalities, single-photon emission computed tomography (SPECT), positron emission tomography (PET) and cardiac magnetic resonance (CMR) have attained a major position when it comes to myocardial perfusion imaging [8][9][10][11][12].In the May 2012 issue of the Journal of the American College of Cardiology (JACC), Jaarsma et al. [13] from Maastricht University Medical Center evaluated the diagnostic accuracy of SPECT, PET and CMR for the diagnosis of obstructive CAD.Studies published between 1990 and 2010 identified by PubMed search and citation tracking were examined.A study was included if a perfusion imaging modality was used as a diagnostic test for the detection of obstructive CAD and coronary angiography as the reference standard (50 % diameter luminal stenosis).Out of a total of 3635 studies, 166 articles (including 17,901 patients) met the inclusion criteria: 114 SPECT, 37 CMR, and 15 PET studies.There were insufficient publications on perfusion echocardiography and computed tomography to include these modalities in the study.Patient-based analysis per imaging modality demonstrated pooled sensitivities of 88 % for SPECT, 84 % for PET , and 89 % for CMR; pooled specificities were 61 %, 81 %, and 76 %, respectively.The authors concluded that SPECT, PET, and CMR all yielded high sensitivities, whereas a broad range of specificities were observed.CMR and especially PET showed a significantly higher diagnostic accuracy than SPECT.However, SPECT is more widely available, less expensive, and most extensively validated.In addition, the use of attenuation programs improved the specificity of SPECT.CMR may provide a valid alternative without ionising radiation to the nuclear imaging methods.The authors suggested that referring physicians should consider these findings in the context of local expertise and internal logistics.The authors should be complimented for performing this impressive research.It is the first meta-analysis that has directly compared the three most commonly used techniques for myocardial perfusion imaging, i.e.SPECT, PET, and CMR.The present study emphasises that, from a clinical perspective, each of the studied imaging modalities is in principle suited for detection of abnormalities in myocardial perfusion imaging [14].As always, selective use is mostly dependent on the institutional availability of the imaging device(s), familiarity with the technique, and the individual expert knowledge of the treating physician [15].

Whole-body positron emission tomography (PET) with F-fluorodeoxyglucose (FDG) has proven to be a very effective staging imaging modality in manymalignant tumours, particularly in lung cancer, malignant melanoma, lymphoma, colorectal cancer and head and neck tumours [1–7]. Since PET images have a fairly high resolution (,6 mm), even small lesions with an increased FDG uptake can be detected. This represents a critical advantage of PET over the conventional cross-sectional imaging modalities CT and MRI. PET can be used to identify tumour tissue on the basis of FDG uptake, rather than on the basis of morphological appearance or size, and thus also in lesions with a size less than 1 cm. Unfortunately, FDG–PET provides little anatomical information, and therefore it is sometimes difficult to determine where the lesions detected are located and what they represent. It is important for the surgeon to know precisely where lesions are located, especially for small tumours. Currently, comparison and juxtaposition of PET images and CT images serves to define the localization of the lesions. Owing to the different image slice thickness, the different positioning of the patient during the two examinations and the different states of nutrition, i.e. fasting for 4 h prior to FDG–PET, it is often very difficult and time consuming to match the images for exact anatomical localization. Image co-registration has been used to overcome these problems [8]. It has been recognized that proper image co-registration is rather difficult for whole-body examinations with separate scanners. For identical patient positioning during PET and CT scanning, special ‘‘cast forming’’ vacuum mattresses or other immobilization methods should be used. However, patients frequently find these methods of immobilization uncomfortable. Logistic problems also limit the use of image co-registration of PET and CT with separate scanners. Scheduling problems arise when performing the two examinations one after the other. These limitations restrict image co-registration with separate scanners to individual cases. In our experience, the exact localization of lesions is often not possible when juxtaposing PET and CT images. Examinations had to be repeated for exact image co-registration. As a result, image co-registration with separate scanners has never become routine in our practice. To overcome the problems related to software fusion, various prototype systems combining molecular and morphologic imaging have been developed. Hasegawa and colleagues proposed an integrated SPECT/CT scanner [9], and in 1999 Townsend and his colleagues at the University of Pittsburgh presented a prototype integrated PET/CT scanner by combining a CT scanner and a partial ring, rotating PET scanner in a single gantry [10, 11]. Such systems are attractive not only because of the ‘‘hardware’’ image coregistration capabilities but also because the CT data can be used to correct PET scans for patient self-absorption of the PET emission rays. This decreases the acquisition time for the correcting attenuation scans by an order of magnitude compared with the conventional techniques used in PET for this purpose, and decreases the overall imaging time by up to 30% depending on the CT system used. In March 2001, the first clinical integrated PET/ CT device (Discovery LS, GE Medical Systems, Milwaukee, USA) was installed at the University Hospital of Zurich in Switzerland. This novel inline system consists of a dedicated high resolution/ high sensitivity full-ring PET scanner (Advance Nxi) and a very fast high-end multi-detector spiral CT scanner (Light Speed Plus). The axes of both systems are mechanically aligned so that simple translation of the patient table by 60 cm moves the patient from the CT into the PET gantry. The resulting PET and CT images are ‘‘hardware’’ coregistered to an accuracy in the range of 1 mm. Data acquisition in the combined system is as follows. At 45–55 min post-injection of FDG and after bladder emptying a multidetector computed tomography scan is performed from the pelvic floor to the head (scan length, 86.7 cm) and normal end-expiration. Immediately after CT scanning, a PET emission scan is obtained covering the identical axial field of view using six PET fields of view. The acquisition time is 4 min at each table position. With this protocol it is The British Journal of Radiology, 75 (2002), S36–S38 E 2002 The British Institute of Radiology

Small-animal positron emission tomography as a tool for neuropharmacology

We introduce a generalization of the linearized Alternating Direction Method of Multipliers to optimize a real-valued function $f$ of multiple arguments with potentially multiple constraints $g_\circ$ on each of them. The function $f$ may be nonconvex as long as it is convex in every argument, while the constraints $g_\circ$ need to be convex but not smooth. If $f$ is smooth, the proposed Block-Simultaneous Direction Method of Multipliers (bSDMM) can be interpreted as a proximal analog to inexact coordinate descent methods under constraints. Unlike alternative approaches for joint solvers of multiple-constraint problems, we do not require linear operators $L$ of a constraint function $g(L\ \cdot)$ to be invertible or linked between each other. bSDMM is well-suited for a range of optimization problems, in particular for data analysis, where $f$ is the likelihood function of a model and $L$ could be a transformation matrix describing e.g. finite differences or basis transforms. We apply bSDMM to the Non-negative Matrix Factorization task of a hyperspectral unmixing problem and demonstrate convergence and effectiveness of multiple constraints on both matrix factors. The algorithms are implemented in python and released as an open-source package.

11064 Background: Positron emission tomography (PET) using the catecholamine precursor 6-[F-18]fluoro-L-dihydroxyphenylalanine ((18)F-DOPA) has emerged as promising technique to localize tumors with catecholamine excess. This study investigated the sensitivity of (18)F-DOPA PET, compared to (123)I-metaiodobenzylguanidine ((123)I-MIBG) scintigraphy and computer tomography (CT)/ magnetic resonance imaging (MRI) in patients with catecholamine excess. METHODS: In a single center prospective study (18)F-DOPA PET was compared to (123)I-MIBG and CT/MRI in patients with catecholamine excess. The performance of each imaging modality was analyzed for individual patients and individual lesions. (18)F-DOPA PET, (123)I-MIBG, and CT/MRI were compared using a composite reference standard derived from all available imaging, clinical and histological information. Sensitivities were calculated and discordance between imaging techniques was compared. (18)F-DOPA PET uptake was measured to determine whole body metabolic burden. Correlations between (18)F-DOPA PET imaging and biochemical data were evaluated. RESULTS: 48 patients were included. The tumor localization was found in 45 patients, 43 with (18)F-DOPA PET, 31 with (123)I-MIBG and 32 with CT/MRI, resulting with surgery in final diagnosis of pheochromocytoma in 40, adrenal hyperplasia in 2, paraganglioma in 2, ganglioneuroma in 1 and 3 unknown (as yet no lesion detected). Per patient based analysis showed sensitivities for (18)F-DOPA PET, (123)I-MIBG and CT/MRI of 90, 65 and 67% (P<.01 (18)F-DOPA PET vs (123)I-MIBG, P<.01 (18)F-DOPA PET vs CT/MRI, P=1.0 (123)I-MIBG vs CT/MRI). Corresponding sensitivities in the lesion based analysis were 73, 48 and 44%, respectively (P<.001 for both (18)F-DOPA PET vs (123)I-MIBG and vs CT/MRI, P=.51 (123)I-MIBG vs CT/MRI). The (8)F-DOPA PET+CT/MRI combination was superior to (123)I-MIBG+CT/MRI (93 vs 76%, P<.001) Whole body metabolic burden measured with (18)F-DOPA PET correlated with plasma free normetanephrine (r=.82) and 24h urinary total normetanephrine (r=.84) and metanephrine (r=.57). CONCLUSIONS: The sensitivity of (18)F-DOPA PET to localize tumors with catecholamine excess is superior to either (123)I-MIBG scintigraphy or CT/MRI. No significant financial relationships to disclose.

Many technical updates have been made in multi-detector CT. To evaluate image quality and radiation dose of high-pitch second- and third-generation dual-source chest CT angiography and to assess the effects of different levels of advanced modeled iterative reconstruction (ADMIRE) in newborns and children. Chest CT angiography (70 kVp) was performed in 42 children (age 158 ± 267 days, range 1-1,194 days). We evaluated subjective and objective image quality, and radiation dose with filtered back projection (FBP) and different strength levels of ADMIRE. For comparison were 42 matched controls examined with a second-generation 128-slice dual-source CT-scanner (80 kVp). ADMIRE demonstrated improved objective and subjective image quality (P < .01). Mean signal/noise, contrast/noise and subjective image quality were 11.9, 10.0 and 1.9, respectively, for the 80 kVp mode and 11.2, 10.0 and 1.9 for the 70 kVp mode. With ADMIRE, the corresponding values for the 70 kVp mode were 13.7, 12.1 and 1.4 at strength level 2 and 17.6, 15.6 and 1.2 at strength level 4. Mean CTDIvol, DLP and effective dose were significantly lower with the 70-kVp mode (0.31 mGy, 5.33 mGy*cm, 0.36 mSv) compared to the 80-kVp mode (0.46 mGy, 9.17 mGy*cm, 0.62 mSv; P < .01). The third-generation dual-source CT at 70 kVp provided good objective and subjective image quality at lower radiation exposure. ADMIRE improved objective and subjective image quality.

This study evaluates ultra-low-dose computed tomography (ULDCT) protocols concerning the detectability of pulmonary nodules. The influence of tube current settings, kernels, strength levels of third-generation iterative reconstruction algorithms, and pitch was investigated. A chest phantom with artificial spherical nodules of different densities and diameters was examined with a third-generation dual-source CT. Scanning and post-processing protocols, tube current levels, and ultra-high and non-high pitch modes were applied. Images were reconstructed with filtered back-projection (FBP) or advanced model-based iterative reconstruction (ADMIRE) algorithms. Sharp (Bl57) or medium-soft (Br36) convolution kernels were applied. The reading was performed by an experienced and an inexperienced reader. The highest observer sensitivity was found using a non-high pitch protocol at tube currents of 120 mAs and 90 mAs with the sharp kernel and iterative reconstruction level of 5. Non-high pitch protocols showed better detectability of solid nodules. Combinations with the medium-soft kernel achieved slightly higher observer sensitivity than with the sharp kernel. False positives (FP) occurred more often for subsolid nodules, at a tube current level of 120 mAs, and with the sharp kernel. A tube current level of 90 mAs combined with the highest iterative reconstruction level achieved the highest accuracy in lung nodule detection regardless of size, density, and reader experience.

BackgroundHybrid imaging combines nuclear medicine imaging such as single photon emission computed tomography (SPECT) or positron emission tomography (PET) with computed tomography (CT). Through this hybrid design, scanned patients accumulate radiation exposure from both applications. Imaging modalities have been the subject of long-term optimization efforts, focusing on diagnostic applications. It was the aim of this study to investigate the influence of an iterative CT image reconstruction algorithm (ASIR) on the image quality of the low-dose CT images.Methodology/Principal FindingsExaminations were performed with a SPECT-CT scanner with standardized CT and SPECT-phantom geometries and CT protocols with systematically reduced X-ray tube currents. Analyses included image quality with respect to photon flux. Results were compared to the standard FBP reconstructed images. The general impact of the CT-based attenuation maps used during SPECT reconstruction was examined for two SPECT phantoms. Using ASIR for image reconstructions, image noise was reduced compared to FBP reconstructions for the same X-ray tube current. The Hounsfield unit (HU) values reconstructed by ASIR were correlated to the FBP HU values(R2 ≥ 0.88) and the contrast-to-noise ratio (CNR) was improved by ASIR. However, for a phantom with increased attenuation, the HU values shifted for low X-ray tube currents I ≤ 60 mA (p ≤ 0.04). In addition, the shift of the HU values was observed within the attenuation corrected SPECT images for very low X-ray tube currents (I ≤ 20 mA, p ≤ 0.001).Conclusion/SignificanceIn general, the decrease in X-ray tube current up to 30 mA in combination with ASIR led to a reduction of CT-related radiation exposure without a significant decrease in image quality.

Modelling the forward projection or reprojection, that is defined as the operation that transforms a 3D volume into series of 2D set of line integrals, is of interest in several medical imaging applications as iterative tomographic reconstruction (X-ray, Computed Tomography [CT], Positron Emission Tomography [PET], Single Photon Emission Computed Tomography [SPECT]), dose-calculation in radiotherapy and 3D-display volume-rendering. As forward projection is becoming widely used, iterative reconstruction algorithms and their characteristics may affect the reconstruction quality; its accuracy and performance needs more attention. The aim of this chapter is to show the importance of the modelling of the forward projection in the accuracy of medical tomographic data (CT, SPECT and PET) reconstructed with iterative algorithms. Therefore, we first present a brief overview on the iterative algorithms used in tomographic reconstruction in medical imaging. Second, we focus on the projection operators. Concepts and implementation of the most popular projection operators are discussed in detail. Performance of the computer implementations is shown using the well-known Shepp_Logan phantom. In order to avoid possibly confounding perspective effects implied by fan or cone-beam, this study is performed in parallel acquisition geometry.

We describe a fast forward and back projector pair based on inverse Fourier rebinning for use in iterative image reconstruction for fully 3-D positron emission tomography (PET). The projector pair is used as part of a factored system matrix that takes into account detector-pair response by using shift-variant sinogram blur kernels, thereby combining the computational advantages of Fourier rebinning with iterative reconstruction using accurate system models. The forward projector consists of a 2-D projector, which maps 3-D images into 2-D direct sinograms, followed by exact inverse rebinning which maps the 2-D into fully 3-D sinograms. The back projector is implemented as the transpose of the forward projector and differs from the true exact rebinning operator in the sense that it does not require reprojection to compute missing lines of response (LORs). We compensate for two types of inaccuracies that arise in a cylindrical PET scanner when using inverse Fourier rebinning: 1) nonuniform radial sampling and 2) nonconstant oblique angles in the radial direction in a single oblique sinogram. We examine the effects of these corrections on sinogram accuracy and reconstructed image quality. We evaluate performance of the new projector pair for maximum a posteriori (MAP) reconstruction of simulated and in vivo data. The new projector results in only a small loss in resolution towards the edge of the field-of-view when compared to the fully 3-D geometric projector and requires an order of magnitude less computation.

Positron emission tomography (PET) has, since its inception, established itself as the imaging modality of choice for the in vivo quantitative assessment of molecular targets in a wide range of biochemical processes underlying tumour physiology. PET image quantification enables to ascertain a direct link between the time-varying activity concentration in organs/tissues and the fundamental parameters portraying the biological processes at the cellular level being assessed. However, the quantitative potential of PET may be affected by a number of factors related to physical effects, hardware and software system specifications, tracer kinetics, motion, scan protocol design and limitations in current image-derived PET metrics. Given the relatively large number of PET metrics reported in the literature, the selection of the best metric for fulfilling a specific task in a particular application is still a matter of debate. Quantitative PET has advanced elegantly during the last two decades and is now reaching the maturity required for clinical exploitation, particularly in oncology where it has the capability to open many avenues for clinical diagnosis, assessment of response to treatment and therapy planning. Therefore, the preservation and further enhancement of the quantitative features of PET imaging is crucial to ensure that the full clinical value of PET imaging modality is utilized in clinical oncology. Recent advancements in PET technology and methodology have paved the way for faster PET acquisitions of enhanced sensitivity to support the clinical translation of highly quantitative four-dimensional (4D) parametric imaging methods in clinical oncology. In this report, we provide an overview of recent advances and future trends in quantitative PET imaging in the context of clinical oncology. The pros/cons of the various image-derived PET metrics will be discussed and the promise of novel methodologies will be highlighted.

In Reply to Wang and Shi

Cardiac positron emission tomography (PET) and positron emission tomography/computed tomography (PET/CT) are encouraging precise non-invasive imaging modalities that allow imaging of the cellular function of the heart, while other non-invasive cardiovascular imaging modalities are considered to be techniques for imaging the anatomy, morphology, structure, function and tissue characteristics. The role of cardiac PET has been growing rapidly and providing high diagnostic accuracy of coronary artery disease (CAD). Clinical cardiology has established PET as a criterion for the assessment of myocardial viability and is recommended for the proper management of reduced left ventricle (LV) function and ischemic cardiomyopathy. Hybrid PET/CT imaging has enabled simultaneous integration of the coronary anatomy with myocardial perfusion and metabolism and has improved characterization of dysfunctional areas in chronic CAD. Also, the availability of quantitative myocardial blood flow (MBF) evaluation with various PET perfusion tracers provides additional prognostic information and enhances the diagnostic performance of nuclear imaging.