Image quality and radiologists’ subjective acceptance using model-based iterative and deep learning reconstructions as adjuncts to ultrahigh-resolution CT in low-dose contrast-enhanced abdominopelvic CT: phantom and clinical pilot studies

Purpose In contrast-enhanced abdominopelvic CT (CE-APCT) for oncologic follow-up, ultrahigh-resolution CT (UHRCT) may improve depiction of fine lesions and low-dose scans are desirable for minimizing the potential adverse effects by ionizing radiation. We compared image quality and radiologists’ acceptance of model-based iterative (MBIR) and deep learning (DLR) reconstructions of low-dose CE-APCT by UHRCT. Methods Using our high-resolution (matrix size: 1024) and low-dose (tube voltage 100 kV; noise index: 20–40 HU) protocol, we scanned phantoms to compare the modulation transfer function and noise power spectrum between MBIR and DLR and assessed findings in 36 consecutive patients who underwent CE-APCT (noise index: 35 HU; mean CTDIvol: 4.2 ± 1.6 mGy) by UHRCT. We used paired t-test to compare objective noise and contrast-to-noise ratio (CNR) and Wilcoxon signed-rank test to compare radiologists’ subjective acceptance regarding noise, image texture and appearance, and diagnostic confidence between MBIR and DLR using our routine protocol (matrix size: 512; tube voltage: 120 kV; noise index: 15 HU) for reference. Results Phantom studies demonstrated higher spatial resolution and lower low-frequency noise by DLR than MBIR at equal doses. Clinical studies indicated significantly worse objective noise, CNR, and subjective noise by DLR than MBIR, but other subjective characteristics were better (P < 0.001 for all). Compared with the routine protocol, subjective noise was similar or better by DLR, and other subjective characteristics were similar or worse by MBIR. Conclusion Image quality, except regarding noise characteristics, and acceptance by radiologists were better by DLR than MBIR in low-dose CE-APCT by UHRCT. Graphical abstract

Efficient Semidefinite Programming with Approximate ADMM

Tenfold improvements in computation speed can be brought to the alternating direction method of multipliers (ADMM) for Semidefinite Programming with virtually no decrease in robustness and provable convergence simply by projecting approximately to the Semidefinite cone. Instead of computing the projections via “exact” eigendecompositions that scale cubically with the matrix size and cannot be warm-started, we suggest using state-of-the-art factorization-free, approximate eigensolvers, thus achieving almost quadratic scaling and the crucial ability of warm-starting. Using a recent result from Goulart et al. (Linear Algebra Appl 594:177–192, 2020. https://doi.org/10.1016/j.laa.2020.02.014), we are able to circumvent the numerical instability of the eigendecomposition and thus maintain tight control on the projection accuracy. This in turn guarantees convergence, either to a solution or a certificate of infeasibility, of the ADMM algorithm. To achieve this, we extend recent results from Banjac et al. (J Optim Theory Appl 183(2):490–519, 2019. https://doi.org/10.1007/s10957-019-01575-y) to prove that reliable infeasibility detection can be performed with ADMM even in the presence of approximation errors. In all of the considered problems of SDPLIB that “exact” ADMM can solve in a few thousand iterations, our approach brings a significant, up to 20x, speedup without a noticeable increase in ADMM’s iterations.

Quality Enhancement of Gamma Camera SPECT Images Via the Taguchi-Based Optimization of Their Minimum Detectable Difference And a V-Shaped Slit Gauge

Background: This study optimized the minimum detectable difference (MDD) of gamma camera SPECT images via the Taguchi analysis and an indigenous V-shaped slit gauge. The latter was customized to satisfy the Taguchi analysis’ quantitative requirements. Methods: The slit gauge MDD quantification of derived SPECT images was based on a pair of overlapped-peak profiles obtained from a tangent slice of the V-shaped slit with two adjacent peaks. Using the revised Student’s t-test with a multiplied constant, 1.96, the MDD was defined as the minimum distance between two peak centers, which deviation was large enough to ensure a 95% confidence level of their separation. In total, eighteen combinations of six gamma camera scanned factors (A-F), namely (A) collimator, (B) detector to target distance, (C) total counts, (D) acquired energy width, (E) Matrix size, and (F) zoom of collected ROI with each of two or three levels were organized into 18 groups to collect the slit gauge images according to Taguchi L18 orthogonal array. Next, three well-trained radiologists ranked the scanned gauge images to derive the fish-bone-plot of signal-to-noise ratio (S/N, dB) and correlated ANOVA. Results: The quantified MDD was proposed to verify the optimal suggestion of gamma camera scanned protocol, and obtained the MDD as 8.44, 7.88, and 7.40 mm for the 2nd group of the original L18, conventional, and optimal presets, respectively. Conclusions: The optimal preset of gamma camera was achieved according to Taguchi analysis. The MDD-based approach was found more beneficial in evaluating the spatial resolution than the line pair/cm approach in routine quality control in this study.

A first look at the bosonic master-field equation of the IIB matrix model

The bosonic large-[Formula: see text] master field of the IIB matrix model can, in principle, give rise to an emergent classical spacetime. The task is then to calculate this master field as a solution of the bosonic master-field equation. We consider a simplified version of the algebraic bosonic master-field equation and take dimensionality [Formula: see text] and matrix size [Formula: see text]. For an explicit realization of the pseudorandom constants entering this simplified algebraic equation, we establish the existence of a solution and find, after diagonalization of one of the two obtained matrices, a band-diagonal structure of the other matrix.

Playfair with Multi Strata Encryption

Playfair cipher is a substitution scheme. The classical playfair scheme has a limited matrix size containing only uppercase letters, so it is prone to hackers and cryptanalysis. To increase the resistance of playfair cipher, a new encipherment and decipherment method is proposed in this work, which depends on the permutation and its inverse, respectively. In addition, a modified key matrix is utilized, which includes capital and small Alphabets, numbers, and 38 special characters collected from ASCII codes. In the proposed method, both substitution and transposition schemes are used, where the first stratum of the cipher is a substitution by using key matrix and the second stratum is a transposition by using permutation key which provides multi strata resistance to brute force and other cryptanalysis attacks. A comparison between the traditional playfair scheme and the proposed method demonstrates that the encoded text is hard to recognize by cryptanalysts, which improves the security of the encryption process.

Detectability of pulmonary ossifications in fibrotic lung on ultra-high-resolution CT using 2048 matrix size and 0.25-mm slice thickness

To investigate the prevalence of nodular pulmonary ossifications (POs) in patients with honeycombing on ultra-high-resolution CT (UHRCT) and to compare the detectability of nodular POs between images reconstructed using the ultra-high-resolution setting (UHR-setting) and those using the conventional setting (C-setting) on UHRCT. Twenty patients with honeycombing in the lung were evaluated retrospectively. All patients underwent non-contrast-enhanced UHRCT. Images were reconstructed with UHR-setting (matrix, 2048 × 2048; slice thickness, 0.25 mm) and with C-setting (matrix size, 512 × 512; slice thickness, 0.5 mm). Two chest radiologists independently recorded the number of nodular POs (< 4 mm diameter) in each lung lobes. Each lobe was classified as one of the following five categories according to the number of POs: C0, none; C1, 1–4 POs; C2, 5–9 POs; C3, 10–49 POs; and C4, ≥ 50 POs. The maximum CT values of the POs were measured and compared between the two settings. PO categories were significantly higher with UHR-setting than with C-setting (p < 0.001). Maximum CT values were significantly higher with UHR-setting than with C-setting (p < 0.001). Nodular POs were seen in 80% or more of patients with honeycombing and more easily detected in images reconstructed with UHR-setting than in those with C-setting.

Analysis of left ventricular function, left ventricular outflow tract and aortic valve area using computed tomography: Influence of reconstruction parameters on measurement accuracy

Objectives: Computed tomography (CT) allows reproducible assessment of left ventricular (LV) function, left ventricular outflow tract area (LVOTarea) and aortic valve area (AVA). We evaluated the influence of image reconstruction parameters on these measurements. Methods: We analyzed 45 contrast-enhanced, retrospectively ECG-gated CT datasets acquired on a third-generation dual source system. A standard filtered-back-projection data set (20 cardiac phases (5% steps, 0–95%), 0.6-mm-slice thickness, 512 × 512 matrix) and eight reconstructions with modified slice thickness (1–8 mm), number of cardiac phases (5, 10), matrix size (256×256) and an iterative reconstruction (IR) algorithm were obtained. LV parameters (ejection fraction (EF), stroke volume (SV), end-diastolic (EDV), end-systolic volumes (ESV)), LVOTarea and AVA were assessed. Results: Differences in LV parameters, LVOTarea and AVA, were only minimal between standard reconstructions and those with modified matrix size, IR algorithm and ≤2 mm slice thickness, while reconstructions with 8-mm slice thickness significantly overestimated SV (p < 0.001) and EDV (p = 0.016). AVA planimetry in reconstructions with ≥5 mm slice thickness was not feasible in 56% of patients. A decrease in the number of reconstructed phases (10 or 5) underestimated EF, SV, EDV, LVOTarea and AVA and overestimated ESV. Conclusions: Modifications of reconstruction parameters (except a slice thickness ≤2 mm) have only a marginal effect on LV, LVOTarea and AVA assessment. However, a reduced number of reconstructions per cardiac cycle may significantly influence measurements. Advances in knowledge: Substantial modifications in number of reconstructions per cardiac cycle significantly affect the assessment of LV function, LVOTarea and AVA also in modern CT scanners.

A Linear Bound on the k-rendezvous Time for Primitive Sets of NZ Matrices

A set of nonnegative matrices is called primitive if there exists a product of these matrices that is entrywise positive. Motivated by recent results relating synchronizing automata and primitive sets, we study the length of the shortest product of a primitive set having a column or a row with k positive entries, called its k-rendezvous time (k-RT), in the case of sets of matrices having no zero rows and no zero columns. We prove that the k-RT is at most linear w.r.t. the matrix size n for small k, while the problem is still open for synchronizing automata. We provide two upper bounds on the k-RT: the second is an improvement of the first one, although the latter can be written in closed form. We then report numerical results comparing our upper bounds on the k-RT with heuristic approximation methods.