An Optimal-Dimensionality Sampling for Spin-ss Functions on the Sphere

For the representation of spin-$s$ band-limited functions on the sphere, we propose a sampling scheme with optimal number of samples equal to the number of degrees of freedom of the function in harmonic space. In comparison to the existing sampling designs, which require ${\sim}2L^2$ samples for the representation of spin-$s$ functions band-limited at $L$, the proposed scheme requires $N_o=L^2-s^2$ samples for the accurate computation of the spin-$s$ spherical harmonic transform~($s$-SHT). For the proposed sampling scheme, we also develop a method to compute the $s$-SHT. We place the samples in our design scheme such that the matrices involved in the computation of $s$-SHT are well-conditioned. We also present a multi-pass $s$-SHT to improve the accuracy of the transform. We also show the proposed sampling design exhibits superior geometrical properties compared to existing equiangular and Gauss-Legendre sampling schemes, and enables accurate computation of the $s$-SHT corroborated through numerical experiments.Comment: 5 pages, 2 figure

Iterative Residual Fitting for Spherical Harmonic Transform of Band-Limited Signals on the Sphere: Generalization and Analysis

We present the generalized iterative residual fitting (IRF) for the computation of the spherical harmonic transform (SHT) of band-limited signals on the sphere. The proposed method is based on the partitioning of the subspace of band-limited signals into orthogonal subspaces. There exist sampling schemes on the sphere which support accurate computation of SHT. However, there are applications where samples~(or measurements) are not taken over the predefined grid due to nature of the signal and/or acquisition set-up. To support such applications, the proposed IRF method enables accurate computation of SHTs of signals with randomly distributed sufficient number of samples. In order to improve the accuracy of the computation of the SHT, we also present the so-called multi-pass IRF which adds multiple iterative passes to the IRF. We analyse the multi-pass IRF for different sampling schemes and for different size partitions. Furthermore, we conduct numerical experiments to illustrate that the multi-pass IRF allows sufficiently accurate computation of SHTs.Comment: 5 Pages, 7 Figure

Breast cancer management pathways during the COVID-19 pandemic: outcomes from the UK ‘Alert Level 4’ phase of the B-MaP-C study

Abstract: Background: The B-MaP-C study aimed to determine alterations to breast cancer (BC) management during the peak transmission period of the UK COVID-19 pandemic and the potential impact of these treatment decisions. Methods: This was a national cohort study of patients with early BC undergoing multidisciplinary team (MDT)-guided treatment recommendations during the pandemic, designated ‘standard’ or ‘COVID-altered’, in the preoperative, operative and post-operative setting. Findings: Of 3776 patients (from 64 UK units) in the study, 2246 (59%) had ‘COVID-altered’ management. ‘Bridging’ endocrine therapy was used (n = 951) where theatre capacity was reduced. There was increasing access to COVID-19 low-risk theatres during the study period (59%). In line with national guidance, immediate breast reconstruction was avoided (n = 299). Where adjuvant chemotherapy was omitted (n = 81), the median benefit was only 3% (IQR 2–9%) using ‘NHS Predict’. There was the rapid adoption of new evidence-based hypofractionated radiotherapy (n = 781, from 46 units). Only 14 patients (1%) tested positive for SARS-CoV-2 during their treatment journey. Conclusions: The majority of ‘COVID-altered’ management decisions were largely in line with pre-COVID evidence-based guidelines, implying that breast cancer survival outcomes are unlikely to be negatively impacted by the pandemic. However, in this study, the potential impact of delays to BC presentation or diagnosis remains unknown

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Abstract Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries

Sampling and Reconstruction of Spherical Signals for Applications in Cosmology, Acoustics and Beyond

The main focus of this thesis is using the existing spherical signal processing techniques to sample and reconstruct data under different application driven scenarios. The thesis consist of three major parts and the problems of sampling and reconstruction are discussed first. Then, the significance of signal processing techniques like spatial filtering are discussed in the field of acoustics. A sampling scheme is proposed for the representation of spin-$s$ band-limited functions on the sphere, which requires optimal number of samples equal to the number of degrees of freedom. In comparison to the existing sampling designs, which require ${\sim}2L^2$ samples for the representation of spin-$s$ functions band-limited at $L$, the proposed scheme requires $L^2-s^2$ samples for the accurate computation of the spin-$s$ spherical harmonic transform~($s$-SHT). A method is developed to compute the $s$-SHT and samples are taken such that matrices involved in the computation of $s$-SHT are well conditioned. In order to improve the accuracy further, a multi-pass $s$-SHT method is also proposed. Geometrical properties like sampling efficiency, minimum geodesic distance, mesh norm and mesh ratio give us an insight of the nature of distribution of the points on the sphere. A comparative analysis with the existing schemes show that the proposed sampling design exhibits superior geometrical properties. Algorithms for signal reconstruction on the sphere are developed and analysed for two different scenarios: i) when the measurements are not taken over a pre-defined grid and ii) when the estimation is done from incomplete measurements. For the first one, the generalized iterative residual fitting~(IRF) for the computation of the spherical harmonic transform~(SHT) of band-limited signals on the sphere is presented. The proposed method is based on the partitioning of the subspace of band-limited signals into orthogonal subspaces. There exist sampling schemes on the sphere which support accurate computation of SHT. The proposed IRF method enables accurate computation of SHTs of signals with randomly distributed sufficient number of samples. In order to improve the accuracy of the computation of the SHT, multi-pass IRF is proposed which adds multiple iterative passes to the IRF. An iterative algorithm for the extrapolation of band-limited signals from incomplete measurements on the sphere is proposed. The proposed algorithm improves the accuracy of the extrapolation of band-limited signals by using the information contained in the out-of-band harmonic coefficients of the signal to update the extrapolated signal at each iteration. The proposed algorithm does not only exploit the band-limited property of the signal at each iteration but also uses the harmonic coefficients outside the harmonic domain to improve the accuracy of signal extrapolation. To demonstrate the improvement in the accuracy, numerical experiments are conducted and a comparison is done with the results of the existing iterative conjugate gradient method. The signal processing technique of spatial filtering is exploited in order to design an anti-aliasing filter for the applications in acoustics. In acoustics, the performance of spherical microphone arrays is typically limited by spatial aliasing which introduces side-lobes in the array beam pattern. In order to reduce the aliasing error, a spatially constrained anti-aliasing filter is proposed which approximates an ideal anti-aliasing filter used in literature as a weighted sum of concentrated eigenfunctions obtained by solving the Slepian concentration problem on the sphere. Three performance parameters namely white noise gain~(WNG), directivity index~(DI) and processing loss are employed to compare the performance of proposed filter with the ideal filter. A parameter-constrained filter design is also proposed by maximizing WNG subject to constraints on the DI and processing loss of the proposed filter

Comparative analysis of geometrical properties of sampling schemes on the sphere

In this work, we carry out the comparative analysis of the geometrical properties of the sampling schemes on the sphere. Among the sampling schemes devised on the sphere, we focus on equiangular sampling, Gauss-Legendre (GL) quadrature based sampling, optimal-dimensionality sampling, sampling points of extremal systems and spherical design as these schemes support the accurate representation of the band-limited signals. We analyse sampling efficiency, minimum geodesic distance, mesh norm, mesh ratio and Riesz s-energy for these sampling schemes. Since these sampling schemes require different number of samples for the accurate representation of a band-limited signal and therefore have different sampling efficiency, we formulate these geometrical properties to take into account the sampling efficiency for a meaningful comparison. We illustrate that the optimal dimensionality, extremal system and spherical design sampling schemes exhibit desirable geometrical properties. Among these schemes, extremal system sampling scheme has superior geometrical properties. However, the accuracy of the representation of a band-limited signal degrades with the increase in band-limit for extremal system sampling scheme, due to which we propose to use extremal point sampling scheme for small band-limits.We also propose to use optimal dimensional sampling scheme for moderate to large band-limits as it exhibits desirable geometrical properties and has the capability to accurately represent the band-limited signal.This work was supported under the Australian Research Council’s Discovery Projects funding scheme (project no. DP150101011)

Iterative Residual Fitting for Spherical Harmonic Transform of Band-Limited Signals on the Sphere: Generalization and Analysis

We present the generalized iterative residual fitting (IRF) for the computation of the spherical harmonic transform (SHT) of band-limited signals on the sphere. The proposed method is based on the partitioning of the subspace of band-limited signals into orthogonal subspaces. There exist sampling schemes on the sphere which support accurate computation of SHT. However, there are applications where samples~(or measurements) are not taken over the predefined grid due to nature of the signal and/or acquisition set-up. To support such applications, the proposed IRF method enables accurate computation of SHTs of signals with randomly distributed sufficient number of samples. In order to improve the accuracy of the computation of the SHT, we also present the so-called multi-pass IRF which adds multiple iterative passes to the IRF. We analyse the multi-pass IRF for different sampling schemes and for different size partitions. Furthermore, we conduct numerical experiments to illustrate that the multi-pass IRF allows sufficiently accurate computation of SHTs.Usama Elahi, Zubair Khalid and Rodney A. Kennedy are supported by Australian Research Council’s Discovery Projects funding scheme (project no. DP150101011). Jason D. McEwen is partially supported by the Engineering and Physical Sciences Research Council (grant number EP/M011852/1)

Spatially Constrained Anti-Aliasing Filter Using Slepian Eigenfunction Window on the Sphere

Spherical microphone arrays sample the sound field on the sphere in both space and time. The performance of spherical microphone arrays is typically limited by spatial aliasing which introduces side-lobes in the array beam pattern. In order to reduce the aliasing error, anti-aliasing filters, both ideal and spatially constrained, have been presented in the literature. In this paper, we propose a slepian eigenfunction window which spatially truncate the ideal anti-aliasing filter used in literature to design a spatially constrained anti-aliasing filter. We also provide an illustration to show that the aliasing on the beam pattern is reduced by the use of the proposed anti-aliaisng filter and compare the results with the spatially constrained filters obtained by applying rectangular and hamming windows. Robustness analysis such as measurement of the white noise gain and directivity index shows the superiority of the proposed filter over other spatially constrained anti-aliasing filters.This work was supported under the Australian Research Council’s Discovery Projects funding scheme (Project no. DP150101011 and Project no. DP170101897). Zubair Khalid is supported by Pakistan HEC 2016-17 NRPU (Project no. 5925)

Case report of a rare incidentaloma of the adrenal gland—Schwannoma

The Schwannoma is a benign growth of the nerve sheath cells most commonly seen in the vestibulocochlear nerve. Its prevalence in the adrenal gland is 1-3%. Here we discuss a case that presented as an incidentaloma of the right adrenal gland in a young male patient who had vague abdominal symptoms and a normal hormonal profile. He underwent an excisional biopsy of the right adrenal gland due to the large size of the lesion (more than 4cm). The histopathology report helped to establish the diagnosis of Schwannoma. Incidentaloma is defined as a lesion of the adrenal gland encountered on any radiological investigation carried out for symptoms that are not associated with adrenal pathologies. After discovering such lesions, it is imperative to perform radiological and hormonal investigations in an organised manner to plan further management of such cases. Keywords: Schwannoma, Adrenal Incidentaloma, Adrenocortical Adenoma, Adrenocortical Carcinoma, Adrenalectomy