Optimal-Dimensionality Sampling on the Sphere: Improvements and Variations

For the accurate representation and reconstruction of band-limited signals on the sphere, an optimal-dimensionality sampling scheme has been recently proposed which requires the optimal number of samples equal to the number of degrees of freedom of the signal in the spectral (harmonic) domain. The computation of the spherical harmonic transform (SHT) associated with the optimal-dimensionality sampling requires the inversion of a series of linear systems in an iterative manner. The stability of the inversion depends on the placement of iso-latitude rings of samples along co-latitude. In this work, we have developed a method to place these iso-latitude rings of samples with the objective of improving the well-conditioning of the linear systems involved in the computation of the SHT. We also propose a multi-pass SHT algorithm to iteratively improve the accuracy of the SHT of band-limited signals. Furthermore, we review the changes in the computational complexity and improvement in accuracy of the SHT with the embedding of the proposed methods. Through numerical experiments, we illustrate that the proposed variations and improvements in the SHT algorithm corresponding to the optimal-dimensionality sampling scheme significantly enhance the accuracy of the SHT.Comment: 5 Pages, 4 figure

Optimal-Dimensionality Sampling on the Sphere: Improvements and Variations

For the accurate representation and reconstruction of band-limited signals on the sphere, an optimal-dimensionality sampling scheme has been recently proposed which requires the optimal number of samples equal to the number of degrees of freedom of the signal in the spectral (harmonic) domain. The computation of the spherical harmonic transform (SHT) associated with the optimal-dimensionality sampling requires the inversion of a series of linear systems in an iterative manner. The stability of the inversion depends on the placement of iso-latitude rings of samples along co-latitude. In this work, we have developed a method to place these iso-latitude rings of samples with the objective of improving the well-conditioning of the linear systems involved in the computation of the SHT. We also propose a multi-pass SHT algorithm to iteratively improve the accuracy of the SHT of band-limited signals. Furthermore, we review the changes in the computational complexity and improvement in accuracy of the SHT with the embedding of the proposed methods. Through numerical experiments, we illustrate that the proposed variations and improvements in the SHT algorithm corresponding to the optimal-dimensionality sampling scheme significantly enhance the accuracy of the SHT.Rodney A. Kennedy is 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)

Signal analysis on the ball: Design of optimal basis functions with maximal multiplicative concentration in spatial and spectral domains

In this work, we design a set of complete orthonormal optimal basis functions for signals defined on the ball. We design the basis functions by maximizing the product of their energy concentration in some spatial region and that in some spectral region. The optimal basis functions are designed as a linear combination of space-limited functions with maximal concentration in the spectral region and band-limited functions with maximal concentration in the spatial region. The proposed optimal basis functions are shown to form a complete set for signal representation in a subspace formed by the vector sum of the subspaces spanned by space-limited and band-limited functions. We also formulate an integral operator which projects the signal to the joint subspace and maximizes the product of energy concentrations in harmonic as well as spatial domains. Furthermore, with the help of some properties of proposed optimal basis functions we show that these functions are the only eigenfunction of the integral operator.Rodney A. Kennedy is supported by the Australian Research Councils Discovery Projects funding scheme (Project no. DP150101011)

Pattern, frequency and factors associated with inappropriate high dosing in chronic kidney disease patients at a tertiary care hospital in Pakistan

Abstract Background Patients with chronic kidney diseases (CKD) are susceptible to the toxic drug effects if given unadjusted doses. Although Pakistan harbors a high burden of CKD patients, there is limited information available on the frequency, pattern and factors associated with unadjusted drug doses among CKD patients. Methods This cross-sectional study conducted at Sandeman Provincial Hospital, Quetta included 303 non-dialysis ambulatory CKD patients (glomerular filtration rate  60 years (OR = 9.49), hypertension (OR = 2.68), diabetes mellitus (OR = 3.47) and cardiovascular diseases (OR = 2.82) had statistically significant association (p-value < 0.05) with inappropriate high doses. Conclusion The high frequency of inappropriate high doses suggests an important quality gap in medication dosing for patients with ND-CKD at the study site. Special attention should be paid to the drugs and patients with identified risk factors for receiving inappropriate high doses