An Intertwining of Curvelet and Linear Canonical Transforms

In this article, we introduce a novel curvelet transform by combining the merits of the well-known curvelet and linear canonical transforms. The motivation towards the endeavour spurts from the fundamental question of whether it is possible to increase the flexibility of the curvelet transform to optimize the concentration of the curvelet spectrum. By invoking the fundamental relationship between the Fourier and linear canonical transforms, we formulate a novel family of curvelets, which is comparatively flexible and enjoys certain extra degrees of freedom. The preliminary analysis encompasses the study of fundamental properties including the formulation of reconstruction formula and Rayleigh’s energy theorem. Subsequently, we develop the Heisenberg-type uncertainty principle for the novel curvelet transform. Nevertheless, to extend the scope of the present study, we introduce the semidiscrete and discrete analogues of the novel curvelet transform. Finally, we present an example demonstrating the construction of novel curvelet waveforms in a lucid manner

A New Discretization Scheme for the Non-Isotropic Stockwell Transform

To avoid the undesired angular expansion of the sampling grid in the discrete non-isotropic Stockwell transform, in this communication we propose a scale-dependent discretization scheme that controls both the radial and angular expansions in unison. Based on the new discretization scheme, we derive a sufficient condition for the construction of Stockwell frames in L2(R2)

An Interplay of Ridgelet and Linear Canonical Transforms

The present study is the first of its kind, aiming to explore the interface between the ridgelet and linear canonical transforms. To begin with, we formulate a family of linear canonical ridgelet waveforms by suitably chirping a one-dimensional wavelet along a specific direction. The construction of novel ridgelet waveforms is demonstrated via a suitable example supported by vivid graphics. Subsequently, we introduce the notion of linear canonical ridgelet transform, which not only embodies the classical ridgelet transform but also yields another new variant of the ridgelet transform based on the fractional Fourier transform. Besides studying all the fundamental properties, we also present an illustrative example on the implementation of the linear canonical ridgelet transform on a bivariate function

Inhaled nitric oxide in acute pulmonary embolism: a systematic review

Acute pulmonary embolism (PE) is usually a complication secondary to migration of a deep venous clot or thrombi to lungs, but other significant etiologies include air, amniotic fluid, fat, and bone marrow. Regardless of the underlying etiology, little progress has been made in finding an effective pharmacologic intervention for this serious complication. Among the wide spectrum of PE, massive PE is associated with considerable morbidity and mortality, primarily due to severely elevated pulmonary vascular resistance leading to right ventricular failure, hypoxemia, and cardiogenic shock. We currently have limited therapeutic options at our disposal. Inhaled nitric oxide (iNO) has been proposed as a potential therapeutic agent in cases of acute PE in which hemodynamic compromise secondary to increased pulmonary vascular resistance is present, based on iNO\u27s selective dilation of the pulmonary vasculature and antiplatelet activity. A systematic search of studies using the PubMed database was undertaken in order to assess the available literature. Although there are currently no published randomized controlled trials on the subject, except a recently publish phase I trial involving eight patients, several case reports and case series describe and document the use of iNO in acute PE. The majority of published reports have documented improvements in oxygenation and hemodynamic variables, often within minutes of administration of iNO. These reports, when taken together, raise the possibility that iNO may be a potential therapeutic agent in acute PE. However, based on the current literature, it is not possible to conclude definitively whether iNO is safe and effective. These case reports underscore the need for randomized controlled trials to establish the safety and efficacy of iNO in the treatment of massive acute PE. The purpose of this article is to review the current literature in the use of iNO in the setting of PE given how acute PE causes acute onset of pulmonary hypertension