Integrodifferential equations for multiscale wavelet shrinkage : the discrete case

We investigate the relations between wavelet shrinkage and integrodifferential equations for image simplification and denoising in the discrete case. Previous investigations in the continuous one-dimensional setting are transferred to the discrete multidimentional case. The key observation is that a wavelet transform can be understood as derivative operator in connection with convolution with a smoothing kernel. In this paper, we extend these ideas to the practically relevant discrete formulation with both orthogonal and biorthogonal wavelets. In the discrete setting, the behaviour of the smoothing kernels for different scales is more complicated than in the continuous setting and of special interest for the understanding of the filters. With the help of tensor product wavelets and special shrinkage rules, the approach is extended to more than one spatial dimension. The results of wavelet shrinkage and related integrodifferential equations are compared in terms of quality by numerical experiments

The continuous shearlet transform in arbitrary dimensions

This paper is concerned with the generalization of the continuous shearlet transform to higher dimensions. Similar to the two-dimensional case, our approach is based on translations, anisotropic dilations and specific shear matrices. We show that the associated integral transform again originates from a square-integrable representation of a specific group, the full n-variate shearlet group. Moreover, we verify that by applying the coorbit theory, canonical scales of smoothness spaces and associated Banach frames can be derived. We also indicate how our transform can be used to characterize singularities in signals

Combines l2 data and gradient fitting in conjunction with l1 regularization

We are interested in minimizing functionals with l2 data and gradient fitting term and (absolute) l1 regularization term with higher order derivatives in a discrete setting. We examine the structure of the solution in 1d by reformulating the original problem into a contact problem which can be solved by dual optimization techniques. The solution turns out to be a discrete polynomial spline whose knots coincide with the contact points. In 2d we modify Chambolle's algorithm to solve the minimization problem with absolute l1 norm and second order derivatives. This requires the application of fast cosine transforms. We demonstrate by numerical denoising examples that the l2 gradient fitting term can be used to avoid both edge blurring and staircasing effects

Integrodifferential equations for multiscale wavelet shrinkage : the discrete case

We investigate the relations between wavelet shrinkage and integrodifferential equations for image simplification and denoising in the discrete case. Previous investigations in the continuous one-dimensional setting are transferred to the discrete multidimentional case. The key observation is that a wavelet transform can be understood as derivative operator in connection with convolution with a smoothing kernel. In this paper, we extend these ideas to the practically relevant discrete formulation with both orthogonal and biorthogonal wavelets. In the discrete setting, the behaviour of the smoothing kernels for different scales is more complicated than in the continuous setting and of special interest for the understanding of the filters. With the help of tensor product wavelets and special shrinkage rules, the approach is extended to more than one spatial dimension. The results of wavelet shrinkage and related integrodifferential equations are compared in terms of quality by numerical experiments

Integrodifferential Equations for Multiscale Wavelet Shrinkage: The Discrete Case

We investigate the relations between wavelet shrinkage and integrodifferential equations for image simplification and denoising in the discrete case. Previous investigations in the continuous one-dimensional setting are transferred to the discrete multidimentional case. The key observation is that a wavelet transform can be understood as a derivative operator in connection with convolution with a smoothing kernel. In this paper, we extend these ideas to a practically relevant discrete formulation with both orthogonal and biorthogonal wavelets. In the discrete setting, the behaviour of smoothing kernels for different scales is more complicated than in the continuous setting and of special interest for the understanding of the filters. With the help of tensor product wavelets and special shrinkage rules, the approach is extended to more than one spatial dimension. The results of wavelet shrinkage and related integrodifferential equations are compared in terms of quality by numerical experiments

M5 Muscarinic Receptors Mediate Striatal Dopamine Activation by Ventral Tegmental Morphine and Pedunculopontine Stimulation in Mice

Opiates, like other addictive drugs, elevate forebrain dopamine levels and are thought to do so mainly by inhibiting GABA neurons near the ventral tegmental area (VTA), in turn leading to a disinhibition of dopamine neurons. However, cholinergic inputs from the laterodorsal (LDT) and pedunculopontine (PPT) tegmental nucleus to the VTA and substantia nigra (SN) importantly contribute, as either LDT or PPT lesions strongly attenuate morphine-induced forebrain dopamine elevations. Pharmacological blockade of muscarinic acetylcholine receptors in the VTA or SN has similar effects. M5 muscarinic receptors are the only muscarinic receptor subtype associated with VTA and SN dopamine neurons. Here we tested the contribution of M5 muscarinic receptors to morphine-induced dopamine elevations by measuring nucleus accumbens dopamine efflux in response to intra-VTA morphine infusion using in vivo chronoamperometry. Intra-VTA morphine increased nucleus accumbens dopamine efflux in urethane-anesthetized wildtype mice starting at 10 min after infusion. These increases were absent in M5 knockout mice and were similarly blocked by pre-treatment with VTA scopolamine in wildtype mice. Furthermore, in wildtype mice electrical stimulation of the PPT evoked an initial, short-lasting increase in striatal dopamine efflux, followed 5 min later by a second prolonged increase in dopamine efflux. In M5 knockout mice, or following systemic pre-treatment with scopolamine in wildtype mice, the prolonged increase in striatal dopamine efflux was absent. The time course of increased accumbal dopamine efflux in wildtype mice following VTA morphine was consistent with both the prolonged M5-mediated excitation of striatal dopamine efflux following PPT electrical stimulation and accumbal dopamine efflux following LDT electrical stimulation. Therefore, M5 receptors appear critical for prolonged PPT excitation of dopamine efflux and for dopamine efflux induced by intra-VTA morphine

Meteorological, impact and climate perspectives of the 29 June 2017 heavy precipitation event in the Berlin metropolitan area

Extreme precipitation is a weather phenomenon with tremendous damaging potential for property and human life. As the intensity and frequency of such events is projected to increase in a warming climate, there is an urgent need to advance the existing knowledge on extreme precipitation processes, statistics and impacts across scales. To this end, a working group within the Germany-based project, ClimXtreme, has been established to carry out multidisciplinary analyses of high-impact events. In this work, we provide a comprehensive assessment of the 29 June 2017 heavy precipitation event (HPE) affecting the Berlin metropolitan region (Germany), from the meteorological, impacts and climate perspectives, including climate change attribution. Our analysis showed that this event occurred under the influence of a mid-tropospheric trough over western Europe and two shortwave surface lows over Britain and Poland (Rasmund and Rasmund II), inducing relevant low-level wind convergence along the German–Polish border. Over 11 000 convective cells were triggered, starting early morning 29 June, displacing northwards slowly under the influence of a weak tropospheric flow (10 m s−1 at 500 hPa). The quasi-stationary situation led to totals up to 196 mm d−1, making this event the 29 June most severe in the 1951–2021 climatology, ranked by means of a precipitation-based index. Regarding impacts, it incurred the largest insured losses in the period 2002 to 2017 (EUR 60 million) in the greater Berlin area. We provide further insights on flood attributes (inundation, depth, duration) based on a unique household-level survey data set. The major moisture source for this event was the Alpine–Slovenian region (63 % of identified sources) due to recycling of precipitation falling over that region 1 d earlier. Implementing three different generalised extreme value (GEV) models, we quantified the return periods for this case to be above 100 years for daily aggregated precipitation, and up to 100 and 10 years for 8 and 1 h aggregations, respectively. The conditional attribution demonstrated that warming since the pre-industrial era caused a small but significant increase of 4 % in total precipitation and 10 % for extreme intensities. The possibility that not just greenhouse-gas-induced warming, but also anthropogenic aerosols affected the intensity of precipitation is investigated through aerosol sensitivity experiments. Our multi-disciplinary approach allowed us to relate interconnected aspects of extreme precipitation. For instance, the link between the unique meteorological conditions of this case and its very large return periods, or the extent to which it is attributable to already-observed anthropogenic climate change.</p

Meteorological, impact and climate perspectives of the 29 June 2017 heavy precipitation event in the Berlin metropolitan area

Extreme precipitation is a weather phenomenon with tremendous damaging potential for property and human life. As the intensity and frequency of such events is projected to increase in a warming climate, there is an urgent need to advance the existing knowledge on extreme precipitation processes, statistics and impacts across scales. To this end, a working group within the Germany-based project, ClimXtreme, has been established to carry out multidisciplinary analyses of high-impact events. In this work, we provide a comprehensive assessment of the 29 June 2017 heavy precipitation event (HPE) affecting the Berlin metropolitan region (Germany), from the meteorological, impacts and climate perspectives, including climate change attribution. Our analysis showed that this event occurred under the influence of a mid-tropospheric trough over western Europe and two shortwave surface lows over Britain and Poland (Rasmund and Rasmund II), inducing relevant low-level wind convergence along the German–Polish border. Over 11 000 convective cells were triggered, starting early morning 29 June, displacing northwards slowly under the influence of a weak tropospheric flow (10 m s$^{−1}$ at 500 hPa). The quasi-stationary situation led to totals up to 196 mm d$^{−1}$, making this event the 29 June most severe in the 1951–2021 climatology, ranked by means of a precipitation-based index. Regarding impacts, it incurred the largest insured losses in the period 2002 to 2017 (EUR 60 million) in the greater Berlin area. We provide further insights on flood attributes (inundation, depth, duration) based on a unique household-level survey data set. The major moisture source for this event was the Alpine–Slovenian region (63 % of identified sources) due to recycling of precipitation falling over that region 1 d earlier. Implementing three different generalised extreme value (GEV) models, we quantified the return periods for this case to be above 100 years for daily aggregated precipitation, and up to 100 and 10 years for 8 and 1 h aggregations, respectively. The conditional attribution demonstrated that warming since the pre-industrial era caused a small but significant increase of 4 % in total precipitation and 10 % for extreme intensities. The possibility that not just greenhouse-gas-induced warming, but also anthropogenic aerosols affected the intensity of precipitation is investigated through aerosol sensitivity experiments. Our multi-disciplinary approach allowed us to relate interconnected aspects of extreme precipitation. For instance, the link between the unique meteorological conditions of this case and its very large return periods, or the extent to which it is attributable to already-observed anthropogenic climate change