Compactly Supported Shearlets are Optimally Sparse

Cartoon-like images, i.e., C^2 functions which are smooth apart from a C^2 discontinuity curve, have by now become a standard model for measuring sparse (non-linear) approximation properties of directional representation systems. It was already shown that curvelets, contourlets, as well as shearlets do exhibit (almost) optimally sparse approximation within this model. However, all those results are only applicable to band-limited generators, whereas, in particular, spatially compactly supported generators are of uttermost importance for applications. In this paper, we now present the first complete proof of (almost) optimally sparse approximations of cartoon-like images by using a particular class of directional representation systems, which indeed consists of compactly supported elements. This class will be chosen as a subset of shearlet frames -- not necessarily required to be tight -- with shearlet generators having compact support and satisfying some weak moment conditions

Modelling Suspended Sand Transport Under Breaking Waves

The modelling of coastal morphodynamics has often been hindered by the lack of robustness/accuracy of constituent formulae, especially sediment transport formulae in the breaking and swash zones. Consequently, modellers are often forced to rely on crude calibration efforts and practical models consisting of empirical tuning-constants, to obtain favourable model results. Such methods are often unavoidable however due to theoretical limitations of existing models. The aim of this thesis is therefore to improve accuracy and applicability of suspended sand transport models for breaking wave conditions, for implementation into morphodynamic modelling studies. Several existing suspended sand transport models (6 reference concentration C₀ + 5 concentration profile C[z]) models were evaluated quantitatively and qualitatively against one another, and against state-of-the-art high-resolution datasets which were collected under large-scale breaking wave conditions. Numerous limitations were observed in existing models, with the most common of these being their inability to accurately replicate suspended transport patterns in multiple cross-shore regions. This was due to various issues, such as not adequately accounting for the effects of breaking-induced turbulent kinetic energy on resulting sand transport. This resulted in large discrepancies between computed and measured transport particularly in the highly turbulent breaking zone. Such poor performance in computing C₀ and C[z] had residual effects on the resulting suspended flux (uC[z]) and current-related transport rate (qsc) computations also, which are essential to the accurate modelling of morphodynamics, particularly in the medium- to long-term. A novel set of suspended sand transport (C₀ + C[z]) models (“L19”) were developed for breaking wave conditions and evaluated against the aforementioned existing models and datasets. The L19 formulae showed significantly greater performance than all existing models, indicating excellent agreement with measured data in all tested cross-shore regions. These improvements led to considerably better estimations of uC[z] and qsc, which have promising implications for future morphodynamic modelling

CENTRAL BANK LEARNING, TERMS OF TRADE SHOCKS & CURRENCY RISKS: SHOULD ONLY INFLATION MATTER FOR MONETARY POLICY?

This paper examines the role of interest rate policy in a small open economy subject to terms of trade shocks, and time-varying currency risks. The private sector makes optimal decisions in an intertemporal non-linear setting with rational, forward-looking expectations. In contrast, the monetary authority practices "least-squares learning" about the evolution of inflation, output growth, and exchange rate depreciation in alternative policy scenarios. Interest rates are set by linear quadratic optimization, with the objectives for inflation, output growth, or depreciation depending on current conditions. The simulation results show that the prefered stance is one which targets inflation only. Including other targets such as growth and exchange rate changes significantly increases output variability, and unambiguously decreases welfare.Currency risks, learning, parameterized expectations, policy targets

Tracking in a space variant active vision system

Without the ability to foveate on and maintain foveation, active vision for applications such as surveillance, object recognition and object tracking are difficult to build. Although foveation in cartesian coordinates is being actively pursued by many, multi-resolution high accuracy foveation in log polar space has not been given much attention. This paper addresses the use of foveation to track a single object as well as multiple objects for a simulated space variant active vision system. Complex logarithmic mapping is chosen firstly because it provides high resolution and wide angle viewing. Secondly, the spatially variant structure of log polar space leads to an object increasing in size as it moves towards the fovea. This is important as we know which object is closer to the fovea at any instant in time.<br /