Image denoising with multi-layer perceptrons, part 1: comparison with existing algorithms and with bounds

Image denoising can be described as the problem of mapping from a noisy image to a noise-free image. The best currently available denoising methods approximate this mapping with cleverly engineered algorithms. In this work we attempt to learn this mapping directly with plain multi layer perceptrons (MLP) applied to image patches. We will show that by training on large image databases we are able to outperform the current state-of-the-art image denoising methods. In addition, our method achieves results that are superior to one type of theoretical bound and goes a large way toward closing the gap with a second type of theoretical bound. Our approach is easily adapted to less extensively studied types of noise, such as mixed Poisson-Gaussian noise, JPEG artifacts, salt-and-pepper noise and noise resembling stripes, for which we achieve excellent results as well. We will show that combining a block-matching procedure with MLPs can further improve the results on certain images. In a second paper, we detail the training trade-offs and the inner mechanisms of our MLPs

Why do households without children support local public schools? linking house price capitalization to school spending

While residents receive similar benefits from many local public expenditures, only about one-third of all households have children in the public schools. In this paper the authors argue that capitalization of school spending into house prices can encourage residents to support spending on schools, even if the residents themselves will never have children in the schools. To examine this hypothesis, the authors take advantage of differences across communities in the extent of house price capitalization based on the availability of land or population density. They show that fiscal variables and amenities are capitalized to a much greater extent in Massachusetts cities and towns with little available land and that these localities also spend more on schools. Next, the authors use data from school districts in 49 states to show that per pupil spending is positively related to population density, a proxy for the availability of land. Consistent with a model tying house price capitalization to school spending, the authors show that the positive correlation between density and spending persists only in locations with high homeownership rates. Communities with a higher percentage of residents above 65 years old have increased school expenditures only in places with high population densities, and this correlation grows for the percentage of elderly above 75 or 85 years old who have a shorter expected duration in their house. The positive relationship between percentage elderly and school spending is confined to central cities and suburbs of large metropolitan areas and does not exist in places where land for new construction may be easier to obtain. These results support models in which house price capitalization encourages more efficient provision of public services and provide an explanation for why some elderly residents might support local spending on schools.Education

Why Do Households Without Children Support Local Public Schools?

While residents receive similar benefits from many local government programs, only about one-third of all households have children in public schools. We argue that capitalization of school spending into house prices can encourage residents to support spending on schools, even if the residents themselves will never have children in schools. We identify a proxy for the extent of capitalization—the supply of land available for new development—and show that in response to a plausibly exogenous spending shock in Massachusetts, towns with little undeveloped land have larger changes in house prices, but smaller changes in quantity (construction). Towns with little available land also spend more on schools. We extend these results using data from school districts in 46 states, showing that per pupil spending is positively related to the percentage of developed land. This positive correlation persists only in districts where the median resident is a homeowner and is stronger in districts with more elderly residents who do not use school services and have a shorter expected duration in their home. These findings support models in which house price capitalization encourages more efficient provision of public services and may explain why some elderly residents support school spending.

Impact of nonlinear loss on Stimulated Brillouin Scattering

We study the impact of two-photon absorption (2PA) and fifth-order nonlinear loss such as 2PA-induced free-carrier absorption in semiconductors on the performance of Stimulated Brillouin Scattering devices. We formulate the equations of motion including effective loss coefficients, whose explicit expressions are provided for numerical evaluation in any waveguide geometry. We find that 2PA results in a monotonic, algebraic relationship between amplification, waveguide length and pump power, whereas fifth-order losses lead to a non-monotonic relationship. We define a figure of merit for materials and waveguide designs in the presence of fifth-order losses. From this, we determine the optimal waveguide length for the case of 2PA alone and upper bounds for the total Stokes amplification for the case of 2PA as well as fifth-order losses. The analysis is performed analytically using a small-signal approximation and is compared to numerical solutions of the full nonlinear modal equations

Power limits and a figure of merit for stimulated Brillouin scattering in the presence of third and fifth order loss

We derive a set of design guidelines and a figure of merit to aid the engineering process of on-chip waveguides for strong Stimulated Brillouin Scattering (SBS). To this end, we examine the impact of several types of loss on the total amplification of the Stokes wave that can be achieved via SBS. We account for linear loss and nonlinear loss of third order (two-photon absorption, 2PA) and fifth order, most notably 2PA-induced free carrier absorption (FCA). From this, we derive an upper bound for the output power of continuous-wave Brillouin-lasers and show that the optimal operating conditions and maximal realisable Stokes amplification of any given waveguide structure are determined by a dimensionless parameter $\mathcal{F}$ involving the SBS-gain and all loss parameters. We provide simple expressions for optimal pump power, waveguide length and realisable amplification and demonstrate their utility in two example systems. Notably, we find that 2PA-induced FCA is a serious limitation to SBS in silicon and germanium for wavelengths shorter than 2200nm and 3600nm, respectively. In contrast, three-photon absorption is of no practical significance