The performance of inverted perovskite solar cells is highly dependent on hole extraction and surface properties of hole transport layers. To highlight the important role of hole transport layers, a facile and simple method is developed by adding sodium chloride (NaCl) into poly(3,4-ethylenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS). The average power conversion efficiency of the perovskite solar cells prepared on NaCl-doped PEDOT:PSS is 17.1% with negligible hysteresis, compared favorably to the control devices (15.1%). Particularly, they exhibit markedly improved V and fill factor (FF), with the best FF as high as 81.9%. The enhancement of photovoltaic performance is ascribed to two effects. Better conductivity and hole extraction of PEDOT:PSS are observed after NaCl doping. More intriguingly, the perovskite polycrystalline film shows a preferred orientation along the (001) direction on NaCl-doped PEDOT:PSS, leading to a more uniform thin film. The comparison of the crystal structure between NaCl and MAPbCl indicates a lattice constant mismatch less than 2% and a matched chlorine atom arrangement on the (001) surface, which implies that the NaCl crystallites on the top surface of PEDOT:PSS might serve as seeds guiding the growth of perovskite crystals. This simple method is fully compatible with printing technologies to mass-produce perovskite solar cells with high efficiency and tunable crystal orientations.

To avoid the irregularities during the level set evolution, a fractional distance regularized variational model is proposed for image segmentation. We first define a fractional distance regularization term which punishes the deviation of the level set function (LSF) and the signed distance function. Since the fractional derivative of the constant value function outside the starting point is nonzero, the fractional gradient modular of the LSF does not approach infinity where the integer order gradient modular is close to 0. This prevents the sharp reverse diffusion of LSF in flat areas and ensures the smooth evolution of LSF. Then, we use the Grünwald-Letnikov (G-L) fractional derivative to derive the discrete forms of the conjugate of fractional derivatives and fractional divergence. To facilitate the calculation of fractional derivatives and their conjugates, we designed their covering templates. Finally, a numerical solution to the minimization of the energy functional is obtained from these discrete forms and covering templates. Numerical experiments of medical images with different modalities show that the model in this paper can well segment weak images and intensity inhomogeneity images.

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Detecting boundary of an image based on noisy observations is a fundamental problem of image processing and image segmentation. For a d-dimensional image (d = 2, 3, . . .), the boundary can often be described by a closed smooth (d − 1)-dimensional manifold. In this paper, we propose a nonparametric Bayesian approach based on priors indexed by S d−1 , the unit sphere in R d . We derive optimal posterior contraction rates for Gaussian processes or finite random series priors using basis functions such as trigonometric polynomials for 2-dimensional images and spherical harmonics for 3-dimensional images. For 2-dimensional images, we show a rescaled squared exponential Gaussian process on S 1 achieves four goals of guaranteed geometric restriction, (nearly) minimax optimal rate adapting to the smoothness level, convenience for joint inference and computational efficiency. We conduct an extensive study of its reproducing kernel Hilbert space, which may be of interest by its own and can also be used in other contexts. Several new estimates on the modified Bessel functions of the first kind are given. Simulations confirm excellent performance and robustness of the proposed method.