In this paper, we introduce a criterion for maximal operators associated with Fourier multipliers to be bounded on Lp(Rd) for each p∈(1,∞). Noteworthy examples satisfying the criterion are ...multipliers of the Mikhlin type or limited decay which are not necessarily radial. To do so, we make use of modified square function estimates and bilinear interpolation. For the bilinear interpolation we introduce a function space Σ2(B) where B denotes a Banach space of functions on Rd, which is a variant of weighted Sobolev spaces. In result, we obtain convergence results for fractional half-wave equations and surface averages as well as the Lp boundedness for the maximal operators.
A bilinear interpolation technique is proposed for flexible representations of quantum images (FRQIs). In this process, several quantum modules were developed, including assignment, increment, and ...quarter modules, for use in an interpolation circuit. The network structure of these circuits, capable of both up-sampling and down-sampling FRQIs, was investigated as part of the study. Additionally, the proposed method was verified using a series of simulation experiments in which test samples were enlarged and reduced, for comparison with nearest-neighbor interpolation. The up-scaled images produced using the proposed technique were of higher quality than those produced using nearest-neighbor interpolation, as measured using the peak signal-to-noise ratio (PSNR) and the structural similarity index (SSIM). Finally, with the extension of the FRQI model from square to rectangular shapes, the proposed algorithm is used to process rectangular FRQIs with special and arbitrary sizes.
Aerosol optical depth (AOD) is one of the most crucial parameters for reflecting aerosol characteristics. This study systematically evaluated daily AOD from Modern-Era Retrospective Analysis for ...Research and Applications Version 2 (MERRA-2), Visible Infrared Imaging Radiometer Suite (VIIRS), and Moderate-resolution Imaging Spectroradiometer (MODIS) daily gridded products over China from 2012 to 2019. Both the VIIRS aerosol Deep Blue (DB) and MODIS Deep Blue algorithm products had significant missing values in areas, for example, the Qinghai-Tibet Plateau, Xinjiang, and Northeast China. High AODs were mainly concentrated in areas closely related to economic development and population density geomorphology factors, such as the North China Plain, Yangtze River Delta, Pearl River Delta, and Sichuan Basin. Notably, VIIRS products captured higher AOD values in desert regions than the other products. In overall accuracy, MODIS DB product was characterized by a correlation coefficient (R) of 0.82, root mean square error (RMSE) of 0.21, and mean absolute error (MAE) of 0.14, and VIIRS (RMSE = 0.23 and MAE = 0.15) and MERRA-2 (RMSE = 0.27 and MAE = 0.17) had a slightly larger bias. MODIS performed best, with 55% of matched samples falling within the expected error (within EE), higher than the 53% of VIIRS. However, the MERRA-2 product performed worst, with only 48% of matched samples falling within the EE. Based on the accuracy comparison of the same number of matched samples, MODIS DB product still performed best, with R = 0.88, RMSE = 0.17, MAE = 011 and 64% of matched samples falling within the EE. Moreover, snow cover and the complex surface features in South-West areas may limit the performance of DB algorithm products, but MODIS DB products are available in most other areas of China. Land cover type applicability analysis demonstrated that DB algorithm products performed well in low vegetation cover and impervious surface types. In the analysis of elevation applicability, the MERRA-2 product has obviously higher robustness at high elevations than the MODIS and VIIRS products. These evaluation results are expected to guide users of aerosol products in China.
•AERDB captured higher AOD values in desert regions than the other products.•MODIS performed best, with 55% of matched samples falling within the expected error.•snow cover and the complex surface features in South-West areas may limit the performance of DB products.•DB products performed well in low vegetation cover and impervious surface.
When rendering light field images for a light field display, there is an issue of image quality. To address this issue, we employ the bilinear interpolation for image processing and conduct ...quantitative data analysis by using Peak Signal‐to‐Noise Ratio (PSNR) and Structural Similarity Index (SSIM) 1.
•The processing range of the femtosecond laser platform was limited by shifting of the focus.•A defocus compensation scheme (DCS) for femtosecond laser direct writing was proposed.•The DCS comprises ...of an optimized DFF method and the bilinear interpolation algorithm.•A Laplace-DWT evaluation function combining Laplace and DWT functions was proposed.
The optical path error, the position-independent geometric error, and the form and position tolerance of the substrate will lead to position deviations of the laser focus resulting in the inconsistency of the large area micro-structure and limiting the processing range of the femtosecond laser fabrication platform. To realize continuous defocus compensation along the processing trajectory, an autofocus scheme consisting of an optimized depth from focus (DFF) method based on grid division and the bilinear interpolation algorithm is proposed in this paper. The optimized DFF method includes the Laplace-DWT evaluation function combining the advantages of spatial domain and frequency domain sharpness evaluation function, an adaptive focusing window selection method, and an adaptive step length three-step hill-climbing search method. The optimized DFF method was used to obtain the best focus position of each grid point. Compared with the traditional DFF method, the optimized algorithm has higher focusing precision and avoids the disadvantage of time-consuming focusing. Then, to compensate for interpolating points of the processing trajectory, the bilinear interpolation algorithm was introduced to achieve online focusing during two-photon lithography processing. Finally, the feasibility and effectiveness of the auto-focusing scheme were validated by experiments. Through defocus compensation, the sharpness evaluation value of the focus image on the processing trajectory improved by 90%, which indicated the successful focus of the laser beam on the workpiece surface. Moreover, a high-precision and large-area encoded micro-polarizer array with consistent structure were fabricated successfully. This paper provides a simple way to identify and compensate the defocus errors online with high accuracy and efficiency. The proposed method can improve the machining accuracy and quality of the femtosecond laser direct writing.
As a part of quantum image processing, quantum image scaling is a significant technology for the development of quantum computation. At present, most of the quantum image scaling schemes are based on ...grayscale images, with relatively little processing for color images. This paper proposes a quantum color image scaling scheme based on bilinear interpolation, which realizes the 2
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quantum color image scaling. Firstly, the improved novel quantum representation of color digital images (INCQI) is employed to represent a 2
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quantum color image, and the bilinear interpolation method for calculating pixel values of the interpolated image is presented. Then the quantum color image scaling-up and scaling-down circuits are designed by utilizing a series of quantum modules, and the complexity of the circuits is analyzed. Finally, the experimental simulation results of MATLAB based on the classical computer are given. The ultimate results demonstrate that the complexities of the scaling-up and scaling-down schemes are quadratic and linear, respectively, which are much lower than the cubic function and exponential function of other bilinear interpolation schemes.
This paper introduces an upscaler technology which is proven to be effective in improving power reduction for IT products at the system level. Proposed upscaler algorithm utilizes Lanczos and ...bilinear interpolation both of which are widely used in currently existing upscaler designs on the industry, and carefully analyzes the image distortion caused by 2x scaling of the input image and manipulates the possible artifacts by considering the key performance criteria in the up‐scaling. Our experimental results show that image quality distortion due to the proposed scaling algorithm is significantly improved while the small details in the images are preserved at most thanks to the combination of “blended upscale” and “edge enhancement” sub‐functions in the proposed upscaling design. According to our subjective evaluation, we got the average score of 4.39 over 15 persons with 21 images from well‐known image benchmark suites.
Bilinear interpolation is widely used in classical signal and image processing. Quantum algorithms have been designed for efficiently realizing bilinear interpolation. However, these quantum ...algorithms have limitations in circuit width and garbage outputs, which block the quantum algorithms applied to noisy intermediate-scale quantum devices. In addition, the existing quantum bilinear interpolation algorithms cannot keep the consistency between the geometric centers of the original and target images. To save the above questions, we propose quantum bilinear interpolation algorithms based on geometric centers using fault-tolerant implementations of quantum arithmetic operators. Proposed algorithms include the scaling-up and scaling-down for signals (grayscale images) and signals with three channels (color images). Simulation results demonstrate that the proposed bilinear interpolation algorithms obtain the same results as their classical counterparts with an exponential speedup. Performance analysis reveals that the proposed bilinear interpolation algorithms keep the consistency of geometric centers and significantly reduce circuit width and garbage outputs compared to the existing works.
Traditional compressed sensing algorithm is used to reconstruct images by iteratively optimizing a small number of measured values. The computation is complex and the reconstruction time is long. The ...deep learning-based compressed sensing algorithm can greatly shorten the reconstruction time, but the algorithm emphasis is placed on reconstructing the network part mostly. The random measurement matrix cannot measure the image features well, which leads the reconstructed image quality to be improved limitedly. Two kinds of networks are proposed for solving this problem. The first one is ReconNet's improved network IReconNet, which replaces the traditional linear random measurement matrix with an adaptive nonlinear measurement network. The reconstruction quality and anti-noise performance are greatly improved. Because the measured values extracted by the measurement network also retain the characteristics of image spatial information, the image is reconstructed by bilinear interpolation algorithm (Bilinear) and dilate convolution. Therefore a second network USDCNN is proposed. On the BSD500 dataset, the sampling rates are 0.25, 0.10, 0.04, and 0.01, the average peak signal-noise ratio (PSNR) of USDCNN is 1.62 dB, 1.31 dB, 1.47 dB, and 1.95 dB higher than that of MSRNet. Experiments show the average reconstruction time of USDCNN is 0.2705 s, 0.3671 s, 0.3602 s, and 0.3929 s faster than that of ReconNet. Moreover, there is also a great advantage in anti-noise performance.
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