Image denoising using trivariate prior model in nonsubsampled dual-tree complex contourlet transform domain and non-local means filter in spatial domain

Image denoising is always the basic problem of image processing, and the main challenge is how to effectively remove the noise and preserve the detailed information. This paper presents a new image denoising algorithm based on the combination of trivariate prior model in nonsubsampled dual-tree complex contourlet transformlet transform (NSDTCT) domain and non-local means filter (NLMF) in spatial domain. Firstly, NSDTCT is constructed by combining the dual-tree complex wavelet transform (DTCWT) and nonsubsampled directional filter banks (NSDFB). The noisy image is decomposed by using NSDTCT. Secondly, based on the correlation between the interscale and intrascale dependencies of NSDTCT coefficients, the distribution of the high frequency coefficients is modeled with the trivariate non-Gaussian distribution model. A nonlinear trivariate shrinkage function is derived in the framework of Bayesian theory, and then the denoised coefficients are obtained and inverse NSDTCT is performed to get the initial denoised image. Finally, NLMF is used to smooth the initial denoised image. Simulation experiment shows that our algorithm can obtain better performances than those outstanding denoising algorithms in terms of peak signal-to-noise ratio (PSNR), mean structural similarity (MSSIM) as well as visual quality.     

Generating and shifting a spherical focal spot in a 4Pi focusing system illuminated by azimuthally polarized beams

We aim to theoretically investigate the focusing property of a 4Pi configuration under the illumination of azimuthally polarized high-order Bessel–Gaussian beams. The radial component is produced in the focal region through the introduction of a spiral phase plate. The focal region differs from the zero radial intensity component of the azimuthally polarized beams without the spiral phase plate. The spherical focal spot is generated by selecting an appropriate annular obstruction. The position of the focal spot can be shifted.     

An upper bound for the first eigenvalue of a spherical cap

By working with suitable test functions, we obtain an upper bound for the principal eigenvalue of a geodesic ball on a sphere of arbitrary dimension. This bound is sharp in the limiting case when the radius of the ball approaches the diameter of the sphere.This research was supported by ARO Grant 28905-MA.     

基于Retinex理论与概率非局部均值的红外图像增强方法

针对传统红外图像增强算法中细节模糊及过度增强的问题,提出了一种基于Retinex理论与概率非局部均值相结合的红外图像增强方法.首先通过单尺度Retinex方法调整图像中过暗与过亮部分的灰度级;然后利用概率非局部均值对图像进行分解处理得到基本层与细节层,对基本层采用直方图均衡化拉伸对比度,对细节层采用非线性函数进行增强;最后,将不同层次的结果融合得到对比度与细节增强的红外图像.用该方法对多组不同场景的红外图像进行仿真实验,并将其与多种增强方法进行主、客观对比分析,结果表明所提方法在红外图像的细节及对比度增强方面都获得了更好的效果.     

Shape stability of a gas bubble in a soft solid

Predicting the onset of non-spherical oscillations of bubbles in soft matter is a fundamental cavitation problem with implications to sonoprocessing, polymeric materials synthesis, and biomedical ultrasound applications. The shape stability of a bubble in a Kelvin-Voigt viscoelastic medium with nonlinear elasticity, the simplest constitutive model for soft solids, is analytically investigated and compared to experiments. Using perturbation methods, we develop a model reducing the equations of motion to two sets of evolution equations: a Rayleigh-Plesset-type equation for the mean (volume-equivalent) bubble radius and an equation for the non-spherical mode amplitudes. Parametric instability is predicted by examining the natural frequency and the Mathieu equation for the non-spherical modes, which are obtained from our model. Our theoretical results show good agreement with published experiments of the shape oscillations of a bubble in a gelatin gel. We further examine the impact of viscoelasticity on the time evolution of non-spherical mode amplitudes. In particular, we find that viscosity increases the damping rate, thus suppressing the shape instability, while shear modulus increases the natural frequency, which changes the unstable mode. We also explain the contributions of rotational and irrotational fields to the viscoelastic stresses in the surroundings and at the bubble surface, as these contributions affect the damping rate and the unstable mode. Our analysis on the role of viscoelasticity is potentially useful to measure viscoelastic properties of soft materials by experimentally observing the shape oscillations of a bubble.     

Optimization of the parameters of the ideal 180° spherical analyzer

Resolution and intensity behaviour of the spherical analyzer are mainly determined by the entrance parameters (aperture angle 2α _m , relative width of the entrance slita/r ₀) and by the relative width of the exit slitb/r ₀. The mutual relation of these parameteres can be so optimized that independent of the required resolution the quantities étendue or luminosity of the spherical analyzer attain a maximum.     

Synthesis of spherical LiNi1/3Co1/3Mn1/3O2 cathode materials for Li-ion batteries

Spherical LiNi_1/3Co_1/3Mn_1/3O₂ was successfully prepared by controlled crystallization. The preparation started with the spherical coprecipitate of Ni_1/3Co_1/3Mn_1/3CO₃ from NiSO₄, CoSO₄, MnSO₄, NH₄HCO₃, and NH₃·H₂O, followed by pyrolysis of Ni_1/3Co_1/3Mn_1/3CO₃ at 600°C for 3 h. The X-ray diffraction analysis showed that the homogeneous cubic (Ni_1/3Co_1/3Mn_1/3)₃O₄ was obtained after the pyrolysis. Spherical LiNi_1/3Co_1/3Mn_1/3O₂ was obtained by sintering of the mixture of as-obtained (Ni_1/3Co_1/3Mn_1/3)₃O₄ and LiOH·H₂O at 900°C for 6 h in air. As-prepared spherical LiNi_1/3Co_1/3Mn_1/3O₂ presented initial discharge capacity of 162.9 mA h g⁻¹ and capacity retention of 98% at 50th cycle.     

Multiple information encryption by user-image-based gyrator transform hologram

A novel multiple information encryption by user-image-based gyrator transform hologram is proposed. In encryption process, each channel of the user image is phase encoded, modulated by random phase function and then gyrator transformed to get the gyrator spectrum of user image. Subsequently, each channel of the secret image is normalized, phase encoded, multiplied by modulated user image, and then gyrator transformed to obtain the gyrator spectrum of secret image. The encrypted digital hologram is recorded by the interference between the gyrator spectrum of user image and the spherical wave function. Similarly, the digital hologram for decryption is recorded by the interference between the gyrator spectrum of secret image and the spherical wave function. The multiple encrypted digital holograms are multiplexed into a final encoded hologram and the corresponding digital holograms for decryption are multiplexed into a final hologram for decryption. The wavelength and radius of the spherical wave function, and angle of gyrator transform are all essential keys for decryption. The proposed system has two main features. First, the encrypted hologram has no information about secret image. Second, the hologram for decryption used as identification key. Consequently the two marked security layers of information protection are achieved. The proposal can be realized by optoelectronic system. Numerical simulation results demonstrate the feasibility and security of the proposed technique.     

Inner invariant means and conjugation operators

It is shown that Paschke's result cannot be generalized to the [IN]-group setting given by Lau and Paterson. This resolves negatively a problem raised by Lau and Paterson.

     

Field of a Point Source Within Perfectly Conducting Parallel-Plates in a Homogeneous Biisotropic Medium

The spherical wave scattering response by a perfectly conducting open–ended waveguide in a biisotropic medium is obtained. Interestingly, the vector diffraction problem is reduced to the scattering of a single scalar field, this scalar field being the normal component of either a left–handed or a right–handed Beltrami field. Here, we explicitly consider the scattering of the left–handed field component, that of the other scalar field being analogously tractable. The solution is constructed with the aid of the Wiener–Hopf technique.