A nonlinear filter is presented by using a formal linearization method and the Extended Kalman Filter (EKF) approach in this paper. Defining a linearization function that consists of polynomials, a given nonlinear dynamic system is transformed into an augmented linear one with respect to this linearization function. Introducing a new augmented measurement vector that consists of polynomials of measurement data for a given measurement equation, this equation is also transformed into an augmented linear one with respect to the linearization function in the same way. As a result, the EKF theory can be applied to these augmented linearized systems and a nonlinear filter is synthesized. In order to show the performance of the method, numerical experiments are carried out by comparing with the EKF as a conventional method.

We propose a blind image quality assessment (BIQA) method of using the multitask-learning-based end-to-end convolutional neural network (CNN) approach. The architecture of the proposed method is integrated by two streams. In the first stream, multiscale image features are extracted by using the inception and pyramid pooling modules. Natural scene statistics (NSS)-based features are extracted in the second stream. The two streams are then integrated into fully connected layers to estimate the image quality score. The performance of the proposed method is validated with four public IQA databases and the obtained experimental results show the superiority of the proposed method over conventional IQA methods.

In this paper, we propose the incorporation of noisy image patches and the impulse response of a low-pass filter (LPF) in a convolutional neural network (CNN) to denoise Poisson–Gaussian noise in low-dose computed tomography (LDCT) images. The approach is referred to as fast and flexible denoising CNN (FFDNet)-impulse response (FFDNet-IR) in this paper. The power spectrum sparsity LPF (SLPF) allows low-frequency components to pass through while suppressing higher frequency components by the sparsity approach of the power spectrum, and it is employed to determine the impulse response of LPF. Three well-known types of LPF, namely, Direct LPF, Gaussian LPF, and Butterworth LPF, are also considered to obtain the impulse response of LPF. In the FFDNet-IR, both the noisy image patches and the IR of the LPF are sequentially inputted into the FFDNet to eliminate the Poisson–Gaussian noise. This approach enhances the denoising performance in LDCT images compared with the conventional FFDNet in the evaluation metrics of the peak signal-to-noise ratio (PSNR), structural similarity (SSIM), and feature similarity (FSIM). Moreover, the FFDNet-IR trained with the Poisson–Gaussian noise model demonstrates the generalization ability and effectively eliminates only Poisson or Gaussian noise. The experiments indicate that the FFDNet-IR more effectively suppresses the noise artifacts and preserves image details compared with the baseline FFDNet, as well as traditional methods such as block-matching and 3D filtering (BM3D) and nonlocal mean (NLM) for LDCT image denoising.

Current physics is considered to be based on Newtonian mechanics. The existence of electromagnetic waves was demonstrated by the Maxwell equations. It is also possible to assume that the constitution of electromagnetic waves forms the fundamental principles of physics, including the composition of materials. To demonstrate this assumption, we introduced electromagnetic waves in coaxial cables and determined the propagation constant of these waves, as reported in this Session. The result showed that the real part of the propagation constant, known as the attenuation constant, can be set to zero. In this case, by expressing the variable of the electromagnetic waves as angular frequency (ω), it is possible to treat the variable of the function as an angle (in radians). As a consequence, we are able to introduce a mathematical representation of phase (neighborhood and metric) for electromagnetic waves. Thus, we demonstrate that the mathematical representation of electromagnetic waves is possible.