Response to Comments on PCA Based Hurst Exponent Estimator for fBm Signals Under Disturbances

In this response, we try to give a repair to our previous proof for PCA Based Hurst Exponent Estimator for fBm Signals by using orthogonal projection. Moreover, we answer the question raised recently: If a centered Gaussian process $G_t$ admits two series expansions on different Riesz bases, we may possibly study the asymptotic behavior of one eigenvalue sequence from the knowledge on the asymptotic behaviors of another.Comment: This is a response for a mistake in Li Li, Jianming Hu, Yudong Chen, Yi Zhang, PCA based Hurst exponent estimator for fBm signals under disturbances, IEEE Transactions on Signal Processing, vol. 57, no. 7, pp. 2840-2846, 200

Multi-frame image restoration method for novel rotating synthetic aperture imaging system

Abstract The novel rotating synthetic aperture (RSA) optical imaging system is an important development direction for future high-resolution optical remote sensing satellites in geostationary orbit. However, owing to the rotating rectangular pupil, the point spread function of the RSA system has an asymmetric spatial distribution, and the images obtained using the primary mirror from different rotation angles have nonuniform blur degradation. Moreover, platform vibration and pupil rotation have coupling effects on the RSA imaging, resulting in further radiometric and geometric quality degradation. To address these problems, the image degradation characteristics are first analyzed according to the imaging mechanism. Then, combined with the theory of mutual information, an image registration method is suggested by introducing the orientation gradient information. From this, a multi-frame image restoration model is proposed based on the directional gradient prior of the RSA system image. From the perspective of interpretation and application, when the aspect ratio is less than 3, the proposed inversion restoration method can achieve a satisfactory processing performance. This work can provide engineering application reference for the future space application of RSA imaging technology

An Efficient Method for Traffic Image Denoising

AbstractIn this paper, a novel method for traffic image denoising based on the low-rank decomposition is proposed. Firstly, the low-rank decomposition is carried out. Under the sparse and low-rank constraints of low-rank decomposition, the foreground images with complanate background and moving vehicles and the background images with similar road scene are obtained. Then the foreground image is segmented into blocks of a certain size. The variance of each block is calculated, among that the minimum is considered the estimate of the noise power. KSVD algorithm is performed for the foreground image denoising. Furthermore, the noisy pixel discrimination algorithm is performed to distinguish the noisy pixels from the noiseless pixels and the eight- neighborhood weight interpolation algorithm is performed to reconstruct the noisy pixels, where the weighted coefficients are inversely proportional to the Euclidean distances between the pixels. And PCA recovery combined with noisy pixel discrimination and eight-neighborhood weight interpolation is adopted for the background image denoising. Finally, our proposed method is conducted based on the traffic videos obtained under the same view and angle. Moreover, our proposed method is compared with several state-of-the-art denoising methods including BM3D, KSVD and PCA recovery. The experiment results illustrate that our proposed method can more effectively remove the noise, preserve the useful information and achieve a better performance in terms of both PSNR index and visual qualities

Continual Driving Policy Optimization with Closed-Loop Individualized Curricula

The safety of autonomous vehicles (AV) has been a long-standing top concern, stemming from the absence of rare and safety-critical scenarios in the long-tail naturalistic driving distribution. To tackle this challenge, a surge of research in scenario-based autonomous driving has emerged, with a focus on generating high-risk driving scenarios and applying them to conduct safety-critical testing of AV models. However, limited work has been explored on the reuse of these extensive scenarios to iteratively improve AV models. Moreover, it remains intractable and challenging to filter through gigantic scenario libraries collected from other AV models with distinct behaviors, attempting to extract transferable information for current AV improvement. Therefore, we develop a continual driving policy optimization framework featuring Closed-Loop Individualized Curricula (CLIC), which we factorize into a set of standardized sub-modules for flexible implementation choices: AV Evaluation, Scenario Selection, and AV Training. CLIC frames AV Evaluation as a collision prediction task, where it estimates the chance of AV failures in these scenarios at each iteration. Subsequently, by re-sampling from historical scenarios based on these failure probabilities, CLIC tailors individualized curricula for downstream training, aligning them with the evaluated capability of AV. Accordingly, CLIC not only maximizes the utilization of the vast pre-collected scenario library for closed-loop driving policy optimization but also facilitates AV improvement by individualizing its training with more challenging cases out of those poorly organized scenarios. Experimental results clearly indicate that CLIC surpasses other curriculum-based training strategies, showing substantial improvement in managing risky scenarios, while still maintaining proficiency in handling simpler cases