This work investigates a fractional-order multi-wing chaotic system for detecting weak signals. The influence of the order of fractional calculus on chaotic systems’ dynamical behavior is examined using phase diagrams, bifurcation diagrams, and SE complexity diagrams. Then, the principles and methods for determining the frequencies and amplitudes of weak signals are examined utilizing fractional-order multi-wing chaotic systems. The findings indicate that the lowest order at which this kind of fractional-order multi-wing chaotic system appears chaotic is $2.625$ at $a=4$, $b=8$, and $c=1$, and that this value decreases as the driving force increases. The four-wing and double-wing change dynamics phenomenon will manifest in a fractional-order chaotic system when the order exceeds the lowest order. This phenomenon can be utilized to detect weak signal amplitudes and frequencies because the system parameters control it. A detection array is built to determine the amplitude using the noise-resistant properties of both four-wing and double-wing chaotic states. Deep learning images are then used to identify the change in the array’s wing count, which can be used to determine the test signal’s amplitude. When frequencies detection is required, the MUSIC method estimates the frequencies using chaotic synchronization to transform the weak signal’s frequencies to the synchronization error’s frequencies. This solution adds to the contact between fractional-order calculus and chaos theory. It offers suggestions for practically implementing the chaotic weak signal detection theory in conjunction with deep learning.

We developed a novel method based on self-supervised learning to improve the ghost imaging of occluded objects. In particular, we introduced a W-shaped neural network to preprocess the input image and enhance the overall quality and efficiency of the reconstruction method. We verified the superiority of our W-shaped self-supervised computational ghost imaging (WSCGI) method through numerical simulations and experimental validations. Our results underscore the potential of self-supervised learning in advancing ghost imaging.

The detection of weak signals is a well-established application in chaos theory. This theory leverages the inherent robustness of chaotic systems, enabling them to resist noise and thus serve as effective tools for identifying weak signals. However, challenges remain in selecting appropriate chaotic systems and in their practical implementation—areas that are still under-explored. In this paper, we analyze a simplified fractional-order Genesio–Tesi chaotic system, which exhibits a unique chaos-divergence characteristic. Based on this characteristic, we propose a new detection method that uses the chaos-divergence state as a criterion for determining the presence or absence of a signal when detecting weak signal amplitudes. This approach makes the simplified fractional-order Genesio–Tesi chaotic system more suitable for chaotic weak signal detection. Notably, the significant variance observed in the divergent state’s independent variables emerges as a key feature, enhancing the system’s ability to detect the frequencies of weak signals. Our numerical simulations focus on detecting weak cosine signals masked by three different types of noise. The results demonstrate successful detection of a weak signal at a frequency of 100 rad/s under the specified conditions, with the lowest detectable signal-to-noise ratio of −40.83 dB. Overall, these results highlight the effectiveness and feasibility of our proposed method for weak signal detection.

Ghost imaging (GI) has been received more and more attention in past thirty years. However, it has some limitations in the resolution. In this paper, we propose a scheme to improve the resolution of GI by a new imaging information, i.e. the coefficient of skewness coming from the fluctuations of the second-order correlation function, and put forward an enhanced GI protocol exploiting those fluctuations. We demonstrate experimentally that the additional information obtained from the new information makes it possible to improve resolution compared to the traditional GI scheme.