Blind Source Separation (BSS) is essential in many domains where mixed signals must be separated into their original sources without prior knowledge of the mixing process. Applications span audio and biomedical signal processing, telecommunications, image analysis, finance, electronic warfare, and industrial monitoring. Reinforcement Learning (RL), a decision-making framework based on interaction with an environment to maximize cumulative rewards, has shown promise in tasks such as financial trading, anomaly detection, and predictive maintenance. In this paper, we propose a novel approach that integrates a three-dimensional chirp spectrogram (3D chirogram) representation to model multisource data and capture their intrinsic structures. We then apply RL to learn these structures and perform source separation. The proposed RL-guided 3D chirogram method demonstrates strong performance in separating mixed signals, even under extremely noisy conditions, highlighting its robustness and effectiveness for real-world BSS tasks.

The past decade has undergone an explosion of image data collection from various sensors. The extreme increase of high dimensional data poses significant challenges for processing vast amounts of new data. Since most of the important and useful features are contained in low dimensional subspaces of the high dimensional data, subspace clustering techniques have been extensively developed to process these high dimensional data. In this paper, a diffusion equation evolution approach is proposed to extract subspaces from high dimensional image sensor data. Iterative exponential filtering is introduced to implement this diffusion equation evolution. Theoretical analysis and simulation tests show that the computational cost of the proposed method is independent of the number of neighboring points and much lower than the traditional methods. As an application, the proposed method is applied to K-Means implementation for image data. Test results show that the proposed method is over 20 times faster in computing time and over 20% higher in clustering performance than the traditional Floyd implementation.

In this paper, a conventional discrete implementation of the diffusion equation is analyzed. It is shown that when the evolution time step is less than 1/4 , the conventional discrete implementation satisfies the scale-space condition. As the evolution time increases, the image becomes smoother and smoother, thus making the evolution increasingly slow and the computing time lengthy. To solve this problem, a new discrete implementation is proposed. It is shown that the proposed implementation satisfies the scale-space condition when discrete time steps are arbitrarily large. The new discrete implementation of the diffusion equation not only preserves the scale-space condition but also effectively reduces the evolution time. The experiments in range image segmentation show that the proposed method has a similar segmentation effect as the conventional methods, but with much less computing time.

Describes an efficient approach to calculate geometric moments of a 2-D gray-level image. It is shown both theoretically and experimentally that the new method compares favorably with previous techniques, especially for high-order moments.

In this paper, we proposed a linear-transform-based method to compute 3D moments. Instead of computing the conventional moments directly, we compute the so-called LT moments which are related with the conventional moments by three linear transforms. By choosing appropriately these transforms, it is shown that the computational complexity can be considerably reduced.

In this paper, we present a novel method to estimate the parameters of a quadratic curve. We show that by grouping the data points and by estimating the so-called moments difference (MD) which are unbiased and consistent, the parameters of a quadratic curve can be estimated with higher accuracy than the existing methods.

Fourier descriptor and geometric moments are respectively the contour and region representations of objects in a binary image. In this paper, the authors reveal the relation between these two representations. The authors first generalize the Fourier descriptor to make it suitable for objects with more complex form. Then it is shown that the two representations are related by a simple linear transformation.

Fractal Brownian random (FBR) field is an extension of fractional Brownian motion (FBM) and has been successfully used in image analysis, the generation of natural scenes, fractal geometry, and other areas. But its implementation is difficult and limits its applications. In this paper, by extending the AR model, we propose a new approach, the pyramid-AR-model approach, to implement FBR fields. The new method has the same computational complexity as A. Fournier's, but it can generate FBR fields much more accurately.

In the paper, a novel method is proposed to calculate three-dimensional (3-D) moments. First, a discrete Gaussian theorem is proposed to convert the summation in a 3-D volume domain to that on a 2-D plane region, which decreases computational complexity from O(N/sup 3/) to O(N/sup 2/). Second, a Pascal triangle transform, a Pascal triangle matrix, and a systolic structure are proposed to calculate the monomials on a 3-D object boundary surface, which simplifies the monomial calculation. Third, a range-image measurement system is used to implement the new method. Finally, a comparison of the authors' method with the known ones is provided, showing that the authors' method is much simpler.>