This article first introduces the concept of wavelet q-Fisher information and then derives a closed-form expression of this quantifier for scaling signals of parameter α. It is shown that this information measure appropriately describes the complexities of scaling signals and provides further analysis flexibility with the parameter q. In the limit of q → 1, wavelet q-Fisher information reduces to the standard wavelet Fisher information and for q > 2 it reverses its behavior. Experimental results on synthesized fGn signals validates the level-shift detection capabilities of wavelet q-Fisher information. A comparative study also shows that wavelet q-Fisher information locates structural changes in correlated and anti-correlated fGn signals in a way comparable with standard breakpoint location techniques but at a fraction of the time. Finally, the application of this quantifier to H.263 encoded video signals is presented.

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This article defines the concept of wavelet-based Fisher's information measure (wavelet FIM) and develops a closed-form expression of this measure for 1/f α signals.Wavelet Fisher's information measure characterizes the complexities associated to 1/f α signals and provides a powerful tool for their analysis. Theoretical and experimental studies demonstrate that this quantity is exponentially increasing for α > 1 (non-stationary signals) and almost constant for α < 1 (stationary signals). Potential applications of wavelet FIM are discussed in some detail and its power and robustness for the detection of structural breaks in the mean embedded in stationary fractional Gaussian noise signals studied.

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Detecting and counting elliptical objects are an interesting problem in digital image processing. There are real-world applications of this problem in various disciplines. Solving this problem is harder when there is occlusion among the elliptical objects, since in general these objects are considered as part of the bigger object (conglomerate). The solution to this problem focusses on the detection and segmentation of the precise number of occluded elliptical objects, while omitting all noninteresting objects. There are a variety of computational approximations that focus on this problem; however, such approximations are not accurate when there is occlusion. This paper presents an algorithm designed to solve this problem, specifically, to detect, segment, and count elliptical objects of a specific size when these are in occlusion with other objects within the conglomerate. Our algorithm deals with a time-consuming combinatorial process. To optimize the execution time of our algorithm, we implemented a parallel GPU version with CUDA-C, which experimentally improved the detection of occluded objects, as well as lowering processing times compared to the sequential version of the method. Comparative test results with another method featured in literature showed improved detection of objects in occlusion when using the proposed parallel method.

This work presents an algorithm to reduce the multiplicative computational complexity in the creation of digital holograms, where an object is considered as a set of point sources using mathematical symmetry properties of both the core in the Fresnel integral and the image. The image is modeled using group theory. This algorithm has multiplicative complexity equal to zero and an additive complexity ( − 1) 2 for the case of sparse matrices or binary images, where is the number of pixels other than zero and 2 is the total of points in the image.

This article proposes a methodology for the classification of fractal signals as stationary or nonstationary. The methodology is based on the theoretical behavior of two-parameter wavelet entropy of fractal signals. The wavelet (q, q )-entropy is a wavelet-based extension of the (q, q )-entropy of Borges and is based on the entropy planes for various q and q ; it is theoretically shown that it constitutes an efficient and effective technique for fractal signal classification. Moreover, the second parameter q provides further analysis flexibility and robustness in the sense that different (q, q ) pairs can analyze the same phenomena and increase the range of dispersion of entropies. A comparison study against the standard signal summation conversion technique shows that the proposed methodology is not only comparable in accuracy but also more computationally efficient. The application of the proposed methodology to physiological and financial time series is also presented along with the classification of these as stationary or nonstationary.