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This contribution presents a wavelet-based algorithm to detect patterns in images. A two-dimensional extension of the DST-II is introduced to construct adapted wavelets using the equation of the tensor product corresponding to the diagonal coefficients in the 2D discrete wavelet transform. A 1D filter was then estimated that meets finite energy conditions, vanished moments, orthogonality, and four new detection conditions. These allow, when performing the 2D transform, for the filter to detect the pattern by taking the diagonal coefficients with values of the normalized similarity measure, defined by Guido, as greater than 0.7, and α = 0.1 . The positions of these coefficients are used to estimate the position of the pattern in the original image. This strategy has been used successfully to detect artificial patterns and localize mass-like abnormalities in digital mammography images. In the case of the latter, high sensitivity and positive predictive value in detection were achieved but not high specificity or negative predictive value, contrary to what occurred in the 1D strategy. This means that the proposed detection algorithm presents a high number of false negatives, which can be explained by the complexity of detection in these types of images. [ABSTRACT FROM AUTHOR]

The electroencephalography (EEG) signal contains important information about the electrical activity of the brain, which can reveal many pathologies. This information is transmitted in certain waveforms and events, one of which is the K-complex. Detection of these patterns is essential in sleep studies to diagnose neurophysiological and cognitive disorders. Existing detection methods rely heavily on tedious, time-consuming and error-prone manual inspection of the EEG waveform. Therefore, automatic identification of K-complexes is of great interest. In this paper, adapted wavelets are constructed to detect K-complexes using a variant of the Discrete ÓtextitShapelet Transform II (DST-II). This transform is designed to detect patterns (such as these K-complexes) by localizing them in time and frequency. This is achieved by numerically solving a system of nonlinear equations that estimates a wavelet filter adapted to the pattern. In this research, a numerical strategy for solving the nonlinear system of DST-II is presented. The influence of such a strategy on the detection of K-complexes in different signals and the detection accuracy versus other classical wavelet filters were evaluated. [ABSTRACT FROM AUTHOR]

The Discrete Shapelet Transform II is designed to detect patterns, locating them in time and frequency. This transform solves a system of nonlinear equations to obtain the high--pass filter of the pattern--adapted wavelet (shapelet). This paper presents an exploratory study case to inquire about the impact of the numerical method for estimating shapelets, considering numerical indicators and the detection of two artificial patterns. Powell's method with Anderson pre--iteration get orthogonal, perfect reconstruction, finite impulse response, near--linear phase and compact support filters. For pattern detection, we take the detail coefficient with the highest value of the normalized measure S, instead of S = 1 used in the original publications. Compared to other wavelet filters, higher values of S were obtained where the pattern was inserted. Accurate detection of repeated patterns and robust detection when modifying the amplitudes were obtained. Modest noise robustness of detection was verified. The results showed the need for further study to evaluate the impact of the numerical method and the choice of the initial guess to estimate the shapelet using a larger number of numerical methods, patterns and signals. As a consequence of the analysis and discussion, we suggest new research questions about this transform to be answer in further research. [ABSTRACT FROM AUTHOR]