International Journal of Wavelets, Multiresolution and Information Processing

The evolutionary periodogram has been introduced to mechanical fault diagnosis and relationship between the evolutionary periodogram and time-frequency spectrogram has been investigated. The evolutionary periodogram is unveiled as an especially windowed spectrogram, and is applied to gearbox fault diagnosis. It has been shown that the window used in the evolutionary periodogram is not a single function but a combination of a set of functions. Two cases of gearbox diagnosis are presented as examples of application. Vibration signals and a synchronous signal are collected for the analysis. The time synchronous averaging is used to reduce background noise or random transients to enhance the periodicity of a specific gear rotation. The performance of the evolutionary periodogram has been compared with the spectrogram for gear diagnosis, showing that the evolutionary periodogram is an alternative technique in time-frequency analysis for fault detection and better resolution can be obtained as more choices are offered by the way of constructing the window.

In this paper, we consider the problem of local risk minimization on the basis of empirical data, which is a generalization of the problem of global risk minimization. A new local risk regularization scheme is proposed. The error estimate for the proposed algorithm is obtained by using probabilistic estimates for integral operators. Experiments are presented to illustrate the general theory. Simulation results on several artificial real datasets show that the local risk regularization algorithm has better performance.

Mammographic images suffer from low contrast and signal dependent noise, and a very small size of tumoral signs is not easily detected, especially for an early diagnosis of breast cancer. In this context, many methods proposed in literature fail for lack of generality. In particular, too weak assumptions on the noise model, e.g., stationary normal additive noise, and an inaccurate choice of the wavelet family that is applied, can lead to an information loss, noise emphasizing, unacceptable enhancement results, or in turn an unwanted distortion of the original image aspect. In this paper, we consider an optimal wavelet thresholding, in the context of Discrete Dyadic Wavelet Transforms, by directly relating all the parameters involved in both denoising and contrast enhancement to signal dependent noise variance (estimated by a robust algorithm) and to the size of cancer signs. Moreover, by performing a reconstruction from a zero-approximation in conjunction with a Gaussian smoothing filter, we are able to extract the background and the foreground of the image separately, as to compute suitable contrast improvement indexes. The whole procedure will be tested on high resolution X-ray mammographic images and compared with other techniques. Anyway, the visual assessment of the results by an expert radiologist will be also considered as a subjective evaluation.

In an effort to characterize uniform and pointwise Hölder regularities, we obtain necessary decay rates and sufficient decay rates of continuous and discrete shearlet transform across scales. They are the same rates as those of the Hart Smith and continuous curvelet transforms. We then consider the situation where the regularity on a line in a non-parallel direction is significantly lower than the directional regularity along the line in a neighborhood of the line. Similar to that of the Hart Smith and continuous curvelet transforms, a set of necessary conditions for this direction of singularity is that the continuous shearlet transform decays half an order faster in directions "away" from the direction of the line and that the decay rate in directions "near" the line depends also on the horizontal distance from the line to the parallel line containing the center of the shearlet function. These similarities among the three transforms call for a general theory of transforms "with parabolic scaling."

This paper presents an application of wavelet networks (WNs) in identification and control design for a class of structures equipped with a type of semiactive actuators, which are called magnetorheological (MR) dampers. The nonlinear model is identified based on a WN framework. Based on the technique of feedback linearization, supervisory control and H_∞ control, an adaptive control strategy is developed to compensate for the nonlinearity in the structure so as to enhance the response of the system to earthquake type inputs. Furthermore, the parameter adaptive laws of the WN are developed. In particular, it is shown that the proposed control strategy offers a reasonably effective approach to semiactive control of structures. The applicability of the proposed method is illustrated on a building structure by computer simulation.

It has been known that the distribution of the discrete cosine transform (DCT) coefficients of most natural images follow a Laplace distribution. However, recent work has shown that the Laplace distribution may not be a good fit for certain types of images and that the Gaussian distribution will be a realistic model in such cases. A model that contains both Laplace and Gaussian distributions as particular cases is the generalized Gaussian (GG) distribution. Assuming this generalized model, we derive a comprehensive collection of formulas for the distribution of the actual DCT coefficients. The corresponding estimation procedures are derived by the method of moments and the method of maximum likelihood. Finally, the superior performance of the derived distributions over the standard Gaussian and Laplace models is illustrated. It is expected that this work could serve as a useful reference and lead to improved modeling with respect to image analysis and image coding.

We introduce the concept of adaptive decomposition of signals into basic building blocks, of which each of the non-negative analytic instantaneous frequency are called mono-components. We propose certain methods based on p-starlike functions and Fourier expansions for such decomposition. We justify the terminology mono-component used in signal analysis.

In this paper, we propose a Locality Preserving Nonnegative Matrix Factorization (LPNMF) method to discover the manifold structure embedded in high-dimensional face space that is applied for face recognition. It is done by incorporating locality preserving constraints inside the cost function of NMF, then a new decomposition of a face with locality preserving can be obtained. As a result, the proposed LPNMF method shares some properties with the Locality Preserving Projection (LPP) such that it can effectively discover the manifold structure embedded in a high-dimensional face space. Experimental results show that LPNMF provides a better representation and achieves higher recognition rates in face recognition.