Recently, the wavelet-based estimation method has gradually been becoming popular as a new tool for software reliability assessment. The wavelet transform possesses both spatial and temporal resolution which makes the wavelet-based estimation method powerful in extracting necessary information from observed software fault data, in global and local points of view at the same time. This enables us to estimate the software reliability measures in higher accuracy. However, in the existing works, only the point estimation of the wavelet-based approach was focused, where the underlying stochastic process to describe the software-fault detection phenomena was modeled by a non-homogeneous Poisson process. In this paper, we propose an interval estimation method for the wavelet-based approach, aiming at taking account of uncertainty which was left out of consideration in point estimation. More specifically, we employ the simulation-based bootstrap method, and derive the confidence intervals of software reliability measures such as the software intensity function and the expected cumulative number of software faults. To this end, we extend the well-known thinning algorithm for the purpose of generating multiple sample data from one set of software-fault count data. The results of numerical analysis with real software fault data make it clear that, our proposal is a decision support method which enables the practitioners to do flexible decision making in software development project management.

This letter proposes an efficient local descriptor for wide-baseline dense matching. It improves the existing Daisy descriptor by combining intensity-based Haar wavelet response with a new color-based ratio model. The color ratio model is invariant to changes of viewing direction, object geometry, and the direction, intensity and spectral power distribution of the illumination. The experiments show that our descriptor has high discriminative power and robustness.

A multi-stage approach -- which is fast, robust and easy to train -- for a face-detection system is proposed. Motivated by the work of Viola and Jones [1], this approach uses a cascade of classifiers to yield a coarse-to-fine strategy to reduce significantly detection time while maintaining a high detection rate. However, it is distinguished from previous work by two features. First, a new stage has been added to detect face candidate regions more quickly by using a larger window size and larger moving step size. Second, support vector machine (SVM) classifiers are used instead of AdaBoost classifiers in the last stage, and Haar wavelet features selected by the previous stage are reused for the SVM classifiers robustly and efficiently. By combining AdaBoost and SVM classifiers, the final system can achieve both fast and robust detection because most non-face patterns are rejected quickly in earlier layers, while only a small number of promising face patterns are classified robustly in later layers. The proposed multi-stage-based system has been shown to run faster than the original AdaBoost-based system while maintaining comparable accuracy.

This paper presents a new bearing fault detection algorithm based on analyzing singular points of vibration signals using the Haar wavelet. The proposed Haar Fault Detection (HFD) algorithm is compared with a previously-developed algorithm associated with the Morlet wavelet. We also substitute the Haar wavelet with Daubechies wavelets with larger compact supports and evaluate the results. Simulations carried on real data demonstrate that the HFD algorithm achieves a comparable accuracy while having a lower computational cost. This makes the HFD algorithm an appropriate candidate for fast processing of bearing faults.

This paper analytically formulates both the optimal quantization noise allocation ratio and the coding gain of the two-dimensional morphological Haar wavelet transform. The two-dimensional morphological Haar wavelet transform has been proposed as a nonlinear wavelet transform. It has been anticipated for application to nonlinear transform coding. To utilize a transformation to transform coding, both the optimal quantization noise allocation ratio and the coding gain of the transformation should be derived beforehand regardless of whether the transformation is linear or nonlinear. The derivation is crucial for progress of nonlinear transform image coding with nonlinear wavelet because the two-dimensional morphological Haar wavelet is the most basic nonlinear wavelet. We derive both the optimal quantization noise allocation ratio and the coding gain of the two-dimensional morphological Haar wavelet transform by introducing appropriate approximations to handle the cumbersome nonlinear operator included in the transformation. Numerical experiments confirmed the validity of formulations.

Fractional calculus is the generalization of the operators of differential and integration to non-integer order, and a differential equation involving the fractional calculus operators such as d1/2/dt1/2 and d-1/2/dt-1/2 is called the fractional differential equation. They have many applications in science and engineering. But not only its analytical solutions exist only for a limited number of cases, but also, the numerical methods are difficult to solve. In this paper we propose a new numerical method based on the operational matrices of the orthogonal functions for solving the fractional calculus and fractional differential equations. Two classical fractional differential equation examples are included for demonstration. They show that the new approach is simper and more feasible than conventional methods. Advantages of the proposed method include (1) the computation is simple and computer oriented; (2) the scope of application is wide; and (3) the numerically unstable problem never occurs in our method.

This paper proposes a technique for indexing, clustering and retrieving images based on their edge features. In this technique, images are decomposed into several frequency bands using the Haar wavelet transform. From the one-level decomposition sub-bands an edge image is formed. Next, the higher order auto-correlation function is applied on the edge image to extract the edge features. These higher order autocorrelation features are normalized to generate a compact feature vector, which is invariant to shift, image size. We used direction cosine as measure of distance not to be influenced by difference of each image's luminance. Then, these feature vectors are clustered by a self-organizing map (SOM) based on their edge feature similarity. The performed experiments show higher precision and recall of this technique than traditional ways in clustering and retrieving images in a large image database environment.

In this paper, we present a new state space-based approach for the two-dimensional (2-D) frequency estimation problem which occurs in various areas of signal processing and communication problems. The proposed method begins with the construction of a state space model associated with the noiseless data which contains a summation of 2-D harmonics. Two auxiliary Hankel-block-Hankel-like matrices are then introduced and from which the two frequency components can be derived via matrix factorizations along with frequency shifting properties. Although the algorithm can render high resolution frequency estimates, it also calls for lots of computations. To alleviate the high computational overhead required, a highly parallelizable implementation of it via the principle subband component (PSC) of some appropriately chosen transforms have been addressed as well. Such a PSC-based transform domain implementation not only reduces the size of data needed to be processed, but it also suppresses the contaminated noise outside the subband of interest. To reduce the computational complexity induced in the transformation process, we also suggest that either the transform of the discrete Fourier transform (DFT) or the Haar wavelet transform (HWT) be employed. As a consequence, such an approach of implementation can achieve substantial computational savings; meanwhile, as demonstrated by the provided simulation results, it still retains roughly the same performance as that of the original algorithm.