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Bridge inspection usually is done visually on the spot. For this reason, inspection is very difficult in the case where humans can not enter, and it has become a problem. Therefore, in order to overcome this problem, we propose a new method in which pictures are taken by Drone and cracks are detected by image processing using a wavelet transform. Since bridge crack include many directional components, the characteristics of directional selection is useful for feature extraction. In this study, a 2-Dimensional Complex Discrete Wavelet Packet Transform with excellent directional selection is applied to bridge floor crack detection, and encouraging results are obtained.

The main drawback of abnormality diagnosis using the wavelet transform (WT) is that it needs much time. In order to improve this problem, a new real signal mother wavelet (RMW) that is made from all objective frequency components has been suggested. Thus the RMW can be greatly shorten the WT calculation time, and this WT is named the Wavelet Instantaneous Correlation (WIC). However, in order to construct the conventional RMW, it is essential to gather the target sounds, namely “sound samples” beforehand. In general, these are gathered by professionals using sensors. Furthermore it is possible that the abnormality diagnosis accuracy may decrease, because of a frequency component difference between the actual sound and the “sound sample”. In this study, therefore, we propose an improved method in which the expected characteristic frequency is extracted from actual sounds automatically, without requiring the “sound sample” to be obtained by professionals.

In this study, a novel direction selection method using the two-dimensional complex discrete wavelet transform (2D-CDWT) is proposed. In order to achieve arbitrary direction selection, the directional filters are first designed. Calculation procedure of directional selection can be shown as follows: (1) The 16 sub-images are generally generated from the original image by the 2D-CDWT without a down-sampling process and the 12 sub-images that correspond to the high-frequency components are selected. (2) The 12 sub-images are filtered by using the designed directional filter. (3) The down-sampling process is carried out and the resulting images are obtained. Furthermore, this method is applied to the surface analysis of a wafer, and it is confirmed that our method is effective in detecting irregular direction components.

Independent component analysis (ICA) is a useful method for blind source separation of two or more signals. We have previously proposed a new method combining ICA with the complex discrete wavelet transform (CDWT), in which voice and noise signals were separated using a new method. At that time, we used a simulated signal. In this study, we analyze measured biological signals by using a new method, and discuss its effectiveness. As an experiment, we try to separate an electromyogram (EMG) signal from an electrocardiogram (ECG) signal.

We restore a blurred image caused by defocus of a lens using the shift-invariant wavelet transform created using RI-Spline wavelets.In a defocus blurred image,the blurring kernel varies depending on its position in the image,so a positional frequency representation,such as a wavelet space,is required in order to deblur it.To restore the defocus blur,we assume that the blurring kernel can be obtained regardless of its position in an image.In experiments we conducted using synthesized images,our method using the shift-invariant wavelet transform showed better deblurring performance than that of the ordinary wavelet transform.We also show that our method can be applied to real images if additional range data is used.

In this study, in order to improve effectiveness of the abnormal signal detection, the technique of constituting an Average Real signal Mother Wavelet (A-RMW) from two or more real signals has been proposed and its effectiveness has been confirmed. The main results obtained can be summarized as follows : (1) For constructing A-RMW by two or more signals, the Symmetric Complex Real signal Mother Wavelet (SCRMW) first was constructed respectively and then the average SCRMW was obtained by adding them. Finally the average SCRMW obtained above was normalized and the A-RMW was obtained. (2) The proposed constructing method of the SCRMW is different from the traditional Complex Real signal Mother Wavelet that the phase information of all the frequency components has been cut off and symmetric property can be obtained. (3) The proposal method is applied to the rattle noise source detection of a car, and its effectiveness is examined.

It is well known that the continuous wavelet transform using the Gabor wavelet is useful and has high precision. However, its calculation amount is very large, and generally, its practical calculation is discretized depending on experience. In this paper, we consider the discretization method for the continuous wavelet transform using the Gabor wavelet set, and propose some approximate tight wavelet frames using the Gabor wavelet set, and based on them, we propose how to thin the Gabor wavelets in the continuous wavelet transform.

The complex discrete wavelet transform (CDWT) can be carried out by using a complex mother wavelet that is designed based on the Meyer wavelet, and achieves perfect translation invariance. However, it is calculated by the parallel Multi-resolution algorithm (MRA) using the imaginary part and the real part of the complex mother wavelet and the calculation amount is more than double that of the traditional discrete wavelet transform (DWT). In order to reduce the calculation amount, using the lifting scheme instead of the MRA is considered, although the lifting scheme was only used in the case of the mother wavelet with a compact support. In this research, we design a lifting scheme filter of Meyer wavelet without compact support in order to achieve high-speed computation by application to the CDWT, and have obtained encouraging results.

In our first report, we have proposed a complex type wavelet, the Real-Imaginary Spline Wavelet (RI-Spline wavelet) for the continuous wavelet transform and demonstrated the advantages of our approach. In this study, we develop our RI-Spline wavelet for the Discrete Wavelet Transform (DWT) that uses a fast algorithm based on Multi-resolution analysis. The DWT has a translation variance problem, so it can not catch features of the signals exactly although it has been widely used in signal analysis. In order to overcome this translation variance problem, we first develop a Complex Discrete Wavelet Transform (CDWT) using the RI-Spline wavelet and propose the Coherent Dual-Tree algorithm for the RI-Spline wavelet without increasing the computational cost very much. Then we apply this translation invariant CDWT to translation invariant de-noising. Experimental results show that our method, when applied to ECG data and music data, can obtain better de-noising results than conventional Wavelet Shrinkage.

It is well known that a mother wavelet for the discrete wavelet transform (DWT) has the band-pass filter characteristic with octave width in the frequency domain and can be used for octave analysis. However, it is possible that the octave analysis is not necessarily the most suitable to match the analysis signal. In this study, a novel variable-filter band discrete wavelet transform (VFB-DWT) is proposed. It is achieved by using variable-band filters instead of conventional decomposition and reconstruction sequences, which are designed in consideration of the real signal characteristics. Furthermore, the VFB-DWT is applied to the fetal electrocardiogram de-noising and good performance has ben obtained.

Previously, Discrete wavelet Transform(DWT) is well known for useful image processing method. Complex Discrete Wavelet Transform(CDWT) is one of the DWT and has the function called directional selection. This is the expected to be applied into shape and texture analysis. But the principle of directional selection is still not clear. In this paper, we consider the principle of directional selection. After that, we propose the evaluation method for directional selection based on the principle. Finally, we confirm the validity of evaluation method.

In this paper, we propose a design method for directional selection in the 2-Dimensional Complex Wavelet Packet Transform. Previous 2-Dimensional Complex Discrete Wavelet Transforms break up direction components, but the number of directions is small, and the directions and resolutions are fixed. So, they are not flexible enough. In this study, we propose a new design method that can detect desirable directions and resolutions. Finally, the proposed method is applied to defect detection in semiconductor wafer circuits in order to validate the proposed method.

In the variable filter band discrete wavelet transform (VFB-DWT), the frequency components in a specific frequency range has energy losses, and it also makes to reduce the extraction accuracy. In the previous study, this problem was improved by applying stationary wavelet transform (SWT) with redundancy. However, the SWT has a larger calculation cost more than that of previous method because it does not do down-sampling. In this paper, we propose the method of reducing the calculation cost and their effectiveness have been examined.

In this study, a new design method for Variable-Band Filters (VBFs) corresponding to the Real-signal Mother Wavelet (RMW), which is constructed from a real signal, is proposed. In order to detect and extract unsteady abnormal signals, the designed VBFs are used in the discrete wavelet transform (DWT) instead of traditional wavelets. The DWT that uses the VBFs is called the Variable-Band Filter Discrete Wavelet Transform (VBF-DWT). The VFB-DWT is applied to remove the pulse noise in the ion current waveform, which is measured in a spark-ignition engine and extracts the knocking components. The obtained results show that the VFB-DWT is effective in the detection and extraction of abnormal signals.

In this paper, we expand the perfect translation invariant complex discrete wavelet packet transform (PTI-CWPT) to the 2-dimensional PTI-CWPT for separating more directional components. A new definition is made for evaluating its directional selection and resolution properties. The results show that the 2-dimensional PTI-CWPT is capable of separating 30 directional components with each directional component having uniform energy.

It is well imown that parasitic discrete wavelet transform (PDWT) proposed by authors is a useful tool for abnormal signal detection, although it uses only for the signal decomposition and detection. In this study, a reconstruction possible new parasitic discrete wavelet transform (N-PDWT) has been proposed for traditional PDWT. The N-PDWT is different from the PDWT and the traditional DWT that it enabled the detailed decomposition corresponding to the purpose signal. In addition, the N-PDWT has been applied to the Korona noise removal form the ion current waveform of the engine and confirmed that the N-PDWT has bester performance than ihat of conventional impulse noise removal technique used the CDWT.

In this study, we first analyze the characteristics of knocking and the standing-wave by the wavelet transform using the ion current waveform, which is measured in a spark-ignition engine. Based on this result, we design wavelets to detect knocking from the ion current waveform. We next define an evaluation parameter E, and apply it to knocking detection and show its effectiveness.

In this study, a novel direction selection method using the two dimensional complex discrete wavelet transform is proposed. In order to achieve arbitrary direction selection, direction extraction filters are designed. And then, this method is applied to the surface analysis of a wafer, and it is confirmed that our method is effective in detecting irregular direction components.

In this study, in order to improve effectiveness of the abnormal signal detection, first the technique of constituting an average real signal mother wavelet (A-RMW) from two or more real signals was proposed. Then a novel parasitic discrete wavelet transform by using the RMW designed is proposed and it effectiveness has been conformed in the identification of the rattle noise that steering operation mechanism causes.

It is well known that independent component analysis (ICA) is a useful method for blind source separation although it does have some drawbacks, such as performing poorly on unsteady sounds. In this study, in order to improve this deficiency, a new method combining ICA with the complex discrete wavelet transform is proposed and verification of source separation with relation to the problems of permutation and scaling in the ICA are performed. Through comparison of the results according to the signal noise ratio (SNR), the effectiveness of the proposed method is confirmed.

We propose a 2-dimensional translation invariant real-imaginary spline wavelet (RI-spline wavelet) and develop a 2-dimensional complex discrete wavelet transform (2D CDWT). The main results obtained can be summarized as follows: (1) the problem of 2D translation variance which is caused by the DWT using a real mother wavelet can be solved by using the 2D RI-spline wavelet; (2) the 2D RI-spline wavelet is applied to image processing, and encouraging results are obtained.

It is well-known that a mother wavelet for the discrete wavelet transform (DWT) has the band-pass filter characteristic with octave width in the frequency domain and can be used for octave analysis. However, it is possible that the octave analysis is not necessarily the most suitable to match the analysis signal. In this study, in order to construct the most suitable basis to match the analysis signal, a novel variable-filter band discrete wavelet transform (VFB-DWT) is proposed. It is achieved by using variable-band filters instead of conventional decomposition and reconstruction sequences, which are designed in consideration of the real signal characteristics. Additionally, it is proven that perfect reconstruction of the analysis signal by VFB-DWT is guaranteed using the perfect shift invariant theorem that underlies the theory of the PTI-CDWT having base DWT.

In this study, in order to verify the effectiveness of the variable filter band discrete wavelet transform (VFB-DWT) and construction method of the variable-band filter (VBF), a fetal ECG extraction has been carried out and the main results obtained are as follows. The approach to configuration VBF by selecting the frequency band only where the fetal ECG component is present was effective to configure the optimal base sensible signal. The extraction of the fetal ECG was successful by applying the wavelet shrinkage to VFB-DWT, which used the constructed VBF. The information entropy was selected as an evaluation index, and two kinds of ECG signals are used to evaluate the wavelet transform basis between the wavelet packet transform (WPT) and the VFB-DWT. One is a synthesized signal composed of white noise, the maternal ECG and the fetal ECG. The other signal is the real target signal separated by independent component analysis (ICA) and has the mother's body noise, the maternal ECG and the fetal ECG. The result shows that the basis by VBF of the VFB-DWT is better than the basis of the WPT that was chosen by the best basis algorithm (BBA).

In this paper, we propose a design method for directional selection in the two-dimensional complex wavelet packet transform (2D-CWPT). Current two-dimensional complex discrete wavelet transforms (2D-CDWT) can extract directional components from images, but the number of directions is small, and the directions and resolutions are fixed. Thus the current 2D-CDWTs are not flexible enough. In this study, we propose a new design method of the directional filters that can detect desirable direction components. Additionally flexible directional selection is achieved because the directional filters are added to the 2D-CWPT. Finally, the proposed method is applied to defect detection in semiconductor wafer circuits and an encouraging result is obtained.