Hiroshi Toda

A new complex wavelet transform by using RI-spline wavelet

We propose a new complex wavelet, the RI-spline wavelet, which is constructed using spline wavelets for dual-tree DWT. In the RI-spline wavelet, the real and imaginary components become an approximate Hilbert pair to each other. Then we propose a new dual-tree algorithm which uses an interpolation method for providing a half-sample-delay between the two filters of the trees. Finally, we experimentally show that the translation invariance, which can not be obtained by the ordinary DWT, is obtained by RI-spline wavelet.

Translation Invariant Ri-Spline Wavelet And Its Application On De-Noising

Wavelet Shrinkage using DWT has been widely used in de-noising although DWT has a translation variance problem. In this study, we solve this problem by using the translation invariant DWT. For this purpose, we propose a new complex wavelet, the Real-Imaginary Spline Wavelet (RI-Spline wavelet). We also propose the Coherent Dual-Tree algorithm for the RI-Spline wavelet and extend it to the 2-Dimensional. Then we apply this translation invariant RI-Spline wavelet for translation invariant de-noising. Experimental results show that our method, when applied to ECG data, the medical image and the textile surface inspection can obtain better de-noising results than that of conventional Wavelet Shrinkage.

Textile surface inspection by using translation invariant wavelet transform

It is known that texture can be modeled better using both deterministic and random components. The wavelet transform, which can be computed efficiently, is a well-know multiresolution analysis method. However, when it is applied to texture analysis method. However, then it is applied to texture analysis, the wavelet transform has the problem that the transformed result of the deterministic component of the texture is no longer translation invariant. In this paper, we will constitute 2D RI-spline wavelets, which can be considered to be one variation of complex wavelets, we can obtain translation invariance. Then, we apply the translation invariant 2-D RI-spline wavelets to the automated inspection of textile surfaces. In our approach, first to remove textile textures from textile surfaces we use the 2-D RI-spline wavelets. Once the textural information is removed from textile surfaces, the remaining inspection process becomes a tractable problem, which we can handle using a standard statistical method. The experimental results show that our inspection method is effective for real textile surfaces.