Hilbert Pair Of Wavelets Research Articles

Person Recognition by Hilbert Pair of Wavelets using Facial Images

In human identification, the face acts as an important tool that carries the identity of each person. The human mind has the ability to re-cognize faces after the first view of a human face. Though there are many types of face detection/recognition system found no method can give the 100% accurate outputs. In this proposed system we are implementing and analyzing a new method that can be used for person recognition system that can produce better output accuracies. In the proposed system of person recognition method, one of the robust wavelet transform methods is used for the extraction of the features from the original images. The wavelet type used is known as the Dual Tree M-Band Wavelet Transform (DTMBWT) method. Using this transform the low and high sub-bands is obtained. These low and high sub-band coefficients are given as the input for the classification purpose. The sub-band obtained from the DTMBWT transform is given as the inputs for the classification purpose. The classification process is done using the K-Nearest Neighbor (KNN) classifier scheme. The system is implemented by using the facial images from the ORL database. By using this dataset images the performance measures of the proposed system is calculated in the form of graphical results such as Receiver Operating Characteristic (ROC), Inverse ROC and Expected Performance Curve (EPC) curves. Results show that proposed DTMBWT based face recognition provides better results than other approaches.

A New Approach to the Common-Factor Design Technique for Hilbert-Pair of Wavelets

A Hilbert-Pair consists of a pair of filter banks whose corresponding wavelets are Hilbert transforms of each other. Selesnick proposed the simple common-factor technique for its design. The filter transfer functions consist of the product of a factor that is common to both filter banks and a phase factor which gives the (approximate) half-sample-delay requirement. Previously the design of the phase factor has been based on designing an allpass filter approximating the half-sample-delay. This paper proposes a different approach to designing the phase factor by exploiting a basic multirate identity. The downsampling approach allows greater flexibility and can yield filters and wavelets with better properties.

Image analysis using a dual-tree M-band wavelet transform

We propose a two-dimensional generalization to the M-band case of the dual-tree decomposition structure (initially proposed by Kingsbury and further investigated by Selesnick) based on a Hilbert pair of wavelets. We particularly address: 1) the construction of the dual basis and 2) the resulting directional analysis. We also revisit the necessary pre-processing stage in the M-band case. While several reconstructions are possible because of the redundancy of the representation, we propose a new optimal signal reconstruction technique, which minimizes potential estimation errors. The effectiveness of the proposed M-band decomposition is demonstrated via denoising comparisons on several image types (natural, texture, seismics), with various M-band wavelets and thresholding strategies. Significant improvements in terms of both overall noise reduction and direction preservation are observed.