Biorthogonal system

About: Biorthogonal system is a research topic. Over the lifetime, 2190 publications have been published within this topic receiving 32209 citations.

Face recognition based on Independent Component Analysis on wavelet subband

Abstract: In this paper a multi-resolution analysis based on Independent Component Analysis (ICA) for face recognition is examined. We extract image features of facial images from various wavelet transforms (Haar, Daubechies, Coiflet, Symlet, Biothogonal and Reverse Biorthogonal) by decomposing face image in subbands 1 to 8. These features are analyzed by ICA and Euclidean distance measure. A series of experiments based on ORL database were then performed to evaluate the performance. The results show that for the entire wavelets, subbands 2 and 3 give the best accuracy and are computationally most efficient. Reverse Biorthogonal and 8th order Symlet are found to be the best among all. Our experiments also prove that face recognition accuracy using ICA on wavelet subbands is higher than ICA used alone.

An evaluation of wavelet filters performance for steganalysis

Abstract: This paper presents an evaluation of wavelet filters performance for the task of steganalysis. We analyzed six different wavelet filters namely Daubachies, Coiflets, Symlets, Discrete Meyer, Biorthogonal and Reverse Biorthogonal families for feature extraction in a wavelet based steganalysis technique. Two publicly available steganography tools, namely the F5 steganography and the Model Based steganography were used to embed messages in a database of clean images to develop steganographic database of images. A Fisher Linear Discriminant classifier is trained using all six feature sets extracted from both clean and steganographic images separately and subsequently used for classification. Experiments revealed that the features using the ‘Haar(db1)’ wavelet filter gave the best steganalysis performance.

Some results on discrete Gabor transforms for finite periodic sequences

Abstract: In this correspondence, using linear system theory and frame theory, we address computation methods for analysis and synthesis sequences of the discrete Gabor transform (DGT), where all sequences are periodic with the same period L, and show that the minimum energy solution to the Wexler and Raz (1990) biorthogonal condition and the solution to the frame operator are the same via linear system theory and frame theory.

Recursive biorthogonal interpolating wavelets and signal-adapted interpolating filter banks

Abstract: In this paper, by combining the ideas of the recursive wavelets with second-generation wavelets, a family of recursive biorthogonal interpolating wavelets (RBIWs) is developed. The RBIWs have simple shape parameter vectors on each level, which allows a multichannel decomposition algorithm and provides, a flexible structure for designing signal-adapted interpolating filter banks. In the single-level case, an efficient approach to design an optimum two-channel biorthogonal interpolating filter bank is proposed, which maximizes the coding gain under the traditional quantization noise assumption. Furthermore, in the multilevel case, using level-wise optimization of the shape parameter vectors, signal-adapted tree-structured recursive biorthogonal interpolating filter banks (RBIFBs) are designed, which are efficient in computation and can remarkedly improve the coding gain. Finally, numerical results demonstrate the effectiveness of the proposed methods.

Some Biorthogonal Families of Polynomials Arising in Noncommutative Quantum Mechanics

Abstract: In this paper we study families of complex Hermite polynomials and construct deformed versions of them, using a GL(2,C) transformation. This construction leads to the emergence of biorthogonal families of deformed complex Hermite polynomials, which we then study in the context of a two-dimensional model of noncommutative quantum mechanics.