Biorthogonal system

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

Model-based multi-stage compression of human face images

Abstract: This paper describes a multi-stage compression scheme of human face images. Snakes are employed in localisation of facial features and biorthogonal spline filters are used for the decomposition of segmented and normalised face images. Wavelet coefficients are vector quantized in different number of cascaded stages depending on their contribution to the subjective quality of the image.

Evolving Matched Filter Transform Pairs for Satellite Image Processing

Abstract: Wavelets provide an attractive method for efficient image compression. For transmission across noisy or bandwidth limited channels, a signal may be subjected to quantization in which the signal is transcribed onto a reduced alphabet in order to save bandwidth. Unfortunately, the performance of the discrete wavelet transform (DWT) degrades at increasing levels of quantization. In recent years, evolutionary algorithms (EAs) have been employed to optimize wavelet-inspired transform filters to improve compression performance in the presence of quantization. Wavelet filters consist of a pair of real-valued coefficient sets; one set represents the compression filter while the other set defines the image reconstruction filter. The reconstruction filter is defined as the biorthogonal inverse of the compression filter. Previous research focused upon two approaches to filter optimization. In one approach, the original wavelet filter is used for image compression while the reconstruction filter is evolved by an EA. In the second approach, both the compression and reconstruction filters are evolved. In both cases, the filters are not biorthogonally related to one another. We propose a novel approach to filter evolution. The EA optimizes a compression filter. Rather than using a wavelet filter or evolving a second filter for reconstruction, the reconstruction filter is computed as the biorthogonal inverse of the evolved compression filter. The resulting filter pair retains some of the mathematical properties of wavelets. This paper compares this new approach to existing filter optimization approaches to determine its suitability for the optimization of image filters appropriate for defense applications of image processing.

A Digital Image Watermarking Technique Using Cascading of DCT and Biorthogonal Wavelet Transform

Abstract: Modern communication technology facilitates easy transmission of multimedia content. But if copyright protection of multimedia data, prevention of illegal access, and rights of intellectual property are considered, so this field needs more attention of researchers. It is a very simple process to make a copy of the multimedia data, alter it, and then put it back for business profits. Digital watermarking techniques provide a solution for this issue, by embedding some information, which can be further used to claim the ownership of multimedia data. In this paper, a new algorithm for the watermarking of digital images is proposed by cascading of two frequency domain transform techniques, i.e., biorthogonal wavelet transforms (BWT) and discrete cosine transform (DCT). Proposed technique takes the approximation component of the biorthogonal transform of cover image and then applies DCT to embed watermark. Embedding of watermark data is done in middle frequency component by comparison-based correlation technique. Also, this technique has been analyzed and compared with the existing ones by applying various image attacks and subsequently measuring the results and proved to be fairly robust.

Generalized Biorthogonal Daubechies Wavelets

Abstract: We propose a generalization of the Cohen-Daubechies-Feauveau (CDF) and 9⁄7 biorthogonal wavelet families. This is done within the framework of non-stationary multiresolution analysis, which involves a sequence of embedded approximation spaces generated by scaling functions that are not necessarily dilates of one another. We consider a dual pair of such multiresolutions, where the scaling functions at a given scale are mutually biorthogonal with respect to translation. Also, they must have the shortest-possible support while reproducing a given set of exponential polynomials. This constitutes a generalization of the standard polynomial reproduction property. The corresponding refinement filters are derived from the ones that were studied by Dyn et al. in the framework of non-stationary subdivision schemes. By using different factorizations of these filters, we obtain a general family of compactly supported dual wavelet bases of $ L _{ 2 } $ . In particular, if the exponential parameters are all zero, one retrieves the standard CDF B-spline wavelets and the 9⁄7 wavelets. Our generalized description yields equivalent constructions for E-spline wavelets. A fast filterbank implementation of the corresponding wavelet transform follows naturally; it is similar to Mallat's algorithm, except that the filters are now scale-dependent. This new scheme offers high flexibility and is tunable to the spectral characteristics of a wide class of signals. In particular, it is possible to obtain symmetric basis functions that are well-suited for image processing.