We design alternative dual frames for linearly reconstructing signals from Sigma-Delta (Σ∆) quantized finite frame coefficients. In the setting of sampling expansions for bandlimited functions, it is known that a stable rth order Sigma-Delta quantizer produces approximations where the approximation error is at most of order 1/λ , and λ > 1 is the oversampling ratio. We show that the counterpart...

Image fusion is processes of combining complementary information from a set of input images. The resultant fused image give large and reliable information. In this paper we study about Discrete wavelet and Discrete Multiwavelet and there use in image fusion. Discrete wavelet transform (DWT) technique is used for multi Resolution fusion. Multi Resolution fusion uses wavelet transform at multi sc...

The lifting scheme is a flexible method of designing perfect reconstruction multiwavelet filter banks for signal and image processing. This paper is on the usage of the lifting scheme in constructing such filter banks. It is shown that the constructed filter banks can be implemented very efficiently. Two algorithms on the design of multiwavelet filter banks using the lifting scheme are proposed...

We generalize the Second Oversampling Theorem for wavelet frames and dual wavelet frames from the setting of integer dilations to real dilations. We also study the relationship between dilation matrix oversampling of semi-orthogonal Parseval wavelet frames and the additional shift invariance gain of the core subspace.

Booleanization of frames or uniform frames, which is not functorial under the basic choice of morphisms, becomes functorial in the categories with weakly open homomorphisms or weakly open uniform homomorphisms. Then, the construction becomes a reflection. In the uniform case, moreover, it also has a left adjoint. In connection with this, certain dual equivalences concerning uniform spaces and u...

This paper proposes a novel oblivious image watermarking technique for the copyright protection and authentication of still images, based on Discrete Multiwavelet Transform (DMWT) and Quantization Index Modulus Modulation (QIMM). The multiwavelet coefficients of an image are quantized using QIMM and the coefficients are modified according to the binary watermark logo. Watermark extraction does ...

Orthogonal wavelet bases have been developed using multiple mother wavelet functions. Applying the discrete multiwavelet transform requires the input data to be preprocessed to obtain a more economical decomposition. Four characteristics of a preprocessing method are presented: length, degree, orthogonality and frequency response. A minimal preelter is deened to have length one and highest atta...

The subject of this article is the duality principle, which, well beyond its stand at the heart of Gabor analysis, is a universal principle in frame theory that gives insight into many phenomena. Its fiber matrix formulation for Gabor systems is the driving principle behind seemingly different results. We show how the classical duality identities, operator representations and constructions for ...

Multiwavelet transform can be implemented by treestructured matrix lter bank, which operates on vector sequence input instead of scalar ones. Therefore, unlike in scalar wavelet system, preprocessing is usually required to extract vector sequence input from the input signal for better performance. A 2-D approximation-based preprocessing scheme for GHM (Geronimo, Hardin and Massopust) discrete m...