Continuing the thrust of our recent work, but with an important new idea, we find a cutoff regularization of the determinant of a scalar particle in a classical Euclidean gravitational field. The field is assumed asymptotically flat, and the regularization is diffeomorphism-invariant under coordinate changes that are the identity at infinity. The scalar field is expanded in term of variables th...

generally, the presence of noise in geophysical measurements is inevitable and depending on the type and the level it affects the results of geophysical studies. so, denoising is an important part of the processing of geophysical data. on the other hand, geophysicists make inferences about the physical properties of the earth interior based on the indirect measurements (data) collected at or ne...

We present a fast reconstruction method for fluorescence optical tomography with structured illumination. Our approach is based on the exploitation of the wavelet transform of the measurements acquired after wavelet-patterned illuminations. This method, validated on experimental data, enables us to significantly reduce the acquisition and computation times with respect to the classical scanning...

The Adaptive Wavelet Image Compression (AWIC) algorithm is a fast, simple waveletbased image compression technique that follows the classical paradigm of image transformation, quantization, and entropy encoding. A key component of AWIC is a technique of channel symbol definition that provides greatly reduced Huffman table encoding costs, allowing optimal Huffman codewords to be generated and us...

The aim of the paper is to examine the wavelet-Galerkin method for the solution of filtering equations. We use a wavelet biorthogonal basis with compact support for approximations of the solution. Then we compute the Zakai equation for our filtering problem and consider the implicit Euler scheme in time and the Galerkin scheme in space for the solution of the Zakai equation. We give theorems on...

In this paper, we introduce a novel hybrid variational model which generalizes the classical total variation method and the wavelet shrinkage method. An alternating minimization direction algorithm is then employed. And we prove that it converges strongly to the minimizer of the proposed hybrid model. Finally, some numerical examples illustrate clearly that the new model outperforms the standar...

In this paper, we introduce a novel hybrid variational model which generalizes the classical total variation method and the wavelet shrinkage method. An alternating minimization direction algorithm is then employed. We also prove that it converges strongly to the minimizer of the proposed hybrid model. Finally, some numerical examples illustrate clearly that the new model outperforms the standa...

The fractional wavelet transform (FRWT), which generalizes the classical wavelet transform, has been shown to be potentially useful for signal processing. Many fundamental results of this transform are already known, but the theory of multiresolution analysis and orthogonal wavelets is still missing. In this paper, we first develop multiresolution analysis associated with the FRWT and then deri...

This paper presents a matrix factorization method for implementing orthonormal M-band wavelet reversible integer transforms. Based on an algebraic construction approach, the polyphase matrix of orthonormal M-band wavelet transforms can be factorized into a finite sequence of elementary reversible matrices that map integers to integers reversibly. These elementary reversible matrices can be furt...