Due to the lossy transmission in the JPEG2000 image compression standard,the loss of wavelet coefficients heavily af-fects the quality of the received image.In this paper,we propose a novel wavelet inpainting model based on tensor diffusion(TDWI)to restore the missing or damaged wavelet coefficients.A hybrid model is built by combining structure-adaptive anisotropic regu-larization with wavelet representation.Its associated Euler-Lagrange equation is also given for analyzing its regularity performance.Owing to the matrix representation of the structure tensor in the regularization term,the shape of diffusion kernel changes adaptivelyaccording to the image features,including sharp edges,corners and homogeneous regions.Compared with existing wavelet inpaint-ing models,the proposed one can control more adaptively and accurately the geometric regularity in the image and exhibits betterrobustness to noise.In addition,an effective and proper numerical scheme is adopted to improve the computation.Experimentalresults on a variety of loss scenarios are given to demonstrate the advantages of our proposed model.
The frequency domain electromagnetic method has already been widely used for tomographic imaging or electromagnetic well logging. However, different from open hole logging, the metal casing existing in production well logging has a strong shielding effect on the electromagnetic waves, thus bringing some difficulties to the application of the frequency domain electromagnetic method in production well logging. According to the relation of the field source geometry to the ring around the mandrel, the general expressions of frequency domain electromagnetic responses in axially symmetrical layered conductive medium are deduced. The propagation effects caused by the low-frequency electromagnetic waves in cased hole are also analyzed. The distribution curves of eddy current density and magnetic flux density along the radial direction in the mandrel indicate that the eddy loss within the mandrel is proportional to the transmission signal frequency and the mandrel conductivity. The secondary field responses of different casing materials show that the transmission frequency has an important effect on the ability of electromagnetic waves penetrating the metal casing. The transmission frequency should be ultra-low in order to enable the electromagnetic signal to penetrate the casing easily. The numerical results of frequency responses for different casing physical parameters show that the casing thickness has a significant impact on the choice of the transmission frequency. It is also found that the effect of the casing radius on the transmission frequency can be neglected.
