Directional illumination analysis using beamlet decomposition and propagation

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. S147-S159 ◽  
Author(s):  
Ru-Shan Wu ◽  
Ling Chen
Keyword(s):  
Wavelet Transform ◽  
Wave Theory ◽  
Image Space ◽  
Low Velocity ◽  
Numerical Examples ◽  
Depth Migration ◽  
Local Angle ◽  
Spatial Axis ◽  
Local Image

We evaluate directional illumination (DI) and acquisition-aperture efficacy through wave theory-based beamlet decomposition of the wavefield. Beamlet decomposition (wavelet transform along spatial axis) provides localizations in both space and direction of a wavefield. We introduce the image conditions in beamlet domain and local angle domain and then define the local image matrix (LIM). We calculate the DI in the image space for a given source or a group of sources by decomposing Green’s functions into local angle domain at image points. Acquisition-aperture efficacy (AAE) matrix and acquisition dip-response (ADR) vector can be defined to quantify the efficacy of an acquisition configuration for a given subsurface point. As numerical examples, we calculate the DI maps and ADR maps for high- and low-velocity lens models and for the SEG-EAGE 2D salt model. We further investigate the influences of acquisition geometry and overlaying structures on the quality of prestack depth migration image for the subsalt area of the SEG-EAGE model. We find that the ADR maps for different dip angles have good correlation with the image qualities of the corresponding reflectors. DI analysis can be used in the aperture correction for image amplitude in local angle domain for wave theory-based migration methods.

Singular Values Decomposition and Lifting Wavelet Transform for Speech Signal Embedding into Digital Image

2019 ◽  
Vol 12 (2) ◽  
pp. 138-151
Author(s):  
Mourad Talbi ◽  
Med Salim Bouhlel
Keyword(s):  
Wavelet Transform ◽  
Speech Signal ◽  
Signal To Noise Ratio ◽  
Perceptual Quality ◽  
Lifting Wavelet Transform ◽  
Signal To Noise ◽  
Perceptual Evaluation ◽  
Lifting Wavelet ◽  
Noise Ratio

Background: In this paper, we propose a secure image watermarking technique which is applied to grayscale and color images. It consists in applying the SVD (Singular Value Decomposition) in the Lifting Wavelet Transform domain for embedding a speech image (the watermark) into the host image. Methods: It also uses signature in the embedding and extraction steps. Its performance is justified by the computation of PSNR (Pick Signal to Noise Ratio), SSIM (Structural Similarity), SNR (Signal to Noise Ratio), SegSNR (Segmental SNR) and PESQ (Perceptual Evaluation Speech Quality). Results: The PSNR and SSIM are used for evaluating the perceptual quality of the watermarked image compared to the original image. The SNR, SegSNR and PESQ are used for evaluating the perceptual quality of the reconstructed or extracted speech signal compared to the original speech signal. Conclusion: The Results obtained from computation of PSNR, SSIM, SNR, SegSNR and PESQ show the performance of the proposed technique.

scholarly journals An innovative image fusion algorithm based on wavelet transform and discrete fast curvelet transform

2011 ◽  
Vol 1 (3) ◽  
Author(s):  
T. Sumathi ◽  
M. Hemalatha
Keyword(s):  
Wavelet Transform ◽  
Image Fusion ◽  
Curvelet Transform ◽  
Relevant Information ◽  
Good Time ◽  
Discrete Wavelet ◽  
Fusion Algorithm ◽  
Time Frequency ◽  
Fused Image

AbstractImage fusion is the method of combining relevant information from two or more images into a single image resulting in an image that is more informative than the initial inputs. Methods for fusion include discrete wavelet transform, Laplacian pyramid based transform, curvelet based transform etc. These methods demonstrate the best performance in spatial and spectral quality of the fused image compared to other spatial methods of fusion. In particular, wavelet transform has good time-frequency characteristics. However, this characteristic cannot be extended easily to two or more dimensions with separable wavelet experiencing limited directivity when spanning a one-dimensional wavelet. This paper introduces the second generation curvelet transform and uses it to fuse images together. This method is compared against the others previously described to show that useful information can be extracted from source and fused images resulting in the production of fused images which offer clear, detailed information.

CHARACTERIZATION OF IMAGE SPACE OF A WAVELET TRANSFORM

2006 ◽  
Vol 04 (03) ◽  
pp. 547-557 ◽  
Author(s):  
CAIXIA DENG ◽  
YULING QU ◽  
LIJUAN GU
Keyword(s):  
Wavelet Transform ◽  
Truncation Error ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Sampling Theorem ◽  
Image Space ◽  
Kernel Space ◽  
Reproducing Kernel Space ◽  
Scope Of Application

In this paper, Journe wavelet function is introduced as a wavelet generating function. The expression of reproducing kernel function for the image space of this wavelet transform is obtained based on the fact that the image space of the wavelet transform is a reproducing kernel Hilbert space. Then the isometric identity of Journe wavelet transform is obtained. The connections between the image space of the wavelet transform and the image space of the known reproducing kernel space are established by the theories of reproducing kernel. The properties and the structures of the image space of the wavelet transform can be characterized by the properties and the structures of the image space of the known reproducing kernel space. Using the ideas of reproducing kernel, we consider there are relations between the wavelet transform and the sampling theorem. Meanwhile, the approximations in sampling theorems is shown and the truncation error is given. This provides a theoretical basis for us to study the image space of the general wavelet transform and broadens the scope of application of theories of the reproducing kernel space.

Processing of Sonar Image Based on Compressive Sensing

2011 ◽  
Vol 301-303 ◽  
pp. 719-723 ◽  
Author(s):  
Zhi Jing Xu ◽  
Huan Lei Dai ◽  
Pei Pei Cao
Keyword(s):  
Wavelet Transform ◽  
Matching Pursuit ◽  
Experimental Result ◽  
Underwater Acoustic Channel ◽  
Sonar Image ◽  
Underwater Image ◽  
Reconstruction Image ◽  
Observation Matrix ◽  
Efficient Transmission

The particularity of the underwater acoustic channel has put forward a higher request for collection and efficient transmission of the underwater image. In this paper, based on the characteristics of sonar image, wavelet transform is used to sparse decompose the image, and selecting Gaussian random matrix as the observation matrix and using the orthogonal matching pursuit (OMP) algorithm to reconstruct the image. The experimental result shows that the quality of the reconstruction image and PSNR have gained great ascension compared to the traditional compression and processing of image based on the wavelet transform while they have the same measurement numbers in the coding portion. It provides a convenient for the sonar image’s underwater transmission.

DAUBECHIES COMPLEX WAVELET TRANSFORM BASED TECHNIQUE FOR DENOISING OF MEDICAL IMAGES

2007 ◽  
Vol 07 (04) ◽  
pp. 663-687 ◽  
Author(s):  
ASHISH KHARE ◽  
UMA SHANKER TIWARY
Keyword(s):  
Wavelet Transform ◽  
Image Denoising ◽  
Medical Image ◽  
Medical Images ◽  
Universal Method ◽  
Complex Wavelet Transform ◽  
Shrinkage Function ◽  
Daubechies Complex Wavelet Transform ◽  
Complex Wavelet

Wavelet based denoising is an effective way to improve the quality of images. Various methods have been proposed for denoising using real-valued wavelet transform. Complex valued wavelets exist but are rarely used. The complex wavelet transform provides phase information and it is shift invariant in nature. In medical image denoising, both removal of phase incoherency as well as maintaining the phase coherency are needed. This paper is an attempt to explore and apply the complex Daubechies wavelet transform for medical image denoising. We have proposed a method to compute a complex threshold, which does not depend on any assumed model of noise. In this sense this is a "universal" method. The proposed complex-domain shrinkage function depends on mean, variance and median of wavelet coefficients. To test the effectiveness of the proposed method, we have computed the input and output SNR and PSNR of various types of medical images. The method gives an improvement for Gaussian additive, Speckle and Salt-&-Pepper noise as well as for the mixture of these noise types for a range of noisy images with 15 db to 30 db noise levels and outperforms other real-valued wavelet transform based methods. The application of the proposed method to Ultrasound, X-ray and MRI images is demonstrated in the experiments.

Leading-order seismic imaging using curvelets

Geophysics ◽  
2007 ◽  
Vol 72 (6) ◽  
pp. S231-S248 ◽  
Author(s):  
Huub Douma ◽  
Maarten V. de Hoop
Keyword(s):  
Seismic Data ◽  
Order Approximation ◽  
Angular Frequency ◽  
Leading Order ◽  
Numerical Examples ◽  
Depth Migration ◽  
Map Migration ◽  
Kirchhoff Depth Migration ◽  
Homogeneous Media ◽  
Spatial Support

Curvelets are plausible candidates for simultaneous compression of seismic data, their images, and the imaging operator itself. We show that with curvelets, the leading-order approximation (in angular frequency, horizontal wavenumber, and migrated location) to common-offset (CO) Kirchhoff depth migration becomes a simple transformation of coordinates of curvelets in the data, combined with amplitude scaling. This transformation is calculated using map migration, which employs the local slopes from the curvelet decomposition of the data. Because the data can be compressed using curvelets, the transformation needs to be calculated for relatively few curvelets only. Numerical examples for homogeneous media show that using the leading-order approximation only provides a good approximation to CO migration for moderate propagation times. As the traveltime increases and rays diverge beyond the spatial support of a curvelet; however, the leading-order approximation is no longer accurate enough. This shows the need for correction beyond leading order, even for homogeneous media.

scholarly journals Deep Learning-Based Wavelet Threshold Function Optimization on Noise Reduction in Ultrasound Images

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Zhuxiang Shen ◽  
Wei Li ◽  
Hui Han
Keyword(s):  
Wavelet Transform ◽  
Image Denoising ◽  
Similarity Index ◽  
Speckle Noise ◽  
Disease Diagnosis ◽  
Function Optimization ◽  
Threshold Function ◽  
Ultrasound Images ◽  
Better Than

To explore the utilization of the convolutional neural network (CNN) and wavelet transform in ultrasonic image denoising and the influence of the optimized wavelet threshold function (WTF) algorithm on image denoising, in this exploration, first, the imaging principle of ultrasound images is studied. Due to the limitation of the principle of ultrasound imaging, the inherent speckle noise will seriously affect the quality of ultrasound images. The denoising principle of the WTF based on the wavelet transform is analyzed. Based on the traditional threshold function algorithm, the optimized WTF algorithm is proposed and applied to the simulation experiment of ultrasound images. By comparing quantitatively and qualitatively with the traditional threshold function algorithm, the advantages of the optimized WTF algorithm are analyzed. The results suggest that the image is denoised by the optimized WTF. The mean square error (MSE), peak signal-to-noise ratio (PSNR), and structural similarity index measurement (SSIM) of the images are 20.796 dB, 34.294 dB, and 0.672 dB, respectively. The denoising effect is better than the traditional threshold function. It can denoise the image to the maximum extent without losing the image information. In addition, in this exploration, the optimized function is applied to the actual medical image processing, and the ultrasound images of arteries and kidneys are denoised separately. It is found that the quality of the denoised image is better than that of the original image, and the extraction of effective information is more accurate. In summary, the optimized WTF algorithm can not only remove a lot of noise but also obtain better visual effect. It has important value in assisting doctors in disease diagnosis, so it can be widely applied in clinics.

scholarly journals Fusion of Medical Images in Wavelet Domain: A Discrete Mathematical Model

2018 ◽  
Vol 14 (25) ◽  
pp. 1-11
Author(s):  
Satya Prakash Yadav ◽  
Sachin Yadav
Keyword(s):  
Wavelet Transform ◽  
Image Compression ◽  
Image Fusion ◽  
Data Transfer ◽  
Discrete Wavelet ◽  
Related Information ◽  
Medical Domain ◽  
Discrete Mathematical Model ◽  
Treatment Procedures

Introduction: Image compression is a great instance for operations in the medical domain that leads to better understanding and implementations of treatment, especially in radiology. Discrete wavelet transform (dwt) is used for better and faster implementation of this kind of image fusion.Methodology: To access the great feature of mathematical implementations in the medical domain we use wavelet transform with dwt for image fusion and extraction of features through images.Results: The predicted or expected outcome must help better understanding of any kind of image resolutions and try to compress or fuse the images to decrease the size but not the pixel quality of the image.Conclusions: Implementation of the dwt mathematical approach will help researchers or practitioners in the medical domain to attain better implementation of the image fusion and data transmission, which leads to better treatment procedures and also decreases the data transfer rate as the size will be decreased and data loss will also be manageable.Originality: The idea of using images may decrease the size of the image, which may be useful for reducing bandwidth while transmitting the images. But the thing here is to maintain the same quality while transmitting data and also while compressing the images.Limitations: As this is a new implementation, if we have committed any mistakes in image compression of medical-related information, this may lead to treatment faults for the patient. Image quality must not be reduced with this implementation.

Distance Protection Application Based on Wavelet Transform and Traveling Wave Ranging

2012 ◽  
Vol 150 ◽  
pp. 40-44
Author(s):  
Peng Peng Kang ◽  
Xi Fang Zhu
Keyword(s):  
Wavelet Transform ◽  
Power System ◽  
Transmission Line ◽  
Software Design ◽  
Traveling Wave ◽  
Wave Theory ◽  
Distance Measurement ◽  
Distance Protection

This paper describes the wavelet transform theory, and traveling wave theory. When the power system transmission line fault occurs, the fault signal generated by sampling and analysis, and use a method of one-end fault distance measurement in transmission line. Finally the article gives the ranging devices’ hardware and software design.

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