Comparative Survey of the DCT and the Wavelet Transforms for Image Compression

Kammoun, Fahmi; Fourati, Walid; Bouhlel,

doi:10.1520/jte100086

Cited by 4 publications

(5 citation statements)

References 25 publications

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“…The parameters PSNR and bpp are generally used for assessing the quality of the reconstructed image. Earlier studies [1][2][3][4][5][6][7][8]13,14] discussed the image compression and [4][5][6] addressed the compression of images. The results were obtained in the present study, using the preprocessing step followed by the bisection method including thresholding, the quantization, dequantization and the IDWT were compared with the 3-D transforms, such as discrete Hartley transform (DHT), discrete cosine transform (DCT) and discrete Fourier transform (DFT) [6].…”

Section: Discussionmentioning

confidence: 99%

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Compression of MR Images Using DWT by Comparing RGB and YCbCr Color Spaces

Jayprkash¹,

Vijay²

2013

JSIP

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This paper consists of a lossy image compression algorithm dedicated to the medical images doing comparison of RGB and YCbCr color space. Several lossy/lossless transform coding techniques are used for medical image compression. Discrete Wavelet Transform (DWT) is one such widely used technique. After a preprocessing step (remove the mean and RGB to YCbCr transformation), the DWT is applied and followed by the bisection method including thresholding, the quantization, dequantization, the Inverse Discrete Wavelet Transform (IDWT), YCbCr to RGB transform of mean recovering. To obtain the best compression ratio (CR), the next step encoding algorithm is used for compressing the input medical image into three matrices and forward to DWT block a corresponding containing the maximum possible of run of zeros at its end. The last step decoding algorithm is used to decompress the image using IDWT that is applied to get three matrices of medical image.

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Section: Discussionmentioning

confidence: 99%

“…The basic objective of image compression is to reduce the size of image data for transmission or store in an efficient manner, while maintaining the suitable quality of reconstructed images [1][2][3]. The easy and reliable digital transmission and storage of biomedical images would be a tremendous boon to the medical practices.…”

Section: Introductionmentioning

confidence: 99%

Compression of MR Images Using DWT by Comparing RGB and YCbCr Color Spaces

Jayprkash¹,

Vijay²

2013

JSIP

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“…), discrete cosine transform (Jafarpour and McLaughlin ), wavelet transforms (Fernández Martínez et al . ; Kamoun, Fourati, and Bouhlel ), etc., may be applied for reduction of the model parameter space. A discussion about these model parameter reduction methods can be found in (Fernández Martínez et al .…”

Section: Methodsmentioning

confidence: 99%

Regularized sparse‐grid geometric sampling for uncertainty analysis in non‐linear inverse problems

Azevedo

Tompkins²,

Mukerji

2015

Geophysical Prospecting

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A B S T R A C TThis paper introduces an efficiency improvement to the sparse-grid geometric sampling methodology for assessing uncertainty in non-linear geophysical inverse problems. Traditional sparse-grid geometric sampling works by sampling in a reduceddimension parameter space bounded by a feasible polytope, e.g., a generalization of a polygon to dimension above two. The feasible polytope is approximated by a hypercube. When the polytope is very irregular, the hypercube can be a poor approximation leading to computational inefficiency in sampling. We show how the polytope can be regularized using a rotation and scaling based on principal component analysis. This simple regularization helps to increase the efficiency of the sampling and by extension the computational complexity of the uncertainty solution. We demonstrate this on two synthetic 1D examples related to controlled-source electromagnetic and amplitude versus offset inversion. The results show an improvement of about 50% in the performance of the proposed methodology when compared with the traditional one. However, as the amplitude versus offset example shows, the differences in the efficiency of the proposed methodology are very likely to be dependent on the shape and complexity of the original polytope. However, it is necessary to pursue further investigations on the regularization of the original polytope in order to fully understand when a simple regularization step based on rotation and scaling is enough. I N T R O D U C T I O NGeophysical inverse problems aim to infer Earth's subsurface properties given a limited set of indirect measurements, i.e., d obs ∈ R N . Most of geophysical inverse problems can be summarized by the following equation:where F is the physical system under investigation that relates the n subsurface model parameters m ∈ R N , with the observed data d obs . In non-linear geophysical inverse problems, F −1 is not well defined and is often solved as an optimization problem. These types of problems are ill posed and non-unique *

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“…Several orthonormal bases can be constructed, for example, using principal component analysis (Joliffe 2002), SVD (Tompkins et al 2011), discrete cosine transform (Jafarpour and McLaughlin 2009), wavelets transforms (Fernández Martínez et al 2010d; Kamoun, Fourati and Bouhlel 2004) and the spatial indicators or level sets (Fernández Martínez et al 2010f). Of these, the principal component analysis is typically based on the covariance of an ensemble of models and lacks separability and scalability to higher dimensional problems (see Tompkins et al 2011).…”

Section: Methodsmentioning

confidence: 99%

“…. , v p }: (Fernández Martínez et al 2010d;Kamoun, Fourati and Bouhlel 2004) and the spatial indicators or level sets (Fernández Martínez et al 2010f). Of these, the principal component analysis is typically based on the covariance of an ensemble of models and lacks separability and scalability to higher dimensional problems (see Tompkins et al 2011).…”

Section: Geologic Bases and Parameter Reductionmentioning

confidence: 99%

Marine electromagnetic inverse solution appraisal and uncertainty using model‐derived basis functions and sparse geometric sampling

Tompkins

Martínez

Fernández-Muñiz

2011

Geophysical Prospecting

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We summarize, for marine electromagnetic inverse problems, a newly developed inverse solution appraisal and non‐linear uncertainty estimation method based on parameter reduction techniques and efficient posterior model space sampling. This method uses model compression methods to decorrelate parameters in an inverse solution and represent all feasible posterior models as linear combinations of a small number of model‐derived basis vectors and corresponding coefficients. This allows us to reduce the posterior sampling problem by orders of magnitude. We further contract this reduced‐dimensional posterior space by confining all acceptable models to a set of bounds mapped from our original parameter space. As a final step to increase efficiency, we implement a geometric sampling scheme that we use to approximate our restricted posterior by generating feasible models on adaptive, optimally‐sparse grids. The sampled equi‐feasible models are accepted according to a data misfit threshold and constitute an optimally‐sparse representation of the restricted posterior model space. Although very efficient, our method imposes a bias in the posterior space by truncating the basis expansion during the model reduction step. To investigate this, we compare two types of fast and scalable bases, the discrete cosine transform and singular value decomposition. We demonstrate that while the choice of base does influence the type of models sampled and the model rejection rates, the posterior statistics are generally compatible between the methods providing confidence in the uncertainty estimations. For the marine electromagnetic problem, we show that a representative ensemble of equivalent inverse solutions can be generated for realistically‐sized inverse problems and that solution appraisal and uncertainty inference follow directly from ensemble statistics.

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Comparative Survey of the DCT and the Wavelet Transforms for Image Compression

Cited by 4 publications

References 25 publications

Compression of MR Images Using DWT by Comparing RGB and YCbCr Color Spaces

Compression of MR Images Using DWT by Comparing RGB and YCbCr Color Spaces

Regularized sparse‐grid geometric sampling for uncertainty analysis in non‐linear inverse problems

Marine electromagnetic inverse solution appraisal and uncertainty using model‐derived basis functions and sparse geometric sampling

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