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Ashish Khare - One of the best experts on this subject based on the ideXlab platform.

  • Multilevel Analysis in Complex Wavelet Transform Domain for Signal Processing Applications
    2020
    Co-Authors: Ashish Khare, Uma Shanker Tiwary
    Abstract:

    Real valued Wavelets are used widely in signal processing applications. Although Complex valued Wavelets exists, but rarely used. Complex Wavelet transform provides important phase information of the signal and it is almost shift-invariant. Due to these added advantages it can be very much useful for signal processing applications. This paper explores various properties of Daubechies Complex Wavelet transform. It shows that the nature of the Complex Wavelet coefficients does not change at multiple levels. This property provides an opportunity to apply the same function for the signal represented at multiple levels. We have applied the soft-thresholding function for denoising and deblurring of 1D and 2D signals and shown that the result gets improved at multiple levels. We have proposed a Complex Wavelet based method for denoising of signals corrupted with signal dependent and signal independent noise as well as a restoration method for blurred signals corrupted with noise. The proposed method is adaptive as it uses a soft-threshold function based on the standard deviation, the absolute mean and the absolute median of Wavelet coefficients. The proposed threshold is level dependent as well. The effectiveness of the Complex Wavelet based signal restoration method has been tested and it was found that the performance of the proposed method is better than that of other similar type of methods that uses real valued Wavelets. The method can be easily extended for other applications, such as texture analysis, object tracking, registration, segmentation, etc.

  • Daubechies Complex Wavelet-Based Computer Vision Applications
    Research Developments in Biometrics and Video Processing Techniques, 2020
    Co-Authors: Manish Khare, Rajneesh Kumar Srivastava, Ashish Khare
    Abstract:

    Many methods for computer vision applications have been developed using Wavelet theory. Almost all of them are based on real-valued discrete Wavelet transform. This chapter introduces two computer vision applications, namely moving object segmentation and moving shadow detection and removal, using Daubechies Complex Wavelet transform. Daubechies Complex Wavelet transform has advantages over discrete Wavelet transform as it is approximately shift-invariant, has a better edge detection, and provides true phase information. Results after applying Daubechies Complex Wavelet transform on these two applications demonstrate that Daubechies Complex Wavelet transform-based methods provide better results than other real-valued Wavelet transform-based methods, and it also demonstrates that Daubechies Complex Wavelet transform has the potential to be applied to other computer vision applications.

  • Moving object segmentation in Daubechies Complex Wavelet domain
    Signal Image and Video Processing, 2015
    Co-Authors: Manish Khare, Rajneesh Kumar Srivastava, Ashish Khare
    Abstract:

    Motion segmentation is a crucial step in video analysis and is associated with a number of computer vision applications. This paper introduces a new method for segmentation of moving object which is based on double change detection technique applied on Daubechies Complex Wavelet coefficients of three consecutive frames. Daubechies Complex Wavelet transform for segmentation of moving object has been chosen as it is approximate shift invariant and has a better directional selectivity as compared to real valued Wavelet transform. Double change detection technique is used to obtain video object plane by inter-frame difference of three consecutive frames. Double change detection technique also provides automatic detection of appearance of new objects. The proposed method does not require any other parameter except Daubechies Complex Wavelet coefficients. Results of the proposed method for segmentation of moving objects are compared with results of other state-of-the-art methods in terms of visual performance and a number of quantitative performance metrics viz. Misclassification Penalty, Relative Foreground Area Measure, Pixel Classification Based Measure, Normalized Absolute Error, and Percentage of Correct Classification. The proposed method is found to have high degree of segmentation accuracy than the other state-of-the-art methods.

  • fusion of multimodal medical images using daubechies Complex Wavelet transform a multiresolution approach
    Information Fusion, 2014
    Co-Authors: Rajiv Singh, Ashish Khare
    Abstract:

    Multimodal medical image fusion is an important task for the retrieval of complementary information from medical images. Shift sensitivity, lack of phase information and poor directionality of real valued Wavelet transforms motivated us to use Complex Wavelet transform for fusion. We have used Daubechies Complex Wavelet transform (DCxWT) for image fusion which is approximately shift invariant and provides phase information. In the present work, we have proposed a new multimodal medical image fusion using DCxWT at multiple levels which is based on multiresolution principle. The proposed method fuses the Complex Wavelet coefficients of source images using maximum selection rule. Experiments have been performed over three different sets of multimodal medical images. The proposed fusion method is visually and quantitatively compared with Wavelet domain (Dual tree Complex Wavelet transform (DTCWT), Lifting Wavelet transform (LWT), MultiWavelet transform (MWT), Stationary Wavelet transform (SWT)) and spatial domain (Principal component analysis (PCA), linear and sharp) image fusion methods. The proposed method is further compared with Contourlet transform (CT) and Nonsubsampled contourlet transform (NSCT) based image fusion methods. For comparison of the proposed method, we have used five fusion metrics, namely entropy, edge strength, standard deviation, fusion factor and fusion symmetry. Comparison results prove that performance of the proposed fusion method is better than any of the above existing fusion methods. Robustness of the proposed method is tested against Gaussian, salt & pepper and speckle noise and the plots of fusion metrics for different noise cases established the superiority of the proposed fusion method.

  • Multimodal medical image fusion using daubechies Complex Wavelet transform
    2013 IEEE Conference on Information & Communication Technologies, 2013
    Co-Authors: Rajiv Singh, Ashish Khare
    Abstract:

    In the present work, we propose a new weighted fusion scheme using Daubechies Complex Wavelet transform (DCxWT). Shift sensitivity and lack of phase information in real valued Wavelet transforms motivated to use DCxWT for multimodal medical image fusion. It was experimentally found that shift invariance and phase information properties improve the performance of image fusion in Complex Wavelet domain. Therefore, we used DCxWT for fusion of multimodal medical images. To show the effectiveness of the proposed work, we have compared our method with existing DCxWT, dual tree Complex Wavelet transform (DTCWT), discrete Wavelet transform (DWT), non-sub contourlet transform (NSCT) and contourlet transform (CT) based fusion methods using edge strength and mutual information fusion metrics. Comparison results clearly show that the proposed fusion scheme with DCxWT outperforms existing DCxWT, DTCWT, DWT, NSCT and CT based fusion methods.

Ivan W. Selesnick - One of the best experts on this subject based on the ideXlab platform.

  • A Dual-Tree Rational-Dilation Complex Wavelet Transform
    IEEE Transactions on Signal Processing, 2011
    Co-Authors: Ilker Bayram, Ivan W. Selesnick
    Abstract:

    In this correspondence, we introduce a dual-tree rational-dilation Complex Wavelet transform for oscillatory signal processing. Like the short-time Fourier transform and the dyadic dual-tree Complex Wavelet transform, the introduced transform employs quadrature pairs of time-frequency atoms which allow to work with the analytic signal. The introduced Wavelet transform is a constant-Q transform, a property lacked by the short-time Fourier transform, which in turn makes the introduced transform more suitable for models that depend on scale. Also, the frequency resolution can be as high as desired, a property lacked by the dyadic dual-tree Complex Wavelet transform, which makes the introduced transform more suitable for processing oscillatory signals like speech, audio and various biomedical signals.

  • on the dual tree Complex Wavelet packet and m band transforms
    IEEE Transactions on Signal Processing, 2008
    Co-Authors: Ilker Bayram, Ivan W. Selesnick
    Abstract:

    The two-band discrete Wavelet transform (DWT) provides an octave-band analysis in the frequency domain, but this might not be ldquooptimalrdquo for a given signal. The discrete Wavelet packet transform (DWPT) provides a dictionary of bases over which one can search for an optimal representation (without constraining the analysis to an octave-band one) for the signal at hand. However, it is well known that both the DWT and the DWPT are shift-varying. Also, when these transforms are extended to 2-D and higher dimensions using tensor products, they do not provide a geometrically oriented analysis. The dual-tree Complex Wavelet transform , introduced by Kingsbury, is approximately shift-invariant and provides directional analysis in 2-D and higher dimensions. In this paper, we propose a method to implement a dual-tree Complex Wavelet packet transform , extending the as the DWPT extends the DWT. To find the best Complex Wavelet packet frame for a given signal, we adapt the basis selection algorithm by Coifman and Wickerhauser, providing a solution to the basis selection problem for the . Lastly, we show how to extend the two-band to an -band (provided that ) using the same method.

  • Complex Wavelet transforms with allpass filters
    Signal Processing, 2003
    Co-Authors: F C A Fernandes, Rutger L. C. Van Spaendonck, Ivan W. Selesnick, Sidney C Burrus
    Abstract:

    Complex discrete Wavelet transforms (DWT) have significant advantages over real Wavelet transforms for certain signal processing problems. Two approaches to the implementation of Complex Wavelet transforms have been proposed earlier. Both approaches require discrete-time allpass systems having approximately linear-phase and (fractional) delay. This paper compares the results when different allpass systems are used. In the earlier work, maximally flat delay allpass systems were used. In this paper, it is shown that an allpass system designed according to the minimax criterion yields improvements for the Complex DWT.

Zhong Zhang - One of the best experts on this subject based on the ideXlab platform.

  • Tight Wavelet Frame Using Complex Wavelet Designed in Free Shape on Frequency Domain
    2019 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR), 2019
    Co-Authors: Hiroshi Toda, Zhong Zhang
    Abstract:

    In this paper, we propose a construction method of a tight Wavelet frame using a Complex Wavelet designed in a free shape on the frequency domain. This method is divided into two parts. First, based on the designed Complex Wavelet, we construct an approximate tight Wavelet frame. Next, based on it, we construct a tight Wavelet frame with minor modification. Additionally, for example, we show the construction process of the tight Wavelet frame using the approximate Gabor Wavelet.

  • the design of Complex Wavelet packet transforms based on perfect translation invariance theorems
    International Journal of Wavelets Multiresolution and Information Processing, 2010
    Co-Authors: Hiroshi Toda, Zhong Zhang, Takashi Imamura
    Abstract:

    The useful theorems for achieving perfect translation invariance have already been proved, and based on these theorems, dual-tree Complex discrete Wavelet transforms with perfect translation invariance have been proposed. However, due to the complication of frequency divisions with Wavelet packets, it is difficult to design Complex Wavelet packet transforms with perfect translation invariance. In this paper, based on the aforementioned theorems, novel Complex Wavelet packet transforms are designed to achieve perfect translation invariance. These Complex Wavelet packet transforms are based on the Meyer Wavelet, which has the important characteristic of possessing a wide range of shapes. In this paper, two types of Complex Wavelet packet transforms are designed with the optimized Meyer Wavelet. One of them is based on a single Meyer Wavelet and the other is based on a number of different shapes of the Meyer Wavelets to create good localization of Wavelet packets.

  • Perfectly translation-invariant Complex Wavelet packet transforms
    2009 International Conference on Wavelet Analysis and Pattern Recognition, 2009
    Co-Authors: Hiroshi Toda, Zhong Zhang
    Abstract:

    The Complex discrete Wavelet transform having perfect translation invariance has already been proposed. However, due to complication of frequency divisions with Wavelet packets, it is difficult to design a Complex Wavelet packet transform having perfect translation invariance. In this paper, a useful theorem for achieving perfect translation invariance is proved, and a novel Complex Wavelet packet transform is designed to create this perfect translate invariance. This Complex Wavelet packet transform is based on a Meyer Wavelet, which has the important characteristic of having a wide range of shapes. Therefore, the Complex Wavelet packet transform having perfect translation invariance can be designed with the optimized shapes of the Meyer Wavelet. One of them is based on a single Meyer Wavelet and the other is based on a number of different shapes of the Meyer Wavelets to create good localization of Complex Wavelet packets.

  • Perfectly translation-invariant Complex Wavelet packet transforms
    2009 International Conference on Wavelet Analysis and Pattern Recognition, 2009
    Co-Authors: Hiroshi Toda, Zhong Zhang
    Abstract:

    The Complex discrete Wavelet transform having perfect translation invariance has already been proposed. However, due to complication of frequency divisions with Wavelet packets, it is difficult to design a Complex Wavelet packet transform having perfect translation invariance. In this paper, a useful theorem for achieving perfect translation invariance is proved, and a novel Complex Wavelet packet transform is disigned to create this perfect translate invariance. This Complex Wavelet packet transform is based on a Meyer Wavelet, which has the important characteristic of having a wide range of shapes. Therefore, the Complex Wavelet packet transform having perfect translation invariance can be designed with the optimized shapes of the Meyer Wavelet. One of them is based on a single Meyer Wavelet and the other is based on a number of different shapes of the Meyer Wavelets to create good localization of Complex Wavelet packets.

Josiane Zerubia - One of the best experts on this subject based on the ideXlab platform.

  • satellite image deblurring using Complex Wavelet packets
    International Journal of Computer Vision, 2003
    Co-Authors: Andre Jalobeanu, Laure Blancferaud, Josiane Zerubia
    Abstract:

    The deconvolution of blurred and noisy satellite images is an ill-posed inverse problem. Direct inversion leads to unacceptable noise amplification. Usually the problem is regularized during the inversion process. Recently, new approaches have been proposed, in which a rough deconvolution is followed by noise filtering in the Wavelet transform domain. Herein, we have developed this second solution, by thresholding the coefficients of a new Complex Wavelet packet transforms all the parameters are automatically estimated. The use of Complex Wavelet packets enables translational invariance and improves directional selectivity, while remaining of Complexity O(N). A new hybrid thresholding technique leads to high quality results, which exhibit both correctly restored textures and a high SNR in homogeneous areas. Compared to previous algorithms, the proposed method is faster, rotationally invariant and better takes into account the directions of the details and textures of the image, improving restoration. The images deconvolved in this way can be used as they are (the restoration step proposed here can be inserted directly in the acquisition chain), and they can also provide a starting point for an adaptive regularization method, enabling one to obtain sharper edges.

Uwe Kiencke - One of the best experts on this subject based on the ideXlab platform.

  • Analytic Complex Wavelet packets for speech enhancement
    2008 IEEE International Conference on Acoustics Speech and Signal Processing, 2008
    Co-Authors: Thomas Weickert, Claus Benjaminsen, Uwe Kiencke
    Abstract:

    In previous work, the authors found the lack of shift invariance of real Wavelet packets very disadvantageous for speech enhancement in the case of periodic noise. Therefore, this paper investigates the positive properties of the dual-tree Complex Wavelet transform (DTCWT). This transform is nearly shift invariant at moderate additional computational cost. However, the straightforward approach of extending the DTCWT to Wavelet packets by decomposing the high pass coefficients as well led to non-analytic basis functions. Because analytic basis functions were required for the desired properties, a filter swapping scheme was developed to preserve analyticity. This analytic Complex Wavelet packet transform showed improved denoising performance for the application of speech enhancement and promises improvements for other applications like general filtering and signal analysis.