Sub-pixel registration is a crucial step for applications such as super-resolution in remote sensing, motion compensation in magnetic resonance imaging, and nondestructive testing in manufacturing, to name a few. Rece...
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Sub-pixel registration is a crucial step for applications such as super-resolution in remote sensing, motion compensation in magnetic resonance imaging, and nondestructive testing in manufacturing, to name a few. Recently, these technologies have been trending towards wavelet-encoded imaging and sparse/compressive sensing. The former plays a crucial role in reducing imaging artifacts, while the latter significantly increases the acquisition speed. In view of these new emerging needs for applications of wavelet-encoded imaging, we propose a sub-pixel registration method that can achieve direct wavelet domain registration from a sparse set of coefficients. We make the following contributions: (i) We devise a method of decoupling scale, rotation, and translation parameters in the Haar wavelet domain, (ii) we derive explicit mathematical expressions that define in-band sub-pixel registration in terms of wavelet coefficients, (iii) using the derived expressions, we propose an approach to achieve in-band sub-pixel registration, avoiding back and forth transformations. (iv) Our solution remains highly accurate even when a sparse set of coefficients are used, which is due to localization of signals in a sparse set of wavelet coefficients. We demonstrate the accuracy of our method, and show that it outperforms the state of the art on simulated and real data, even when the data are sparse.
In recent years wavelets have been widely used for signal compression, image compression being a prime example, and for signal denoising. What makes wavelets such an attractive tool is their capability of representing...
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ISBN:
(纸本)0780362985
In recent years wavelets have been widely used for signal compression, image compression being a prime example, and for signal denoising. What makes wavelets such an attractive tool is their capability of representing both transient and stationary behaviors of a signal with few coefficients. In this paper we consider the problem of compressing and denoising a particular class of functions: piecewise polynomial signals. We show the limit of usual wavelet coders and present an alternative compression algorithm. The main innovation of the algorithm is that it tries to efficiently compress the significant coefficients of the wavelet decomposition rather then the zero coefficients as in usual coders. The proposed algorithm can potentially be extended to more general signals and represents an effective solution to problems like signal denoising and image compression.
Most digital signalprocessing methods have an underlying assumption of regularly-spaced data samples. However, many real-world data collection techniques generate data sets which are not sampled at evenly-spaced inte...
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ISBN:
(纸本)0819422134
Most digital signalprocessing methods have an underlying assumption of regularly-spaced data samples. However, many real-world data collection techniques generate data sets which are not sampled at evenly-spaced intervals, or which may have significant data dropout problems. Therefore, a method of interpolation is needed to model the signal on an even grid of arbitrary granularity. We propose the interpolation of nonuniformly sampled fields using a least- square fit of the data to a wavelet basis in a multiresolution setting.
14-bit or 16-bit pixel depth high dynamic-range images are acquired from visible band cameras and from infrared imaging devices which are more widely used nowadays. Usually, linear mapping is used to display these ima...
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ISBN:
(纸本)9781467355636;9781467355629
14-bit or 16-bit pixel depth high dynamic-range images are acquired from visible band cameras and from infrared imaging devices which are more widely used nowadays. Usually, linear mapping is used to display these images to operators. However, results of the researches done to map images into 0-255 range in recent years show that different techniques result in major differences at image perception and detail visibility. Successful compression of image dynamic range increases the operator awareness for surveillance systems and ensure more effective display of scene details to user. Besides, dynamic-range compression techniques effect the enhancement of the success rate of image target detection and tracking techniques. In this work, scene components are analyzed using wavelet coefficients and intensity distribution of scene components are extracted. Extracted intensity distribution is used to display scene components effectively.
The construction of smooth, orthogonal compactly supported wavelets is accomplished using fractal interpolation functions and splines. These give rise to multiwavelets. In the latter case piecewise polynomial wavelets...
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ISBN:
(纸本)0819416274;9780819416278
The construction of smooth, orthogonal compactly supported wavelets is accomplished using fractal interpolation functions and splines. These give rise to multiwavelets. In the latter case piecewise polynomial wavelets are exhibited using an intertwining multiresolution analysis.
We present a definition of wavelet-bicoherence based on wavelet-polyspectra. We propose a simple estimator for wavelet-bicoherence, and discuss its statistical properties. In particular it is shown that wavelet-bicohe...
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ISBN:
(纸本)0780370414
We present a definition of wavelet-bicoherence based on wavelet-polyspectra. We propose a simple estimator for wavelet-bicoherence, and discuss its statistical properties. In particular it is shown that wavelet-bicoherence estimates has a larger number of effective degrees of freedom than traditional Fourier-based bicoherence estimates. The proposed estimator is applied to detection of coherent couplings in rocket measurements from the ionospheric E-region. It is concluded that wavelet-bicoherence is a well suited toot for analysis of non-stationary mode coupling.
In this paper, we propose an image restoration algorithm based on state-of-the-art wavelet domain statistical models. We present an efficient method to estimate the model parameters from the observations, and solve th...
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ISBN:
(纸本)0819441929
In this paper, we propose an image restoration algorithm based on state-of-the-art wavelet domain statistical models. We present an efficient method to estimate the model parameters from the observations, and solve the restoration problem in orthonormal and translation-invariant (TI) wavelet domains. Substantial improvements over previous wavelet-based restoration methods are obtained. The use of a TI wavelet transform further enhances the restoration performance. We study the improvement from the viewpoint of Bayesian estimation theory and show that replacing an estimator with its TI version will reduce the expected risk if the signal and the degradation model are stationary.
The objective of Adaptive Optics is to achieve dynamic correction of severely aberrated systems. This effort will develop a novel adaptive optics approach based on wavelets. Distortions are imprinted on the wavefront ...
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ISBN:
(纸本)0819454915
The objective of Adaptive Optics is to achieve dynamic correction of severely aberrated systems. This effort will develop a novel adaptive optics approach based on wavelets. Distortions are imprinted on the wavefront in the form of a spatially varying phase field. A wavelet-based method is being developed to subtract out distortions to yield a fully corrected image. This method will be initially developed for laser systems but aims eventually to be used for adaptive optical systems for ground-based telescopes.
This paper investigates the relationship between the traditional wavelet (or matched filter) detector and the estimator correlator (EC) detector formulated in the wavelet domain. The EC detector is actually a weighted...
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ISBN:
(纸本)0819425915
This paper investigates the relationship between the traditional wavelet (or matched filter) detector and the estimator correlator (EC) detector formulated in the wavelet domain. The EC detector is actually a weighted wavelet detector, weighted by the scattering function that describes the medium and/or model. The wavelet detector is the optimum detector for point objects but it does not incorporate knowledge of the scattering environment. However, when imaging distributed objects, it is advantageous to take a priori information into account. The EC incorporates this information as a weight on the waveletimage and formulates an estimated spreading function which essentially achieves recombination of highlights and multipath energy. It can be shown that the EC reduces to the the wavelet detector when a point object is being imaged.
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