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24
Nonuniform Fast Fourier Transforms Using MinMax Interpolation
 IEEE Trans. Signal Process
, 2003
"... The FFT is used widely in signal processing for efficient computation of the Fourier transform (FT) of finitelength signals over a set of uniformlyspaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e.,a nonuniform FT . Several pap ..."
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Cited by 104 (16 self)
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The FFT is used widely in signal processing for efficient computation of the Fourier transform (FT) of finitelength signals over a set of uniformlyspaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e.,a nonuniform FT . Several papers have described fast approximations for the nonuniform FT based on interpolating an oversampled FFT. This paper presents an interpolation method for the nonuniform FT that is optimal in the minmax sense of minimizing the worstcase approximation error over all signals of unit norm. The proposed method easily generalizes to multidimensional signals. Numerical results show that the minmax approach provides substantially lower approximation errors than conventional interpolation methods. The minmax criterion is also useful for optimizing the parameters of interpolation kernels such as the KaiserBessel function.
Line And Boundary Detection In Speckle Images
 IEEE Trans. Image Processing
, 1997
"... This paper considers the problem of detecting lines in speckle imagery, such as that produced by synthetic aperture radar or ultrasound techniques. Using the physical principles which account for the speckle phenomenon, we derive the optimal detector for lines in fully developed speckle, and we comp ..."
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Cited by 18 (0 self)
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This paper considers the problem of detecting lines in speckle imagery, such as that produced by synthetic aperture radar or ultrasound techniques. Using the physical principles which account for the speckle phenomenon, we derive the optimal detector for lines in fully developed speckle, and we compare the optimal detector to several suboptimal detection rules which are more computationally efficient. We show that when the noise is uncorrelated, a very simple suboptimal detection rule is nearly optimal, and that even in colored speckle, a related class of detectors can approach optimal performance. Finally, we also discuss the application of this technique to medical ultrasonic images, where the detection of tissue boundaries is considered as a problem of line detection. 1 Introduction The problem of detecting linear features in an image is of interest because these features may contain important information. For example, in synthetic aperture radar (SAR) scenery, it may be known a ...
DirectFourier Reconstruction In Tomography And Synthetic Aperture Radar
 Intl. J. Imaging Sys. and Tech
, 1998
"... We investigate the use of directFourier (DF) image reconstruction in computerized tomography and synthetic aperture radar (SAR). One of our aims is to determine why the convolutionbackprojection (CBP) method is favored over DF methods in tomography, while DF methods are virtually always used in SAR ..."
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Cited by 10 (0 self)
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We investigate the use of directFourier (DF) image reconstruction in computerized tomography and synthetic aperture radar (SAR). One of our aims is to determine why the convolutionbackprojection (CBP) method is favored over DF methods in tomography, while DF methods are virtually always used in SAR. We show that the CBP algorithm is equivalent to DF reconstruction using a Jacobianweighted 2D periodic sinckernel interpolator. This interpolation is not optimal in any sense, which suggests that DF algorithms utilizing optimal interpolators may surpass CBP in image quality. We consider use of two types of DF interpolation: a windowed sinc kernel, and the leastsquares optimal Yen interpolator. Simulations show that reconstructions using the Yen interpolator do not possess the expected visual quality, because of regularization needed to preserve numerical stability. Next, we show that with a concentricsquares sampling scheme, DF interpolation can be performed accurately and efficiently...
Holographic representations of images
 IEEE Transactions on Image Processing
, 1998
"... Abstract — We discuss a new type of holographic image representations that have advantages in a “distributed ” world. We call these representations holographic. Arbitrary portions of a holographic representation enable reconstruction of the whole image, with distortions that decrease gradually with ..."
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Cited by 9 (4 self)
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Abstract — We discuss a new type of holographic image representations that have advantages in a “distributed ” world. We call these representations holographic. Arbitrary portions of a holographic representation enable reconstruction of the whole image, with distortions that decrease gradually with the increase in the size of the portions available. Holographic representations enable progressive refinement in image communication or retrieval tasks, with no restrictions on the order in which the data fragments (sections of the representation) are accessed or become available. Index Terms—Holographic representations, progressive refinement, pseudorandom uniform samplings, random phase Fourier transforms. I.
Featurepreserving regularization method for complexvalued inverse problems with application to . . .
, 2006
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Deconvolution Techniques for Passive Radar Imaging
"... Forming images of aircraft using passive radar systems that exploit "illuminators of opportunity," such as commercial television and FM radio systems, involves reconstructing an image from sparse samples of its Fourier transform. For a given flight path, a single receivertransmitter pair ..."
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Cited by 4 (2 self)
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Forming images of aircraft using passive radar systems that exploit "illuminators of opportunity," such as commercial television and FM radio systems, involves reconstructing an image from sparse samples of its Fourier transform. For a given flight path, a single receivertransmitter pair produces one arc of data in Fourier space. Since the resulting Fourier sampling patterns bear a superficial resemblance to those found in radio astronomy, we consider using deconvolution techniques borrowed from radio astronomy, namely the CLEAN algorithm, to form images from passive radar data.
Recognition Performance From Synthetic Aperture Radar Imagery Subject To System Resource Constraints
, 2001
"... The problem of automatic target recognition (ATR) can stated be as the problem of inferring, from the output of one or more sensors directed at a scene, the classes to which objects in the scene belong and the properties of those objects such as subclass, pose, and states of articulation. We consi ..."
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Cited by 3 (1 self)
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The problem of automatic target recognition (ATR) can stated be as the problem of inferring, from the output of one or more sensors directed at a scene, the classes to which objects in the scene belong and the properties of those objects such as subclass, pose, and states of articulation. We consider the specific problem of ATR based upon synthetic aperture radar (SAR) imagery, though the principles employed are applicable in the wider context of object recognition. Approaches to automated recognition are developed in the context of a communicationbased model. The recognition system is viewed as a recipient of information from two sources: a scene containing the object to be recognized and a database characterizing the objects to be recognized. The overall accuracy of the system is dependent upon the properties of the scene and sensor, the accuracy of the imaging model on which the system is based, and the accuracy of approximations made for the purpose of system implementation. These last two items have a direct impact on the computational resource requirements of a recognition system. The accuracy of a system is thus directly related to the available resources, such as the number of processor cycles used, mass storage requirements, network bandwidth utilization, elapsed time, etc. This relationship can be characterized by an accuracyconsumption curve which is useful for comparing alternate approaches to recognition and for exploring the space of system design possibilities. A statistical hypothesis testing approach is followed and several variants of four probab...
MCA: A Multichannel Approach to SAR Autofocus
"... We present a new noniterative approach to synthetic aperture radar (SAR) autofocus, termed the MultiChannel Autofocus (MCA) algorithm. The key in the approach is to exploit the multichannel redundancy of the defocusing operation to create a linear subspace, where the unknown perfectlyfocused imag ..."
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Cited by 3 (2 self)
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We present a new noniterative approach to synthetic aperture radar (SAR) autofocus, termed the MultiChannel Autofocus (MCA) algorithm. The key in the approach is to exploit the multichannel redundancy of the defocusing operation to create a linear subspace, where the unknown perfectlyfocused image resides, expressed in terms of a known basis formed from the given defocused image. A unique solution for the perfectlyfocused image is then directly determined through a linear algebraic formulation by invoking an additional image support condition. The MCA approach is found to be computationally efficient and robust, and does not require prior assumptions about the SAR scene used in existing methods. In addition, the vectorspace formulation of MCA allows sharpness metric optimization to be easily incorporated within the restoration framework as a regularization term. We present experimental results characterizing the performance of MCA in comparison with conventional autofocus methods, and discuss the practical implementation of the technique.
1SYNTHETIC APERTURE RADAR AUTOFOCUS VIA SEMIDEFINITE RELAXATION
"... imaging amounts to estimating unknown phase errors caused by unknown platform or target motion, or a time or spatiallyvarying transmission medium. At the heart of three stateoftheart autofocus algorithms, namely Phase Gradient Autofocus, Multichannel Autofocus (MCA) and Fourierdomain Multichan ..."
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imaging amounts to estimating unknown phase errors caused by unknown platform or target motion, or a time or spatiallyvarying transmission medium. At the heart of three stateoftheart autofocus algorithms, namely Phase Gradient Autofocus, Multichannel Autofocus (MCA) and Fourierdomain Multichannel Autofocus (FMCA), is the solution of a constant modulus quadratic program (CMQP). Currently, these algorithms solve CMQP by using an eigenvalue relaxation approach. We propose an alternative relaxation approach based on semidefinite programming, which has recently attracted considerable attention in other signal processing problems. Experimental results show that our proposed methods provide promising performance improvements for MCA and FMCA through an increase in computational complexity. Index Terms—Synthetic aperture radar, Autofocus, Multichan
Holographic image representations: the Fourier transform method
 in ICIAP'97 Int. Conf. on Image Analysis and Processing
, 1997
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