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19
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 82 (13 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 15 (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 ...
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.
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 9 (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...
Featurepreserving regularization method for complexvalued inverse problems with application to . . .
, 2006
"... ..."
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 produces o ..."
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Cited by 2 (1 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.
Efficient image reconstruction techniques for a multiplereceiver synthetic aperture sonar
, 2001
"... Christchurch, New Zealand. Fast and efficient imaging techniques have been developed for reconstructing data from the singlereceiver synthetic aperture sonar (SAS). Therefore, it is advantageous to be able to combine multiplereceiver SAS data into the singlereceiver data equivalent to employ thes ..."
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Cited by 1 (0 self)
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Christchurch, New Zealand. Fast and efficient imaging techniques have been developed for reconstructing data from the singlereceiver synthetic aperture sonar (SAS). Therefore, it is advantageous to be able to combine multiplereceiver SAS data into the singlereceiver data equivalent to employ these existing algorithms. In this thesis, a method is developed for combining the data efficiently. This method can be used with SAS systems containing any number of hydrophones arbitrarily located in a linear array and with the imaging platform travelling at any velocity. Motion errors resulting from the towed platform deviating from its straight path need to be determined and compensated accordingly. Sway and yaw are the primary motion errors of concern in low glancing angle sidelooking sonar, since they are the major cause of image errors and artifacts in the reconstructions. Algorithms for estimating both sway and yaw are presented based on prominent points. These have shown to work well in simulations.
Holographic Image Representations: the Fourier Transform Method
 in ICIAP'97 Int. Conf. on Image Analysis and Processing
, 1997
"... We discuss holographic image representations. Arbitrary portions of a holographic representation enable reconstruction of the whole image, with distortions that decrease gradually with the increase of the size of the portions available. Holographic representations enable progressive refinement in im ..."
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Cited by 1 (1 self)
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We discuss holographic image representations. Arbitrary portions of a holographic representation enable reconstruction of the whole image, with distortions that decrease gradually with the increase of 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.
Signal Processing Issues In Synthetic Aperture Radar And Computer Tomography
, 1998
"... This paper also proposed another reconstruction method based on a direct approximation of the Fourier inversion formula using a twodimensional (2D) trapezoidal rule. In addition, the possibility of reconstruction from a concentricsquares raster was discussed. Numerous simple interpolators have bee ..."
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Cited by 1 (0 self)
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This paper also proposed another reconstruction method based on a direct approximation of the Fourier inversion formula using a twodimensional (2D) trapezoidal rule. In addition, the possibility of reconstruction from a concentricsquares raster was discussed. Numerous simple interpolators have been tried in DF reconstruction with the results compared with CBP [33]. In [34] and [35], the concept of angular bandlimiting was used to interpolate the polar data onto a Cartesian grid. In [36], a DF reconstruction using bilinear interpolation for diffraction tomography provided image quality that was comparable to that produced by the CBP algorithm. Very good reconstruction quality was obtained in [37] and [38] using a spline interpolator, or a hybrid type of spline interpolator. The notion of "gridding" was introduced in [39] as a method of obtaining optimal inversion of Fourier data. An optimal gridding function was proposed, and successful results were obtained when applied to the tomographic reconstruction problem. In [40], several different gridding functions were tried for DF reconstruction, and the performances were compared. In [41, 42], the linogram reconstruction method was proposed as a form of DF reconstruction. The data collection grid in the linogram method is the same as in the concentricsquares sampling scheme. The inversion of the Fourier data in [41, 42] was accomplished by first applying the chirpz transform in one direction and then computing FFTs in the other direction. In CT, many of these attempts at DF reconstruction have given a poorer result than the CBP algorithm, due to the error incurred in the process of the polartoCartesian interpolation. The attraction of DF reconstruction, however, is that it is thought to require less computation than ...
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 1 (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...