## A Unified Superresolution Approach For Optical And Synthetic Aperture Radar Images (1998)

Citations: | 7 - 2 self |

### BibTeX

@TECHREPORT{Candocia98aunified,

author = {Frank M. Candocia},

title = {A Unified Superresolution Approach For Optical And Synthetic Aperture Radar Images},

institution = {},

year = {1998}

}

### OpenURL

### Abstract

......................................................................................................... viii CHAPTERS 1 INTRODUCTION ............................................................................... 1 2 AN APPROACH TO SUPERRESOLUTION ...................................... 5 2.1 Introducing the Problem .......................................................... 5 2.2 Comments and Observations ................................................... 9 2.3 Motivation and Description of the Superresolution Architecture ............................................................................ 15 3 EXISTING APPROACHES TO RECONSTRUCTION OF OPTICAL AND SYNTHETIC APERTURE RADAR IMAGES .......................... 22 3.1 Optical Image Interpolation with a Single Kernel ..................... 23 3.1.1 Common Kernels ............................................................ 24 3.1.2 Increasing the Sample Density ........................................ 28 3.1.3 Interpolation as Projec...

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Citation Context ...ociative memories considered here are essentially parametric mappings that optimally associate between a set of input exemplars { } N r r 1 = = x X and a set of desired exemplars { } N r r 1 = = d D [=-=Haykin, 1994-=-]. These sets of exemplars can be represented as the columns of a matrix, X and D respectively. The optimal association is typically defined in the least squares or mean squared sense. The process of ... |

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Citation Context ...A recent approach in the neural network literature that is used in modeling the probability density function (PDF) of a set of data conditioned on another set of data is the mixture of experts (MOE) [=-=Jacobs et al., 1991-=-; Jacobs and Jordan, 1991]. The 20 conditional PDF in the MOE is modeled as a mixture Gaussian distribution. This architecture can be used in modeling the transformation between low and high resolutio... |

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Citation Context ...ansform utilizes information across image scales to predict information at finer scales. This exploits the fact that evolution across resolution scales characterizes the local regularity of a signal [=-=Mallat and Zhong, 1992-=-]. The work of Martucci performs the interpolation completely in the DCT domain. Previous work by the author has shown that it is possible to use the DCT to implement digital filters [Martucci, 1993].... |

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Citation Context ...to create the appearance of a wave that is truly not present in the signal. These side lobes can be reduced using special window functions ] , [ 2 1 n n w where 1 ,..., 0 - = i i N n , ( 2 , 1 = i ) [=-=Harris, 1978-=-]. The reduction of these sidelobes comes at the expense of wider main lobe width of the window function thus reducing the ability to distinguish between closely spaced waves. Because spectral estimat... |

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Citation Context ... that are closest in 2D frequency. This resolution, or spectral resolution as it is also referred, is established in the frequency domain and is determined by the main lobe of the rectangular window [=-=Kay, 1988-=-; Stoica and Moses, 1997]. In SAR imaging, the superresolution of objects other than trihedral reflectors would benefit the automatic target detection and recognition (ATD/R) problem and it is the foc... |

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Citation Context ...o a vector quantization (VQ) of our input space based on minimizing an L 2 norm criteria. Techniques which have been developed to perform such VQ include the LGB [Linde, et al., 1980] and Neural Gas [=-=Martinez, et al., 1993-=-] algorithms as well as the topologically ordered Kohonen selforganizing feature map (SOFM) approach [Kohonen, 1990]. These approaches are considered to be unsupervised learning techniques which produ... |

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Citation Context ...8) results when representing the image samples in X as a vector rather than as a matrix. In this case, we draw from the 30 results of Kronecker products in linear algebra to establish our expression [=-=Graham, 1981]. The K-=-ronecker product B A�� of any two matrices A and B is the matrix obtained from the matrix A by replacing each entry a ij of A with the matrix a ij B. If A is any M �� N matrix and a j is its j... |

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Citation Context ...erresolution techniques can be grouped into parametric and nonparametric approaches. Many spectral estimation books exist which describe well the theory and techniques used in SAR imaging [Kay, 1988; =-=Marple, 1987-=-; Stoica and Moses, 1997]. The parametric approaches essentially perform signal detection and model parameter estimation. The nonparametric techniques are generally based on adaptive filtering schemes... |

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Citation Context ...erpolation has an extensive history and has been applied in a variety of fields. An early use of such procedures was to determine function values between mathematically tabulated data [Hamming, 1973; =-=Kreyszig, 1993-=-]. Interpolation has also found use in the design of car and ship bodies. More recently, interpolation has found applications in image coding and video compression [Lim, 1990; Cramer et al., 1996]. Th... |

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Citation Context ...ates each of them are the constraints imposed and/or assumptions made concerning the autocorrelation matrix of the observed samples. The first of these SAR imaging methods can be attributed to Capon [=-=Capon, 1969-=-]. This approach is typically referred to as Capon's method or the minimum variance (MV) method. This method imposes what is known as the unit boresight constraint. Here, the filter should pass a comp... |

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Citation Context ...lation based on variational and/or statistical principles presents a different view of interpolation than from those previously discussed [Karyiannis and Venetsanopoulos, 1991; Saul and Jordan, 1996; =-=Schultz and Stevenson, 1994-=-; Ruderman and Bialek, 1992]. Despite this, some interesting connections between these recent methodologies and some previously mentioned have been made. In fact, certain interpolation techniques prev... |

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Citation Context ...equivalent to constraining the interpolation kernel as follows k t t t t t m T t m T m m Z ( , ) , , ; , 1 2 1 2 1 1 1 2 2 2 1 2 1 0 0 0 = = = = = �� �� �� �� �� �� �� wher=-=e Z is the set of integers [Hamming, 1973-=-]. 2. Signal sample weighting diminishes as the distance from the point being interpolated increases. This property constrains the kernel's envelope to be a decreasing function as we move away from it... |

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Citation Context ...cal process - one for each model used. Examples of the existence of this first trait abound in images. It has recently been exploited to increase gains in compression schemes [Dony and Haykin, 1995a; =-=Kambhatla and Leen, 1997-=-]. The use of image compression has been popular for some time now and is evidenced by the widespread JPEG still image compression standard [Wallace, 1991] and PCA compression schemes [Dony and Haykin... |

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Citation Context ...) ( (2-2) where, by definition, t t t p p �� ) sin( ) ( sinc . We see that our basis functions are given by ) ( sinc ] [ n n k s T t t - = and the basis functions in this infinite set are orthogon=-=al [Woodward, 1964], t-=-hat is, ] [ ) ( sinc ) ( sinc m n T dt m n s T t T t s - d = - - ��s- . 7 The perfect reconstruction can be obtained if the sampling period satisfied T s T cs2 where c c T W = p 2 . For time signa... |

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Citation Context ... features for their interpolation [Zeng and Venetsanopoulos, 1992]. The median filter is known to remove outliers in the local distribution of pixels and to preserve certain types of image structure [=-=Huang and Tang, 1979-=-]. They attempt to exploit this property of the median filter to 41 produce more accurate interpolation results in edge regions. Fathima and Yegnanarayana have used a maximum entropy approach to inter... |

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Citation Context ...losest in 2D frequency. This resolution, or spectral resolution as it is also referred, is established in the frequency domain and is determined by the main lobe of the rectangular window [Kay, 1988; =-=Stoica and Moses, 1997-=-]. In SAR imaging, the superresolution of objects other than trihedral reflectors would benefit the automatic target detection and recognition (ATD/R) problem and it is the focus of the superresolutio... |

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Citation Context ...erresolution methodology. Two gating network structures are reported in the literature: a single layer gating network [Jacobs et al., 1991; Jacobs and Jordan, 1991] and a hierarchical gating network [=-=Jordan and Jacobs, 1992, 1994]. B-=-oth 101 of these structures model P(c|x) as previously discussed but the hierarchical gating structure provides a greater flexibility into how the input space of x is "soft" segmented. The g... |

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Citation Context ...letely represent our signal [Vetterli and Kovacevic, 1995]. To this end, one important result regarding the perfect reconstruction of a signal from its samples comes from the Shannon sampling theory [=-=Marks, 1991-=-; Oppenheim and Schafer, 1989]. In this theory, the original signal can theoretically be reconstructed from its samples provided certain conditions regarding the signal and its samples are met - irres... |

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Citation Context ... detail areas in images most often have a definite geometric structure or pattern, such as in edge regions [Lee and Paik, 1993; Algazi et al., 1991; Bayrakeri and Mersereau, 1995; Marsi et al., 1996; =-=Jensen and Anastassiou, 1995-=-]. In such cases, interpolation in the low frequency direction (along the edge) is much better than interpolation in the high frequency direction (across the edge). Thus, a directional interpolation s... |

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Citation Context ... and Zhong, 1992]. The work of Martucci performs the interpolation completely in the DCT domain. Previous work by the author has shown that it is possible to use the DCT to implement digital filters [=-=Martucci, 1993-=-]. As such, all spatial domain filtering is equivalently performed in the DCT domain. Shinbori and Takagi use an iterative application of the Gerchberg-Papoulis (GP) algorithm with the DCT to obtain a... |

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Citation Context ...the neural network literature that is used in modeling the probability density function (PDF) of a set of data conditioned on another set of data is the mixture of experts (MOE) [Jacobs et al., 1991; =-=Jacobs and Jordan, 1991-=-]. The 20 conditional PDF in the MOE is modeled as a mixture Gaussian distribution. This architecture can be used in modeling the transformation between low and high resolution neighborhoods of images... |

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Citation Context ...he mean of each statistical process - one for each model used. Examples of the existence of this first trait abound in images. It has recently been exploited to increase gains in compression schemes [=-=Dony and Haykin, 1995-=-a; Kambhatla and Leen, 1997]. The use of image compression has been popular for some time now and is evidenced by the widespread JPEG still image compression standard [Wallace, 1991] and PCA compressi... |

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Citation Context ...he mean of each statistical process - one for each model used. Examples of the existence of this first trait abound in images. It has recently been exploited to increase gains in compression schemes [=-=Dony and Haykin, 1995-=-a; Kambhatla and Leen, 1997]. The use of image compression has been popular for some time now and is evidenced by the widespread JPEG still image compression standard [Wallace, 1991] and PCA compressi... |

34 | Reconstruction of a highresolution image by simultaneous matching, restoration, and interpolation of low-resolution images
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Citation Context ...m as an ML problem which is solved by the expectation maximization (EM) algorithm. By exploiting the structure of the matrices involved, the problem can be worked on in the discrete frequency domain [=-=Tom and Katsaggelos, 1995-=-]. Typically, multiple displaced versions of a single image are not available for interpolation. For a video sequence, however, adjacent temporal frames tend 42 to satisfy this assumption particularly... |

31 | An adaptive filtering approach to spectral estimation and SAR imaging - Li, Stoica |

27 |
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Citation Context ... presented as categorically listed. Directional interpolation techniques recognize that high detail areas in images most often have a definite geometric structure or pattern, such as in edge regions [=-=Lee and Paik, 1993-=-; Algazi et al., 1991; Bayrakeri and Mersereau, 1995; Marsi et al., 1996; Jensen and Anastassiou, 1995]. In such cases, interpolation in the low frequency direction (along the edge) is much better tha... |

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Citation Context ... [Koltracht et al., 1996] has focused on using the discrete cosine transform (DCT) [Martucci, 1995; Shinbori and Takagi, 1994; Hong et al., 1996] and the wavelet transform [Keshavmurthy et al., 1996; =-=Chang et al., 1995-=-]. Work involving the wavelet transform utilizes information across image scales to predict information at finer scales. This exploits the fact that evolution across resolution scales characterizes th... |

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Citation Context ...nce D is defined correspondingly as [ ] ] [ ] [ 2 ] [ ) ( 2 2 2 2 v uv u v u E E E E D + - = - = where E[��] denotes the statistical expectation operator. We will make use of the Schwartz inequali=-=ty [Helstrom, 1991-=-] shortly. For vectors, this inequality is given by ( ) 2 u v u uv v T T T and for expected values of random variables it is ( ) . ] [ ] [ ] [ 2 2 2 v u uv E E EsIn an ordinary vector space, the trian... |

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Citation Context ...n by Parker et al. [1983]. There have been recent studies into the development of the theory of interpolating kernels [Lucke, 1993; Lanzavecchia and Bellon, 1994, 1995; Schaum, 1993; Appledorn, 1996; =-=Unser et al., 1992; Knoll, 1-=-991]. These works focus on the developing of an "optimal" single interpolation kernel as a substitute for the sinc kernel. The kernels to develop are local. The assumption made in these work... |

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Citation Context ...eturn grid. This is particularly true for inverse SAR and spotlight mode SAR data collection where a typical grid consists of radially equispaced samples swept out through several angular increments [=-=Odendaal et al., 1994-=-; Mensa, 1991]. As such, the accuracy with which frequency information from the imaged scene can be produced is reduced. 10 In the practical sampling of optical images, the issue concerning quantizati... |

17 |
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Citation Context ...nt to be interpolated. The use of orthogonal transforms for interpolation [Koltracht et al., 1996] has focused on using the discrete cosine transform (DCT) [Martucci, 1995; Shinbori and Takagi, 1994; =-=Hong et al., 1996-=-] and the wavelet transform [Keshavmurthy et al., 1996; Chang et al., 1995]. Work involving the wavelet transform utilizes information across image scales to predict information at finer scales. This ... |

13 |
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Citation Context ...rically listed. Directional interpolation techniques recognize that high detail areas in images most often have a definite geometric structure or pattern, such as in edge regions [Lee and Paik, 1993; =-=Algazi et al., 1991-=-; Bayrakeri and Mersereau, 1995; Marsi et al., 1996; Jensen and Anastassiou, 1995]. In such cases, interpolation in the low frequency direction (along the edge) is much better than interpolation in th... |

13 |
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Citation Context ... kernels for interpolation analyze local image statistics in order to determine an appropriate interpolation kernel for the region under consideration [Wang and Mitra, 1988; Winans and Walowit, 1992; =-=Darwish and Bedair, 1996-=-; Mahmoodi 1993]. The choice of kernels are typically ad hoc and typically two to three classic interpolation kernels are employed by these algorithms. The actual interpolation kernel used in each of ... |

13 |
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(Show Context)
Citation Context ... the 2��2 and the 4��4 block around the point to be interpolated. The use of orthogonal transforms for interpolation [Koltracht et al., 1996] has focused on using the discrete cosine transform=-= (DCT) [Martucci, 1995-=-; Shinbori and Takagi, 1994; Hong et al., 1996] and the wavelet transform [Keshavmurthy et al., 1996; Chang et al., 1995]. Work involving the wavelet transform utilizes information across image scales... |

12 |
A New Method for Directional Image Interpolation
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(Show Context)
Citation Context ...tional interpolation techniques recognize that high detail areas in images most often have a definite geometric structure or pattern, such as in edge regions [Lee and Paik, 1993; Algazi et al., 1991; =-=Bayrakeri and Mersereau, 1995-=-; Marsi et al., 1996; Jensen and Anastassiou, 1995]. In such cases, interpolation in the low frequency direction (along the edge) is much better than interpolation in the high frequency direction (acr... |

12 |
The JPEG Still Picture Compression
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(Show Context)
Citation Context ...n schemes [Dony and Haykin, 1995a; Kambhatla and Leen, 1997]. The use of image compression has been popular for some time now and is evidenced by the widespread JPEG still image compression standard [=-=Wallace, 1991-=-] and PCA compression schemes [Dony and Haykin, 1995b]. The standard schemes for lossy image compression are based around the highly redundant information generally present in small image blocks which... |

10 |
Principles of oversampling A/D conversion
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Citation Context ...llis, 1987]. It is known that oversampling can be utilized in easing the constraints on the interpolation function and for the recovery of the original signal to highly acceptable levels of accuracy [=-=Hauser, 1991-=-]. This is evidenced by the compact digital audio technology used today. The interpolation work that is particular to images used the aforementioned polynomials a great deal up into the early 1980s. T... |

9 |
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Citation Context ...ng, 1973; Kreyszig, 1993]. Interpolation has also found use in the design of car and ship bodies. More recently, interpolation has found applications in image coding and video compression [Lim, 1990; =-=Cramer et al., 1996]. The obj-=-ect of classical interpolation is to find polynomials that fit "well" through sample points in the data set. These polynomials generally fall into one of two categories: unconstrained and co... |

9 | Image interpolation based on variational principles - Karayiannis, Venetsanopoulos - 1991 |

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Citation Context ...nce present in SAR images. We wish to do this in a manner that does not eliminate its effects. This is because the background in a SAR image is used in the automatic detection of targets by computer [=-=Kreithen et al., 1993-=-]. The background clutter here is modeled as zero-mean complex Gaussian noise in the phase history. This corresponds well with the phase history of background chips from the MSTAR data set which we wo... |

9 |
Theory and design of local interpolators
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Citation Context ...e interpolation methods is given by Parker et al. [1983]. There have been recent studies into the development of the theory of interpolating kernels [Lucke, 1993; Lanzavecchia and Bellon, 1994, 1995; =-=Schaum, 1993; Appledor-=-n, 1996; Unser et al., 1992; Knoll, 1991]. These works focus on the developing of an "optimal" single interpolation kernel as a substitute for the sinc kernel. The kernels to develop are loc... |