Reconstruction of 2-D bandlimited discrete signals from nonuniform samples

Kim, S.P.; Bose, N.K.

doi:10.1049/ip-f-2.1990.0030

Cited by 42 publications

(19 citation statements)

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“…The problem is reminiscent to that faced in earlier works on super-resolution. For example, in the early DFT-based procedure (Kim and Bose, 1990), interpolation and noise filtering were simultaneously implemented and it was later shown that blur distortions in the input images can be compensated with regularization during reconstruction (Kim and Su, 1993). In recent super-resolution work, multiframe blur identification followed by deblurring has been done in a separate module from the super-resolution and noise filtering modules (Lertrattanapanich and Bose, 2002).…”

Section: Discussionmentioning

confidence: 99%

“…In the super-resolution problem, after registering all samples in LR images into a HR grid (sampling lattice), it is possible that two samples or more are either transformed to the same location or assumed to be the same because of machine imprecision. In some super-resolution algorithms, certain irregular sampling structures in a HR grid (sampling lattice) that can lead to a singular problem were identified by Kim and Bose (1990). Therefore, here also, the LR frames that give rise to such singular sampling structures are detected and eliminated before the superresolution algorithm is implemented.…”

Section: Preprocessing Process For Super-resolution Algorithmmentioning

confidence: 99%

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A second‐generation wavelet framework for super‐resolution with noise filtering

Bose

Chappalli

2004

Int J Imaging Syst Tech

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ABSTRACT:The use of second-generation wavelets to attain superresolution with noise filtering is described for a captured sequence of low-resolution frames without any assumptions on grid (sampling lattice) structure. The approach is based on 2D methods. The procedure allows the incorporation of the more general projective camera motion model into the framework, instead of only displacement and rotational models. Several simulations that compare the implementations of the algorithm presented here with other related approaches help illustrate the suitability of SGWs (coupled with hard or soft thresholding) in the task of image sequence superresolution with simultaneous noise filtering.

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Section: Discussionmentioning

confidence: 99%

Section: Preprocessing Process For Super-resolution Algorithmmentioning

confidence: 99%

A second‐generation wavelet framework for super‐resolution with noise filtering

Bose

Chappalli

2004

Int J Imaging Syst Tech

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“…But interpolation is usually not lossless. In [15], the authors proposed a data interpolation algorithm which could accurately obtain uniformly spaced data from the available arbitrarily distributed data samples within the same data range. The principle of this method is based on the independency between the data in the spatial domain and frequency domain, i.e., even though data samples f x and f y are arbitrarily distributed, x i and y j can be chosen to be uniformly spaced during the Fourier Transform.…”

Section: A Fusion Based On the Matrix Fourier Transformmentioning

confidence: 99%

Fusion of multiple-look synthetic aperture radar images at data and image levels

Narayanan

Papson

2008

2008 5th International Conference on Electrical Engineering, Computing Science and Automatic Control

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Synthetic aperture radar (SAR) and inverse synthetic aperture radar (ISAR) have proven capabilities for non-cooperative target recognition (NCTR) applications. Multiple looks of the same target (at different aspect angles, frequencies, etc.) can be exploited to enhance target recognition by fusing the information from each look. Such fusion can be performed at the raw data level or at the processed image level depending on what is available. At the data level, physics based image fusion techniques can be developed by processing the raw data collected from multiple inverse synthetic aperture radar (ISAR) sensors, even if these individual images are at different resolutions. The technique maps multiple data sets collected by multiple radars with different system parameters on to the same spatial-frequency space. The composite image can be reconstructed using the inverse 2-D Fourier Transform over the separated multiple integration areas. An algorithm called the Matrix Fourier Transform (MFT) is proposed to realize such a complicated integral. At the image level, a persistence framework can be used to enhance target features in large, aspect-varying datasets. The model focuses on cases containing rich aspect data from a single depression angle. The goal is to replace the data's intrinsic viewing geometry dependencies with target-specific dependencies. Both direct mapping functions and cost functions are presented for data transformation. An intensity-only mapping function is realized to illustrate the persistence model in terms of a canonical example, visualization, and classification.

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“…Their objective is to construct a high-resolution image from a registered sequence of undersampled, noisy and blurred frames, displaced horizontally and vertically from each other (sufficient for LANDSAT type imaging). The attainment of image superresolution was based on the feasibility of reconstruction of two-dimensional bandlimited signals from nonuniform samples [23] arising from frames generated by microscanning, i.e., subpixel shifts between successive frames, each of which provides a unique snapshot of a stationary scene. Kim and Su [24] incorporated explicitly the deblurring computation into the high resolution image reconstruction process since separate deblurring of input frames would introduce the undesirable phase and high wavenumber distortions of those frames.…”

Section: Review Of Superresolution Image Reconstructionmentioning

confidence: 99%

Superresolution image reconstruction using fast inpainting algorithms

Chan

Yau

et al. 2007

Applied and Computational Harmonic Analysis

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The main aim of this paper is to employ the total variation (TV) inpainting model to superresolution imaging problems. We focus on the problem of reconstructing a high-resolution image from several decimated, blurred and noisy low-resolution versions of the high-resolution image. We propose a general framework for multiple shifted and multiple blurred low-resolution image frames which subsumes several well-known superresolution models. Moreover, our framework allows an arbitrary pattern of missing pixels and in particular missing frames. The proposed model combines the TV inpainting model with the framework to formulate the superresolution image reconstruction problem as an optimization problem. A distinct feature of our model is that in regions without missing pixels, the reconstruction process is regularized by TV minimization whereas in regions with missing pixels or missing frames, they are reconstructed automatically by means of TV inpainting. A fast algorithm based on fixed-point iterations and preconditioning techniques is investigated to solve the associated Euler-Lagrange equations. Experimental results are given to show that the proposed TV superresolution imaging model is effective and the proposed algorithm is efficient.

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Reconstruction of 2-D bandlimited discrete signals from nonuniform samples

Cited by 42 publications

References 1 publication

A second‐generation wavelet framework for super‐resolution with noise filtering

A second‐generation wavelet framework for super‐resolution with noise filtering

Fusion of multiple-look synthetic aperture radar images at data and image levels

Superresolution image reconstruction using fast inpainting algorithms

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