Improved resolution from subpixel shifted pictures

Ur, Hanoch; Groß, Daniel

doi:10.1016/1049-9652(92)90065-6

Cited by 244 publications

(132 citation statements)

References 7 publications

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“…We associate with a criterion (7) which we call a quadratic criterion. Conversely, given a quadratic criterion , the associated bilinear form can be obtained as (8) The square-root is a semi-norm, i.e., it satisfies the triangular inequality and semi-linearity . Unlike for a norm, there might be more than one satisfying .…”

Section: Bilinear Formsmentioning

confidence: 99%

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Generalized sampling: a variational approach .I. Theory

Kybic

Blu

Unser

2002

IEEE Trans. Signal Process.

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Abstract-We consider the problem of reconstructing a multidimensional vector function f in : from a finite set of linear measures. These can be irregularly sampled responses of several linear filters. Traditional approaches reconstruct in an a priori given space, e.g., the space of bandlimited functions. Instead, we have chosen to specify a reconstruction that is optimal in the sense of a quadratic plausibility criterion . First, we present the solution of the generalized interpolation problem. Later, we also consider the approximation problem, and we show that both lead to the same class of solutions.Imposing generally desirable properties on the reconstruction largely limits the choice of the criterion . Linearity leads to a quadratic criterion based on bilinear forms. Specifically, we show that the requirements of translation, rotation, and scale-invariance restrict the form of the criterion to essentially a one-parameter family. We show that the solution can be obtained as a linear combination of generating functions. We provide analytical techniques to find these functions and the solution itself. Practical implementation issues and examples of applications are treated in a companion paper.

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Section: Bilinear Formsmentioning

confidence: 99%

“…Papoulis' theory has been extended further to multidimensional [4] ( ) and vector [5] ( ) bandlimited functions . Recent applications of generalized sampling include, among others, deinterlacing [6], [7], and super-resolution [8], [9] reconstruction.…”

mentioning

confidence: 99%

Generalized sampling: a variational approach .I. Theory

Kybic

Blu

Unser

2002

IEEE Trans. Signal Process.

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“…In [22] a method based on multi-channel sampling theorem is introduced. However, this method is implemented in the spatial domain, but fundamentally, this method is a method in the frequency-domain, because transmission characteristics of the Fourier transform of the original image is used to model the translation.…”

Section: Multichannel Sampling Theorem Methodsmentioning

confidence: 99%

A Survey on Super-Resolution Methods for Image Reconstruction

Karimi¹,

Kangarloo²,

Javadi³

2014

IJCA

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Today, in many applications of Machine vision, image SuperResolution is preferred. Super-Resolution is estimation of a high-resolution image from an image or several low resolution images. Popular techniques in the field of enhancing images can be used to remove noise or blurring. In this paper, an overview of super resolution methods has been presented. Types of resolution methods have been used so far can be divided into three groups as frequency-domain methods, spatial domain methods and techniques can be classified as the wavelet domain. Super-resolution methods in different domains have different characteristics and comparison between these methods is usually done using a special index in one domain. In this paper, we will introduce these indexes and review best techniques used in all three domains.

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“…Therefore, to overcome their weaknesses, many kinds of spatial domain approaches have been developed. For instance, Ur et al [9] proposed a non-uniform interpolation by exploiting the structural information in the spatial domain; Irani et al [10] proposed an iterative back projection method, which can be considered as solving a simple least square problem.…”

Section: Introductionmentioning

confidence: 99%

Hyperspectral Image Super-Resolution via Nonlocal Low-Rank Tensor Approximation and Total Variation Regularization

et al. 2017

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Hyperspectral image (HSI) possesses three intrinsic characteristics: the global correlation across spectral domain, the nonlocal self-similarity across spatial domain, and the local smooth structure across both spatial and spectral domains. This paper proposes a novel tensor based approach to handle the problem of HSI spatial super-resolution by modeling such three underlying characteristics. Specifically, a noncovex tensor penalty is used to exploit the former two intrinsic characteristics hidden in several 4D tensors formed by nonlocal similar patches within the 3D HSI. In addition, the local smoothness in both spatial and spectral modes of the HSI cube is characterized by a 3D total variation (TV) term. Then, we develop an effective algorithm for solving the resulting optimization by using the local linear approximation (LLA) strategy and the alternative direction method of multipliers (ADMM). A series of experiments are carried out to illustrate the superiority of the proposed approach over some state-of-the-art approaches.

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Improved resolution from subpixel shifted pictures

Cited by 244 publications

References 7 publications

Generalized sampling: a variational approach .I. Theory

Generalized sampling: a variational approach .I. Theory

A Survey on Super-Resolution Methods for Image Reconstruction

Hyperspectral Image Super-Resolution via Nonlocal Low-Rank Tensor Approximation and Total Variation Regularization

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