3D super-resolution using generalized sampling expansion

Shekarforoush, H.; Berthod, Marc-Antoine; Zerubia, Josiane

doi:10.1109/icip.1995.537474

Cited by 28 publications

(19 citation statements)

References 8 publications

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“…Recent applications of generalized sampling include motion-compensated deinterlacing of televison images [11], [121], and super-resolution [107], [138]. The latter is an attempt to reconstruct a higher resolution image from a series of lower resolution ones, which are shifted slightly with respect to each other.…”

Section: B Generalized (Or Multichannel) Samplingmentioning

confidence: 99%

Sampling-50 years after Shannon

2000

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Section: B Generalized (Or Multichannel) Samplingmentioning

confidence: 99%

Sampling-50 years after Shannon

2000

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“…The corresponding signal approximation admits the expansion (15) and the underlying operator is a projector from into . The synthesis functions are given by (16) where the filter sequences are determined as follows:…”

Section: A Generalized Sampling Theoremmentioning

confidence: 99%

“…A univariate version of such a spline interpolation algorithm is described in [19]. The corresponding cubic spline reconstruction functions, which were specified by (16) and (17), are shown in Fig. 4(a).…”

Section: A Example 1: Interlaced Samplingmentioning

confidence: 99%

“…It is possible, however, to compensate for these effects-including the frequency nulls of the transfer function of the microscope-by combining multiple images acquired with various degrees of defocusing [23]. Super-resolution is another promising application where a series of low-resolution images that are shifted with respect to each other are used to reconstruct a higher resolution picture of a scene [16], [21].…”

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confidence: 99%

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A generalized sampling theory without band-limiting constraints

Unser

Zerubia

1998

IEEE Trans. Circuits Syst. II

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106

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Abstract-We consider the problem of the reconstruction of a continuous-time function from the samples of the responses of linear shift-invariant systems sampled at 1 the reconstruction rate. We extend Papoulis' generalized sampling theory in two important respects. First, our class of admissible input signals (typ.) is considerably larger than the subspace of band-limited functions. Second, we use a more general specification of the reconstruction subspace , so that the output of the system can take the form of a bandlimited function, a spline, or a wavelet expansion. Since we have enlarged the class of admissible input functions, we have to give up Shannon and Papoulis' principle of an exact reconstruction. Instead, we seek an approximation that is consistent in the sense that it produces exactly the same measurements as the input of the system. This leads to a generalization of Papoulis' sampling theorem and a practical reconstruction algorithm that takes the form of a multivariate filter. In particular, we show that the corresponding system acts as a projector from onto . We then propose two complementary polyphase and modulation domain interpretations of our solution. The polyphase representation leads to a simple understanding of our reconstruction algorithm in terms of a perfect reconstruction filter bank. The modulation analysis, on the other hand, is useful in providing the connection with Papoulis' earlier results for the band-limited case. Finally, we illustrate the general applicability of our theory by presenting new examples of interlaced and derivative sampling using splines.

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“…Many of these problems require only re istration at pixel level [5] [B], while others [3] [7] [8]f12] [13] [14] depend on the scene registration at subpixel accuracy.…”

Section: Introductionmentioning

confidence: 99%