Shannon number and degrees of freedom of an image

Gori, F.; Guattari, G.

doi:10.1016/0030-4018(73)90091-6

Cited by 77 publications

(51 citation statements)

References 14 publications

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“…The matrix elements of T j will be denoted by A j , B j , C j , and D j . The associated Iwasawa decomposition parameters will be denoted by a j , M j , and q j , which can be computed from A j , B j , C j , and D j by using formulas (6)- (8). The FRT order in the Iwasawa decomposition begins from 0 at the input of the system, and then monotonically increases as a function of distance [1,19].…”

Section: Phase-space Window Of Optical Systemsmentioning

confidence: 99%

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Phase-space window and degrees of freedom of optical systems with multiple apertures

Özaktaş

Oktem

2013

J. Opt. Soc. Am. A

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We show how to explicitly determine the space-frequency window (phase-space window) for optical systems consisting of an arbitrary sequence of lenses and apertures separated by arbitrary lengths of free space. If the space-frequency support of a signal lies completely within this window, the signal passes without information loss. When it does not, the parts that lie within the window pass and the parts that lie outside of the window are blocked, a result that is valid to a good degree of approximation for many systems of practical interest. Also, the maximum number of degrees of freedom that can pass through the system is given by the area of its spacefrequency window. These intuitive results provide insight and guidance into the behavior and design of systems involving multiple apertures and can help minimize information loss.

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Section: Phase-space Window Of Optical Systemsmentioning

confidence: 99%

“…The conventional space-bandwidth product has been of fundamental importance because of its interpretation as the number of degrees of freedom [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. In most works, the space-bandwidth product, as its name implies, is the product of a spatial extent and a spatial-frequency extent.…”

Section: Introductionmentioning

confidence: 99%

Phase-space window and degrees of freedom of optical systems with multiple apertures

Özaktaş

Oktem

2013

J. Opt. Soc. Am. A

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“…, T and T = min {M × N, K}. The behavior of the σ t 's affects the amount of information conveyed on I by V [44]. Accordingly, among all the possible matrices Z and for a fixed M , it is convenient to choose the locations of the sampling points providing the "flattest" singular values behavior.…”

Section: Optimal Sample Number and Locationsmentioning

confidence: 99%

“…Concerning now the choice of the "optimal" number of samples M , since Φ admits a meaningful interpretation in terms of generalized Shannon number [44], then, on denoting by Φ opt (M ) the maximum of Φ for a given M , we expect that adding further sampling points to the segment (−a, a) of the z = d axis (i.e., increasing M ) will increase Φ opt (M ) until the maximum amount of information which can be gathered from such a domain is reached. Beyond this condition, no further information can be conveyed on I by any newly added field sample.…”

Section: Optimal Sample Number and Locationsmentioning

confidence: 99%

Experimental Field Reconstruction of Incoherent Sources

Capozzoli¹,

Curcio²,

Liseno³

2013

PIER B

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Abstract-The problem of characterizing random sources from near-field measurements and of devising the random field sampling procedure is tackled by a stochastic approach. The presented technique is an extension of that introduced in [22] and successfully adopted to experimentally characterize deterministic (CW and multi-frequency) radiators and fields. Under the assumption that the source is wide sense stationary, quasi-monochromatic and incoherent, its intensity is reconstructed by time-domain field measurements aimed at extracting information from the mutual coherence of the acquired near-field. The linear relation between the field coherence and the source intensity is inverted by using the Singular Value Decomposition (SVD) approach, properly representing the source intensity distribution by exploiting the a priori information (e.g., its size and shape) on the radiator. The sampling of the radiated random field is devised by a singular value optimization procedure of the relevant finite dimensional linear operator. Experimental results using a slotted reverberation chamber as incoherent source assess the performance of the approach.

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“…The conventional space-bandwidth product is of fundamental importance in signal processing and information optics because of its interpretation as the number of degrees of freedom of signals [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. In this paper, we discuss the bicanonical width product, which generalizes the space-bandwidth product and which can often provide a tighter measure of the actual number of degrees of freedom.…”

Section: Introductionmentioning

confidence: 99%

Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space–bandwidth product

Oktem

Özaktaş

2010

J. Opt. Soc. Am. A

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Linear canonical transforms (LCTs) form a three-parameter family of integral transforms with wide application in optics. We show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space-frequency plane. This allows LCT domains to be labeled and ordered by the corresponding fractional order parameter and provides insight into the evolution of light through an optical system modeled by LCTs. If a set of signals is highly confined to finite intervals in two arbitrary LCT domains, the space-frequency (phase space) support is a parallelogram. The number of degrees of freedom of this set of signals is given by the area of this parallelogram, which is equal to the bicanonical width product but usually smaller than the conventional space-bandwidth product. The bicanonical width product, which is a generalization of the space-bandwidth product, can provide a tighter measure of the actual number of degrees of freedom, and allows us to represent and process signals with fewer samples.

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Shannon number and degrees of freedom of an image

Cited by 77 publications

References 14 publications

Phase-space window and degrees of freedom of optical systems with multiple apertures

Phase-space window and degrees of freedom of optical systems with multiple apertures

Experimental Field Reconstruction of Incoherent Sources

Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space–bandwidth product

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