Efficient parallel algorithms for optical computing with the discrete Fourier transform (DFT) primitive

Reif, John H.; Tyagi, Akhilesh K.

doi:10.1364/ao.36.007327

Cited by 33 publications

(23 citation statements)

References 32 publications

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“…These are defined similarly to NC circuits except we allow unbounded fan-in gates, and threshold gates, respectively. The results in the above mentioned paper of Reif and Tyagi [77], and Caulfield's observation on the benefits of unbounded fan-in [16], can be interpreted as exploiting this important and efficient aspect of optics.…”

Section: A Possible Way Forwardmentioning

confidence: 89%

“…Numerous physical implementations of the latter class exist, and example applications include fast pattern recognition and matrix-vector algebra [35,90]. There have been much resources devoted to designs, implementations and algorithms for such optical information processing architectures (for example see [4,15,29,35,52,55,57,62,77,90,101,27] and their references).…”

Section: Optical Models Of Computation and Computational Complexitymentioning

confidence: 99%

“…Reif and Tyagi [77] study two optically inspired models. One model is a 3D VLSI model augmented with a 2D discrete Fourier transform (DFT) primitive and parallel optical interconnections.…”

Section: Optical Models Of Computation and Computational Complexitymentioning

confidence: 99%

“…For the DFT circuit, size is defined as the number of edges plus gates. Constant time, polynomial size/volume, algorithms for a number of problems are reported including matrix multiplication, sorting and string matching [77]. These interesting results are built upon the ability of their models to compute the 2D DFT in one step.…”

Section: Optical Models Of Computation and Computational Complexitymentioning

confidence: 99%

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Optical computing

Woods¹,

Naughton²

2009

Applied Mathematics and Computation

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We consider optical computers that encode data using images and compute by transforming such images. We give an overview of a number of such optical computing architectures, including descriptions of the type of hardware commonly used in optical computing, as well as some of the computational efficiencies of optical devices. We go on to discuss optical computing from the point of view of computational complexity theory, with the aim of putting some old, and some very recent, results in context. Finally, we focus on a particular optical model of computation called the continuous space machine. We describe some results for this model including characterisations in terms of well-known complexity classes.

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Section: A Possible Way Forwardmentioning

confidence: 89%

Section: Optical Models Of Computation and Computational Complexitymentioning

confidence: 99%

“…Reif and Tyagi [77] study two optically inspired models. One model is a 3D VLSI model augmented with a 2D discrete Fourier transform (DFT) primitive and parallel optical interconnections.…”

Section: Optical Models Of Computation and Computational Complexitymentioning

confidence: 99%

Section: Optical Models Of Computation and Computational Complexitymentioning

confidence: 99%

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Optical computing

Woods¹,

Naughton²

2009

Applied Mathematics and Computation

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“…There are many positive aspects to processing information using these (sometimes unwieldy and always inaccurate) physical signals instead of the more accurate digital electronic representations of 2D signals. These include the ability to concurrently modify all parts of an image (spatial light modulation), the capability to substitute space computational complexity for time computational complexity when performing certain transformations [1][2][3][4][5] (such as constant-time Fourier transformation with coherent light), the potential significant energy savings [6] (in both creating the signal and effecting the computation), and the ease with which analog signals can be digitised or resampled at an arbitrary frequency for subsequent digital electronic handling. The most common applications of optical image processing are pattern recognition and numerical matrix computations.…”

Section: Introductionmentioning

confidence: 99%

Phase in Optical Image Processing

Naughton¹,

Rastogi²,

Hack³

2010

AIP Conference Proceedings

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Abstract. The use of phase has a long standing history in optical image processing, with early milestones being in the field of pattern recognition, such as VanderLugt's practical construction technique for matched filters, and (implicitly) Goodman's joint Fourier transform correlator. In recent years, the flexibility afforded by phase-only spatial light modulators and digital holography, for example, has enabled many processing techniques based on the explicit encoding and decoding of phase. One application area concerns efficient numerical computations. Pushing phase measurement to its physical limits, designs employing the physical properties of phase have ranged from the sensible to the wonderful, in some cases making computationally easy problems easier to solve and in other cases addressing mathematics' most challenging computationally hard problems. Another application area is optical image encryption, in which, typically, a phase mask modulates the fractional Fourier transformed coefficients of a perturbed input image, and the phase of the inverse transform is then sensed as the encrypted image. The inherent linearity that makes the system so elegant mitigates against its use as an effective encryption technique, but we show how a combination of optical and digital techniques can restore confidence in that security. We conclude with the concept of digital hologram image processing, and applications of same that are uniquely suited to optical implementation, where the processing, recognition, or encryption step operates on full field information, such as that emanating from a coherently illuminated real-world three-dimensional object.

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Optical Computing and Computational Complexity

Woods

2006

Lecture Notes in Computer Science

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This work concerns the computational complexity of a model of computation that is inspired by optical computers. The model is called the continuous space machine and operates in discrete timesteps over a number of two-dimensional images of fixed size and arbitrary spatial resolution. The (constant time) operations on images include Fourier transformation, multiplication, addition, thresholding, copying and scaling. We survey some of the work to date on the continuous space machine. This includes a characterisation of the power of an important discrete restriction of the model. Parallel time corresponds, within a polynomial, to sequential space on Turing machines, thus satisfying the parallel computation thesis. A characterisation of the complexity class NC in terms of the model is also given. Thus the model has computational power that is (polynomially) equivalent to that of many well-known parallel models. Such characterisations give a method to translate parallel algorithms to optical algorithms and facilitate the application of the complexity theory toolbox to optical computers. In the present work we improve on these results. Specifically we tighten a lower bound and present some new resource trade-offs.1 That is, finding lower and upper bounds on computational power in terms of known complexity classes.

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Efficient parallel algorithms for optical computing with the discrete Fourier transform (DFT) primitive

Cited by 33 publications

References 32 publications

Optical computing

Optical computing

Phase in Optical Image Processing

Optical Computing and Computational Complexity

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