Correspondence between quantum-optical transform and classical-optical transform explored by developing Dirac’s symbolic method

By virtue of the new technique of performing integration over Dirac’s ket–bra operators, we explore quantum optical version of classical optical transformations such as optical Fresnel transform, Hankel transform, fractional Fourier transform, Wigner transform, wavelet transform and Fresnel–Hadmard combinatorial transform etc. In this way one may gain benefit for developing classical optics theory from the research in quantum optics, or vice-versa. We cannot only find some new quantum mechanical unitary operators which correspond to the known optical transformations, deriving a new theorem for calculating quantum tomogram of density operators, but also can reveal some new classical optical transformations. For examples, we find the generalized Fresnel operator (GFO) to correspond to the generalized Fresnel transform (GFT) in classical optics. We derive GFO’s normal product form and its canonical coherent state representation and find that GFO is the loyal representation of symplectic group multiplication rule. We show that GFT is just the transformation matrix element of GFO in the coordinate representation such that two successive GFTs is still a GFT. The ABCD rule of the Gaussian beam propagation is directly demonstrated in the context of quantum optics. Especially, the introduction of quantum mechanical entangled state representations opens up a new area in finding new classical optical transformations. The complex wavelet transform and the condition of mother wavelet are studied in the context of quantum optics too. Throughout our discussions, the coherent state, the entangled state representation of the two-mode squeezing operators and the technique of integration within an ordered product (IWOP) of operators are fully used. All these have confirmed Dirac’s assertion: “...for a quantum dynamic system that has a classical analogue, unitary transformation in the quantum theory is the analogue of contact transformation in the classical theory”.     

Inversion of Umarov–Tsallis–Steinberg’s q-Fourier transform and the complex-plane generalization

We introduce a complex q$q$-Fourier transform as a generalization of the (real) one analyzed in [S. Umarov, C. Tsallis, S. Steinberg, Milan J. Math. 307 (2008)]. By recourse to tempered ultradistributions we show that this complex-plane generalization overcomes all the troubles that afflict its real counterpart.     

Speech compression scheme based on wavelet transform and vector quantization

lIntroductionThemethodoflinearpredictionhasbeendondnatedinspeechcompressiollsince197o's-However,thefreqencyresolutionoflinearpredictionisnotmatchedwellwiththeactualphysicalprocessinthehUInanear-Thewavelettransform,asakindofnewmethodforsignalprocessing,overcomesthedritationsofshort-tAneFourierThansformonthefrequencyresoutfon-Itcanuselilghfrequencyresolutionatlowfreqllencyrangeandusefowfrequencyresohitionathighfrequencyrange-Basedonthispoint,weusewavlettransformtothespeechcomnresslon.Firstthe…     

Double-image encryption based on joint transform correlation and phase-shifting interferometry

An image encryption method combining the joint transform correlator (JTC) architecture with phase- shifting interferometry to realize double random-phase encoding is proposed.The encrypted field and the decrypting key are registered as holograms by phase-shifting interferometry.This method can encrypt two images simultaneously to improve the encryption efficiency of the methods based on JTC architecture,and eliminate the system alignment constraint of the methods based on Mach-Zehnder interferometer (MZI) architecture.Its feasibility and validity are verified by computer simulations.Moreover,image encryption and decryption can be achieved at high speed optically or digitally.The encrypted data are suitable for Internet transmission.     

Geometrically robust image watermarking using scale-invariant feature transform and Zernike moments

In order to resist geometric attacks,a robust image watermarking algorithm is proposed using scale- invariant feature transform(SIFT)and Zernike moments.As SIFT features are invariant to rotation and scaling,we employ SIFT to extract feature points.Then circular patches are generated using the most robust points.An invariant watermark is generated from each circular patch based on Zernike moments. The watermark is embedded into multiple patches for resisting locally cropping attacks.Experimental results show that the proposed scheme is robust to both geometric attacks and signal processing attacks.     

Audio watermarking based on psychoacoustic model and critical band wavelet transform

Watermark embedding algorithm based on critical band wavelet transform of digital audio signal is proposed in this paper. The masking threshold for each audio signal segment was calculated on the basic of psychoacoustic model. According to the similarity between critical band of human auditory system and critical band wavelet transform, a watermark was embedded into the low-band and mid-band coefficients of digital wavelet. The embedding strength was adaptively controlled by the masking threshold. The experiment results show that the embedded watermark signal is inaudible, and the watermarked audio signal has good robustness against many attacks such as compression, noise, re-sampling, low-pass filtering.     

Region-based fusion of infrared and visible images using nonsubsampled contourlet transform

With the nonsubsampled contourlet transform (NSCT),a novel region-segmentation-based fusion algorithm for infrared (IR) and visible images is presented.The IR image is segmented according to the physical features of the target.The source images are decomposed by the NSCT,and then,different fusion rules for the target regions and the background regions are employed to merge the NSCT coefficients respectively. Finally,the fused image is obtained by applying the inverse NSCT.Experimental results show that the proposed algorithm outperforms the pixel-based methods,including the traditional wavelet-based method and NSCT-based method.     

Inversion of the Penrose transform and the Cauchy–Fantappie formula

We discuss the construction of an explicit inversion of the Penrose transform with the focus on connections with the Radon transform, multi-dimensional residues and the Cauchy–Fantappie integral formula following to results [1], [2]. The focus is on the new representation (M) of the inverse Penrose transform as a residue. The proof of this formula can be extracted from [1]. This proof includes an explicit computation of this residue (D). In this formula not the exact values of all coefficients but the existence of a differential operator, inverting the Penrose transform (we call this Leibnitz–Newton’s phenomenon) is important. It is similar to local inversion formulas in integral geometry.     

Segal–Bargmann transform: the <Emphasis Type="Italic">q</Emphasis>-deformation

We give identifications of the q-deformed Segal–Bargmann transform and define the Segal–Bargmann transform on mixed q-Gaussian variables. We prove that, when defined on the random matrix model of ?niady for the q-Gaussian variable, the classical Segal–Bargmann transform converges to the q-deformed Segal–Bargmann transform in the large N limit. We also show that the q-deformed Segal–Bargmann transform can be recovered as a limit of a mixture of classical and free Segal–Bargmann transform.     

A general Mobius inversion transform formula for hcp lattices and its application

In this paper,we present a general Mobius inversion transform formula for hcp lattices.This formula can be applied to hcp lattices with a non-ideal c/a value and to obtain the pair potential between atoms in these lattices from the cohesive energy.Also,the three-body interaction among atoms in the lattices can be taken into account in the method.This method gives a useful means to obtain interatomic interactions in the interatomic force model.The method has been applied to zinc,and the pair potential obtained is used to calculate the phonon dispersion relations for some high-symmetry directions.It is found that,by properly considering a three-body interaction,one can acquire satisfactory results.     

Blind source separation of multichannel electroencephalogram based on wavelet transform and ICA

Combination of the wavelet transform and independent component analysis （ICA） was employed for blind source separation （BSS） of multichannel electroencephalogram （EEG）. After denoising the original signals by discrete wavelet transform, high frequency components of some noises and artifacts were removed from the original signals. The denoised signals were reconstructed again for the purpose of ICA, such that the drawback that ICA cannot distinguish noises from source signals can be overcome effectively. The practical processing results showed that this method is an effective way to BSS of multichannel EEG. The method is actually a combination of wavelet transform with adaptive neural network, so it is also useful for BBS of other complex signals.     

Global and local contrast enhancement algorithm for image using wavelet neural network and stationary wavelet transform

A new contrast enhancement algorithm for image is proposed employing wavelet neural network (WNN) and stationary wavelet transform (SWT). Incomplete Beta transform (IBT) is used to enhance the global contrast for image. In order to avoid the expensive time for traditional contrast enhancement algorithms, which search optimal gray transform parameters in the whole gray transform parameter space, a new criterion is proposed with gray level histogram. Contrast type for original image is determined employing the new criterion. Gray transform parameter space is given respectively according to different contrast types, which shrinks the parameter space greatly. Nonlinear transform parameters are searched by simulated annealing algorithm (SA) so as to obtain optimal gray transform parameters. Thus the searching direction and selection of initial values of simulated annealing is guided by the new parameter space. In order to calculate IBT in the whole image, a kind of WNN is proposed to approximate the IBT. Having enhanced the global contrast to input image, discrete SWT is done to the image which has been processed by previous global enhancement method, local contrast enhancement is implemented by a kind of nonlinear operator in the high frequency sub-band images of each decomposition level respectively. Experimental results show that the new algorithm is able to adaptively enhance the global contrast for the original image while it also extrudes the detail of the targets in the original image well. The computation complexity for the new algorithm is O(MN) log(MN), where M and N are width and height of the original image, respectively.     

Fast Fourier transform processor architecture

This paper describes a VLSI architecture used for implementation offast Fourier transform,of which the computation cell(CC)implement the com-putation of 4-point DFT and multiplication of twiddle factors using radix-4pipeline computation method,and the address generator(AG)gives the ad-dresses of both transform data and twiddle factors simultaneously.In addition,this paper also presents the recursive and cascade circuit configurations usingthe CC,AG and BFP overflow preventing scheme.Up to 64K-point FFT canbe computed quickly and flexibly by using these two circuit configurations.     

The Tsallis–Laplace transform

We introduce here the q$q$-Laplace transform as a new weapon in Tsallis’ arsenal, discussing its main properties and analyzing some examples. The q$q$-Gaussian instance receives special consideration. Also, we derive the q$q$-partition function from the q$q$-Laplace transform.     

Four-quadrant spatial phase-shifting Fourier transform digital holography for recording of cosine transform coefficients

A new one-step four-quadrant spatial phase-shifting Fourier transform digital holography is presented for recording of cosine transform coefficients, because cosine transform is a real-even symmetric Fourier transform. This approach implements four quadrant spatial phase shifting at a time using a special phase mask, which is located in the reference arm, and the phase distributions of its four-quadrants are 0, π/2, π, and 3π/2 respectively. The theoretical analysis and computer simulation results show that cosine transform coefficients of real-valued image can be calculated by capturing single four-quadrant spatial phase-shifting Fourier transform digital hologram.     

Wavelet transform implementation by layers

I.IntroductionWavelettheoryanditsapplicationhavebeendevelopedquicklyformallyyears,whichcoverquitealargeareaandprovideverygeneraltechniquesthatcanbeaPpliedtomanytasksinsignalprocessing,andhavenumerouspotelltialapplications.lnacousticresearchthereisatra-ditionofthefrequencyanalysisintermsofoctave,whichfitstheconceptof"constantQ"inwavelettransform,e.g.thepowerspectrumofmusicismeasuredintermsof1/3octave.Sofartheimplemelltationofwavelettransformha-sbeendevelopedonlyforoneoctave,e.g.themultiresolut…     

Copyright protection in digital museum based on digital holography and discrete wavelet transform

A new method to protect the copyright of digital museum based on digital holography is proposed.The Fresnel hologram of watermark image is embedded in the object to be protected through discrete wavelet transform(DWT).After the watermark detection,the copyright information appears in the reconstructed hologram.With the higher redundancy feature in the hologram,the proposed technique can actually survive several kinds of image processing.Experimental results prove that the presented method has good robustness in image protection.     

The sub-millimeter and Fourier transform microwave spectrum of HZnCl (X Σ)

The pure rotational spectrum of HZnCl (X ¹Σ⁺) has been recorded using sub-millimeter direct-absorption methods in the range of 439-540 GHz and Fourier transform microwave (FTMW) techniques from 9 to 39 GHz. This species was produced by the reaction of zinc vapor and chlorine gas with H₂ or D₂ in a d.c. glow discharge for the sub-millimeter studies. In the FTMW measurements, HZnCl was created in a discharge nozzle from Cl₂ and (CH₃)₂Zn. Between 5 and 10 rotational transitions were measured in the sub-millimeter regime for four zinc and two chlorine isotopologues; four transitions were recorded with the FTMW machine for the main isotopologue, each consisting of several chlorine hyperfine components. The data are consistent with a linear molecule and a ¹Σ⁺ ground electronic state. Rotational and chlorine quadrupole constants were established from the spectra, as well as an r_m⁽²⁾ structure. The Zn-Cl and Zn-H bond lengths were determined to be 2.0829 and 1.5050 Å, respectively; in contrast, the Zn-Cl bond distance in ZnCl is 2.1300 Å, longer by ∼0.050 Å. The zinc-chlorine bond distance therefore shortens with the addition of the H atom. The ³⁵Cl electric quadrupole coupling constant of eQq = −27.429 MHz found for HZnCl suggests that this molecule is primarily an ionic species with some covalent character for the Zn-Cl bond.     

Application of wavelet transform in feature extraction and pattern recognition of wideband echoes

1IntroductionThefeatureextractionofunderwaterobjectsfromactiveechoisadifficultproblem.Thereceivedsignalisaconvolutionofthetransmittedsignalwiththeimpulseresponseoftheob-jects,plusvariousadditivedisturbances,includingnoiseandresonance.Inordertorecognizetheobjectswehavetoextractimportantfeaturesfromtheechoes.Inrecentyearsmanymeth-odshavebeenproposed,andoneoftheapproachesistodeconvolvetheechotogettheimpuIseresponsesequenceoftheobject.Thisisoftenfollowedbyaparametermodelapproximationwhiletheestim…     

Exact interpolation and “integration” of fourier transform nuclear magnetic resonance spectra

A new interpolation procedure for interpolation of Fourier transform spectral data, which is based upon interpolation with the “magnitude-Lorentzian” function, is applied to FT-NMR spectroscopy. In FT-NMR spectroscopy the principal application of the new interpolation method is the determination of the relative number of magnetic nuclei per spectral peak. This measurement derives from a calculation of the “scaling factor” for the FT-NMR FID. It is shown that for well-separated peaks this new method provides a more accurate determination of the relative number of magnetic nuclei per spectral peak than does the widely used method of digital integration of the absorption spectrum. In addition, the scaling factor method has the further advantage of not requiring any phase adjustment of the spectrum.