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…     

Multispectral image compression using three-dimensional transform zeroblock coding

This paper proposes a new multispectral image data compression algorithm (KLT/WT-3DEZB). The proposed coding strategy consists of three main steps. Firstly, a wavelet transform (WT) is applied to reduce the spatial redundancies. Then, a Karhunen-Loeve transform (KLT) is used to reduce the redundancies in the spectral domain. Finally, a modified SPECK algorithm-three-dimensional embedded zeroblock (3DEZB) algorithm is proposed and used to encode the transformed coefficients. Numerical experiments show that the reconstructed images using the proposed algorithm exhibite a better quality and a higher compression ratio than those obtained by traditional KLT/WT-3DSPIHT, 3DSPIHT, and 3DSPECK algorithms.     

Multi-sensor image fusion using discrete wavelet frame transform

An algorithm is presented for multi-sensor image fusion using discrete wavelet frame transform (DWFT). The source images to be fused are firstly decomposed by DWFT. The fusion process is the combining of the source coefficients. Before the image fusion process, image segmentation is performed on each source image in order to obtain the region representation of each source image. For each source image, the salience of each region in its region representation is calculated. By overlapping all these region representations of all the source images, we produce a shared region representation to label all the input images. The fusion process is guided by these region representations. Region match measure of the source images is calculated for each region in the shared region representation. When fusing the similar regions, weighted averaging mode is performed; otherwise selection mode is performed. Experimental results using real data show that the proposed algorithm outperforms the traditional pyramid transfo     

Fractional Fourier transform of apertured paraboloid refracting system

The limitation of paraxial condition of paraboloid refracting system in performing fractional Fourier trans-form acts like an aperture, which makes the system different from ideal systems. With aperture expanded as the sum of finite complex Gaussian terms, a more practical approximate analytical solution of frac-tional Fourier transform of Gaussian beam in an apertured paraboloid refracting system is obtained and also numerical investigation is presented. Complicated and practical fractional Fourier transform systems can be constructed by cascading several apertured paraboloid refracting systems which are the simplest and the most basic units for performing more precise transform.     

Application of wavelet transform to 3D shape measurement

A new method for analyzing the phase distributions of deformed grating images on the surface of three-dimensional (3D) object to obtain its shape information has been presented. In the conventional technique, Fourier transform profilometry (FTP), there is an intrinsic problem of extracting the fundamental frequency component if the deformation of the grating pattern is either considerable or complicated, which will definitely bring bad influence to the analysis' accuracy. That means FTP is not appropriate to deal with the complex surfaces of 3D objects. The approach that we here introduce to solve this problem is to utilize Gabor wavelet transform (GWT), a tool excelling for its multiresolution in time-frequency domain, to analyze the phase distributions.     

A novel image fusion algorithm based on bandelet transform

A novel image fusion algorithm based on bandelet transform is proposed.Bandelet transform can take advantage of the geometrical regularity of image structure and represent sharp image transitions such as edges efficiently in image fusion.For reconstructing the fused image,the maximum rule is used to select source images' geometric flow and bandelet coefficients.Experimental results indicate that the bandelet-based fusion algorithm represents the edge and detailed information well and outperforms the wavelet-based and Laplacian pyramid-based fusion algorithms,especially when the abundant texture and edges are contained in the source images.     

Can the Wigner transform of a two-dimensional rotationally symmetric beam be fully recovered from the Wigner transform of its one-dimensional approximation?

It is shown that the full four-dimensional Wigner transform of a coherent, rotationally symmetric light beam can be completely recovered by measurement, in one step, of the Wigner transform of an equivalent one-dimensional light beam. The method of generating this equivalent light beam from a two-dimensional circular light beam is presented.     

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.     

Super-resolution image restoration algorithm based on orthogonal discrete wavelet transform

By using orthogonal discrete wavelet transform (ODWT) and generalized cross validation (GCV), and combining with Luck-Richardson algorithm based on Poisson-Markov model (MPML), several new superresolution image restoration algorithms are proposed. According to simulation experiments for practical images, all the proposed algorithms could retain image details better than MPML, and be more suitable to low signal-to-noise ratio (SNR) images. The single operation wavelet MPML (SW-MPML) algorithm and MPML algorithm based on single operation wavelet transform (MPML-SW) avoid the iterative operation of self-adaptive parameter in MPML particularly, and improve operating speed and precision. They are instantaneous to super-resolution image restoration process and have extensive application foreground.     

Focusing transform based robust azimuth angles estimation for wideband signals

A focusing transform based minimum variance method (FTMV) is proposed for estimating the azimuth angles of wideband signals. The estimation error of Direction of Arrival (DOA) in the traditional Minimum Variance (MV) method during the array direction changing with the ship can be eliminated by focusing the sample covariance matrices in wideband onto a single narrowband, and accumulating the beamformer outputs on azimuth. Then, the azimuth angles of signals can be estimated accurately. Experimental results show that the FTMV method is more efficient and robust than the MV method in this case.     

De-noising of Raman spectrum signal based on stationary wavelet transform

In this paper, the Raman spectrum signal de-noising based on stationary wavelet transform is discussed. Haar wavelet is selected to decompose the Raman spectrum signal for several levels based on stationary wavelet transform. The noise mean square j is estimated by the wavelet details at every level, and the wavelet details toward 0 by a threshold , where n is length of the detail, then recovery signal is reconstructed. Experimental results show this method not only suppresses noise effectively, but also preserves as many target characteristics of original signal as possible. This de-noising method offers a very attractive alternative to Raman spectrum signal noise suppress.     

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.