Showing papers on "S transform published in 1993"

Discrete Gabor transform

Abstract: A feasible algorithm for implementing the Gabor expansion, the coefficients of which are computed by the discrete Gabor transform (DGT), is presented. For a given synthesis window and sampling pattern, computing the auxiliary biorthogonal function of the DGT is nothing more than solving a linear system. The DGT presented applies for both finite as well as infinite sequences. By exploiting the nonuniqueness of the auxiliary biorthogonal function at oversampling an orthogonal like DGT is obtained. As the discrete Fourier transform (DFT) is a discrete realization of the continuous-time Fourier transform, similarly, the DGT introduced provides a feasible vehicle to implement the useful Gabor expansion. >

Depth from defocus by changing camera aperture: a spatial domain approach

Abstract: The application of a new spatial-domain convolution/deconvolution transform (S transform) for determining the distance of objects using image defocus is described. The method, known as STMAP, involves simple local operations on only two images taken with different aperture diameters and can be easily implemented in parallel. Both images can be arbitrarily blurred, and neither of them needs to be a focused image taken with a pin-hole camera. STMAP is implemented on an actual camera system named the Stonybrook Passive Autofocusing and Ranging Camera System (SPARCS). Experimental results on real-world planar objects are presented. The results indicate that STMAP is useful in practical applications. The utility of the method is demonstrated for rapid autofocusing of electronic cameras. STMAP is computationally more efficient than other depth-from-focus methods. The results are comparable to a Fourier-transform-based approach. >

Local Inversion of the Radon Transform in Even Dimensions Using Wavelets

Abstract: We use the theory of the continuous wavelet transform to derive inversion formulas for the Radon transform on L 1 \L 2 (R d). These inversion formulas turn out to be local in even dimensions in the following sense. In order to recover a function f from its Radon transform in a ball of radius R > 0 about a point x to within error , we can nd () > 0 such that this can be accomplished by knowing the projections of f only on lines passing through a ball of radius R + () about x. We give explicit a priori estimates on the error in the L 2 and L 1 norms.

Signal reconstruction from modified auditory wavelet transform

Abstract: The authors propose a new method for signal modification in auditory peripheral representation: an auditory wavelet transform and algorithms for reconstructing a signal from a modified wavelet transform. They present the characteristics of signal analysis, synthesis, and reconstruction and also the data reduction criteria for signal modification. >

Wavelet transform in human visual channels.

Abstract: In this paper we report on an analysis of visual stimuli models by a wavelet function. The human visual process is compared with a wavelet transform. Wavelet functions have been built from the Haar function. Two stimuli were analyzed by a wavelet function: a sinusoidal luminance stimulus (spatial frequency f) and a luminance-varying regular stimulus. The theoretical results obtained from the wavelet transform are compared with the physiological results of R. Blake [in Frontiers in Visual Science, S. J. Cool and E. L. Smith, eds. (Springer-Verlag, Berlin, 1978), pp. 209–219] and K. K. De Valois [in Frontiers in Science, S. J. Cool and E. L. Smith, eds. (Springer-Verlag, Berlin, 1978), pp. 277–285]. A theoretical curve conforms to the shape of the contrast sensitivity curves. Hence it can be concluded that the wavelet transform is a new approach to human visual mechanisms.

Singularities of the Radon Transform

Abstract: The singular support of the Radon transform Rf of a function f with a compact support is described in terms of the Generalized Legendre transform. The asymptotic behavior of Rf near the singular support modulo smooth functions is described in terms of a geometrical invariant, introduced in the paper.

Windowed radon transforms, analytic signals, and the wave equation

Abstract: . The act of measuring a physical signal or field suggests a generalization of the wavelet transform that turns out to be a windowed version of the Radon transform. A reconstruction formula is derived which inverts this transform. A special choice of window yields the “Analytic-Signal transform” (AST), which gives a partially analytic extension of functions from R n to C n . For n 1, this reduces to Gabor's classical definition of “analytic signals.” The AST is applied to the wave equation, giving an expansion of solutions in terms of wavelets specifically adapted to that equation and parametrized by real space and imaginary time coordinates (the Euclidean region).

Computation-rate-distortion in transform coders for image compression

Abstract: We consider the computational complexity of block transform coding and tradeoffs among computation, bit rate, and distortion. In particular, we illustrate a method of coding that allows decompression time to be traded with bit rate under a fixed quality criteria, or allows quality to be traded for speed with a fixed average bit rate. We provide a brief analysis of the entropy coded infinite uniform quantizer that leads to a simple bit allocation for transform coefficients. Finally, we consider the computational cost of transform coding for both the discrete cosine transform (DCT) and the Karhunen-Loeve transform (KLT). In general, a computation-rate- distortion surface can be used to select the appropriate size transform and the quantization matrix for a given bandwidth/CPU channel.

Application of spatial-domain convolution/deconvolution transform for determining distance from image defocus

Abstract: This paper describes the application of a new Spatial-Domain Convolution/Deconvolution transform (S transform) for determining distance of objects and rapid autofocusing of camera systems using image defocus The method of determining distance, named STM, involves simple local operations on only a few (about 2 to 4) images and it can be easily implemented in parallel STM has been implemented on an actual camera system named SPARCS Experiments on the performance of STM and their results on real-world objects are presented The results indicate that STM is useful in practical applications The utility of the method is demonstrated for rapid autofocusing of electronic cameras STM is computationally more efficient than other methods, but for our camera system, it is somewhat less robust in the presence of noise than a Fourier transform based approach STM is a useful technique in many applications such as rapid autofocusing© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering Downloading of the abstract is permitted for personal use only

New insights and results on transform domain VQ of images

Abstract: An attempt is made to determine whether there is a fundamental difference between the idea of vector transform coding and the well known transform/VQ (vector quantization) schemes. To answer this question, a unified framework for studying transform domain VQ is developed. Based on such a framework, some new insights are obtained and a new image coding technique is proposed. This study indicates that there is indeed a fundamental difference between vector transform coding and the existing transform/VQ schemes. The results of this study may also have a broader implication for developing other VQ-based two-step image coding techniques. >

A study on the optimal attributes of transform domain vector quantization for image and video compression

Abstract: The concept of vector transform coding (VTC) is examined. It is noted that the optimal transform for the purpose of vector quantization should reduce the correlation between the transform domain vectors and preserve the correlation among the components within each vector. An intrinsic coupling factor is defined to quantitatively measure how closely the components are coupled within a vector, and a bit-allocation mechanism is derived to assign bits to the transform domain vectors. Following the guidance of such a general study, a new scheme is proposed for image and video compression. Simulation results show excellent subjective quality at a bit-rate of 3.3 Mb/s. >

Signal transform covariant to scale changes

Abstract: A unitary signal transformation that is covariant by translation to scale changes (dilations and compressions) in the signal is formulated and justified. Unlike the Mellin transform, which is invariant to scale changes, this new transform is a true indicator of the scale content of a signal

Local inversion of the radon transform in the plane using wavelets

Abstract: We use the theory of the continuous wavelet transform to derive inversion formulas for the Radon transform. These inversion formulas are local in even dimensions in the following sense. In order to recover a function f from its Radon transform in a ball of radius R > 0 about a point x to within error (epsilon) > 0, we can find (alpha) ((epsilon) ) > 0 such that this can be accomplished by knowing the projections of f only on lines passing through a ball of radius R + (alpha) ((epsilon) ) about x. We give explicit a priori estimates on the error in the L2 and L(infinity ) norms.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Discrete cosine transform on irregular shape for image coding

Abstract: Segmentation-based image coding methods yield improved image quality over block-based schemes at high compression ratio. The paper presents a transform scheme on irregular shaped image segments based on the DCT for the purpose of image coding. The 2-dimensional transform is carried out in the horizontal and vertical directions separately. The alignment of the coefficients after the first 1-dimensional transform is studied and a table-look-up method for the best alignment is proposed with which the correlation between different rows after the first 1D transform can be exploited to its maximum. >

Fast approximate Karhunen-Loève transform with applications to digital image coding

Abstract: The Karhunen-Loeve transform (KLT) is known to be the optimal transform for data compression. However, since it is signal dependent and lacks a fast algorithm, it is not used in practice. In this paper, a fast approximate Karhunen-Loeve transform (AKLT) is presented. This new transform is derived using perturbation theory of linear operators. Both the forward and inverse AKLT are analytically derived in closed forms. In addition, fast computational algorithms are developed for both the forward and inverse transforms. The order of computational complexity for the AKLT is N log2 N, which is the same as that of the DCT, the transform presently used in industrial practice. Performance comparisons reveal for a first-order Markov sequence that the AKLT performs better than the DCT in its energy compaction and signal decorrelation capabilities. Experiments on real images also demonstrate a definite superiority of the AKLT over the DCT when an adaptive scheme is used.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

On the optimal transform for vector quantization of images

Abstract: Transform coding is widely used for image compression. If vector quantization is used in the transform domain, the definition of the optimal transform should be modified because the performance of vector quantization is better when the components within each vector are more correlated. The attributes of the optimal transform for vector quantization are discussed. It is shown how to construct the optimal transform for vector quantization based on the first order Markov model of images. >

Efficient image coding method based on adaptive Gabor discrete cosine transforms

Abstract: The Gabor transform is very useful for image compress/ on, but its implementation is very complicated and time consuming because the Gabor elementary functions are not mutually orthogonal. An efficient algorithm that combines the successive overrelaxation iteration and the look-up table techniques can be used to carry out the Gabor transform. The performance of the Gabor transform can be improved by using a modified transform, a Gabor discrete cosine transform (DCT). We present an adaptive Gabor DCT image coding algorithm. Experimental results show that a better performance can be achieved with the adaptive Gabor OCT than with the Gabor OCT.

Transform edge detection

Abstract: The blockwise transform edge detection method consists of segmenting the image into a number of small blocks, with neighboring blocks overlapping slightly; transforming each block by a fast transform; multiplying the transform coefficients of each block by a bandpass mask; inverse transforming the modified transform coefficients; detecting zero crossings and deciding an edge according to a thresholding scheme. Simulation results with the blockwise transform edge detection method in comparison to other bandpass filtering techniques indicate that higher performance is achieved with the new technique on the average. This is believed to result from the use of blockwise generalized filtering with appropriate transforms rather than linear convolutional filtering, as in other bandpass filtering techniques. The new method also has less computational complexity, and is well-suited to parallel processing.

Optical wavelet transform classifier with positive real Fourier transform wavelets

Abstract: A wavelet transform is used to transform data so as to improve discrimination between objects for classification. The wavelet transform is implemented in optics using the Fourier transform of the wavelets. Further, the wavelet chosen has a Fourier transform that is real and positive to avoid the use of holographic techniques. An optical setup is described in which an electronic analog sensor signal drives an acousto-optic cell that controls the intensity of an argon laser. A mechanical scanner writes the information as a line onto a spatial light rebroadcaster module containing an optical liquid crystal light valve. A lens system expands the line into a 2-D array. A real positive Fourier transform wavelet filter is placed in the Fourier transform plane of a 4- f correlator. An optical demonstration shows the formation of a wavelet transform and agreement with computer simulations. An approximation of the inverse wavelet transform is possible using only a real filter, and this is demonstrated in an optical experiment.

Accurate interpolation via the discrete W transform

Abstract: Two transform interpolation schemes which take advantage of the periodicity and antiperiodicity of different types of discrete W transform (DWT) are proposed. Results show that these new schemes achieve much higher accuracy than the standard approach.

Wavelet transform based optimal receivers

Abstract: A generalized orthogonal series expansion should reflect the natural modes of a signal. In doing so, the transform becomes precise and useful. The most precise transform is the Karhunen-Loeve (KL) transform. In this paper wavelets are are analyzed for their appropriateness as KL transforms. It is shown that optimum filters for detection of signals in noise can be designed adaptively using an arbitrary wavelet basis. >

Time-recursive architectures and wavelet transform

Abstract: The time-recursive computation has been proved as a particularly useful tool in real-time data compression and in transform domain adaptive filtering, with applications in the areas of audio, radio, sonar, and video. An architectural framework for parallel time-recursive computation is proposed. The authors consider a class of linear operators that consists of the discrete time, time invariant, compactly supported, but otherwise arbitrary kernel functions. They define a shift property of the linear operators and reveal its relation with the time-recursive implementation. The potential of the proposed framework is demonstrated by designing a time-recursive architecture for the discrete wavelet transform. >

A Coding Theorem for Low-Rate Transform Codes

Abstract: Transform codes are used to study low-rate quantization of stationary Gaussian sources. The transform decorrelates the source samples and then scalar quantization is applied to the vector of transform coefficients. Two bit allocations are considered: the first permits only zero or one bit to be allocated to each transform coefficient (i.e., the scalar quantizers have only one or two levels), and the second is an optimal bit allocation. For the transform codes with the "0-1" bit allocation, a closed-form, parametric expression is derived for the asymptotic (with dimension) rate vs. distortion performance. This expression is compared to the rate-distortion function, as well as to the performance of transform codes with optimal bit allocations. The principal result is that there is a critical rate, determined by the power spectral density, below which (and only below which) 0-1 allocations are optimal. This is a unique result in that it determines optimal theoretical performance for an important class of vector quantizes at low rates. Quantitative results are presented for Gauss-Markov sources.

Phase space analysis of the identity decompositions

Abstract: The connections between the decompositions of the identity operator on L2(Rn) and the decompositions of the function 1 on the phase space R2n are considered. The phase space properties of various transformations (such as the Fourier transform, Gabor transform, and wavelet transform, etc.) are investigated.

Why adaptive wavelet transform

Abstract: The freedom of choosing an appropriate kernel of a linear transform, which is given to us by the recent mathematical foundation of the wavelet transform, is exploited fully and is generally called the adaptive wavelet transform However, there are several levels of adaptivity: (1) Optimum Coefficients: adjustable transform coefficients chosen with respect to a fixed mother kernel for better invariant signal representation; (2) Super-Mother: grouping different scales of daughter wavelets of same or different eother wavelets at different shift locations into a new family called a superposition mother kernel for better speech signal classification; (3) Variational Calculus to determine ab initio a constraint optimization mother for a specific task The tradeoff between the mathematical rigor of the complete orthonormality and the speed of order (N) with the adaptive flexibility is finally up to the users' decisions to get their jobs done with the desirable properties Then, to illustrate (1), a new invariant optoelectronic architecture of a wedge-shape filter in the WT domain is given for a scale-invariant signal classification by neural networks© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering Downloading of the abstract is permitted for personal use only

Wavelet transform techniques and signal analysis

Abstract: Traditionally, the most widely used signal analysis tool is the Fourier transform which, by producing power spectral densities (PSDs), allows time dependent signals to be studied in the frequency domain. However, the Fourier transform is global -- it extends over the entire time domain -- which makes it ill-suited to study nonstationary signals which exhibit local temporal changes in the signal's frequency content. To analyze nonstationary signals, the family of transforms commonly designated as short-time Fourier transforms (STFTs), capable of identifying temporally localized changes in the signal's frequency content, were developed by employing window functions to isolate temporal regions of the signal. For example, the Gabor STFT uses a Gaussian window. However, the applicability of STFTs is limited by various inadequacies. The Wavelet transform (NW), recently developed by Grossman and Morlet and explored in depth by Daubechies (2) and Mallat, remedies the inadequacies of STFTs. Like the Fourier transform, the WT can be implemented as a discrete transform (DWT) or as a continuous (integral) transform (CWT). This paper briefly illustrates some of the potential applications of the wavelet transform algorithms to signal analysis.

Use of the wavelet transform for signal detection

Abstract: In this paper, the wavelet transform is used for the purpose of noise reduction and signal enhancement in order to aid in the detection of randomly occurring short duration signals in noisy environments with signal to noise ratios of about -30 dB. The noise is characterized as being additive and consists of correlated interference as well as Gaussian noise. Such problems are encountered in many applications, such as health diagnostics (e.g. electrocardiograms, echo-cardiograms and electroencephalograms), underwater acoustics and geophysical applications where a signature signal passes through multiple media. The wavelet transform, with its basis functions localized both in time and frequency, provides the user with a signal representation suitable for detection purposes. Following the introduction, a brief description of the problem with the characteristics of the signal to be detected and the noise that is present in the environment is given. Then, background information on the wavelet transform is presented. Finally, our results obtained by applying the wavelet transform to signal detection are shown.