Showing papers on "S transform published in 1987"

Discrete radon transform

Abstract: This paper describes the discrete Radon transform (DRT) and the exact inversion algorithm for it. Similar to the discrete Fourier transform (DFT), the DRT is defined for periodic vector-sequences and studied as a transform in its own right. Casting the forward transform as a matrix-vector multiplication, the key observation is that the matrix-although very large-has a block-circulant structure. This observation allows construction of fast direct and inverse transforms. Moreover, we show that the DRT can be used to compute various generalizations of the classical Radon transform (RT) and, in particular, the generalization where straight lines are replaced by curves and weight functions are introduced into the integrals along these curves. In fact, we describe not a single transform, but a class of transforms, representatives of which correspond in one way or another to discrete versions of the RT and its generalizations. An interesting observation is that the exact inversion algorithm cannot be obtained directly from Radon's inversion formula. Given the fact that the RT has no nontrivial one-dimensional analog, exact invertibility makes the DRT a useful tool geared specifically for multidimensional digital signal processing. Exact invertibility of the DRT, flexibility in its definition, and fast computational algorithm affect present applications and open possibilities for new ones. Some of these applications are discussed in the paper.

The Radon transform and its application to shape parametrization in machine vision

Abstract: A general method is presented that uses the Radon transform as a means of defining a two-dimensional transform space in which information about different, analytically defined shape primitives in an edge image space may be encoded simultaneously. Examples are given illustrating how the shape-indicative distributions within the transform space may be deduced. The results show that each set of coded information is transparent to any other and that each shape-indicative distribution may be located using a convolution mask peculiar to that distribution.

Time and frequency representation of acoustic signals by means of the Wigner distribution function: Implementation and interpretation

Abstract: The Wigner distribution function, originally introduced in quantum mechanics, is shown to have a similar formulation as the Fourier transform of the time‐dependent correlation function for a time‐varying signal. Review of its mathematical properties indicates that such an expression is suitable for representing the signal simultaneously in the time and frequency domains. Furthermore, reformating the Wigner distribution function with a certain window function leads to a proof that this modified version, the pseudo‐Wigner distribution function, always has a positive value and hence can be interpreted as a proper description of the dynamics for the signal’s power density spectrum change with time. The implementation of the Wigner distribution function for digital processing can be carried out simply by adapting the fast Fourier transform algorithm. Examples of its application to several types of acoustic signals are used to illustrate their dynamic features jointly in time and frequency representation.

VLSI Architectures for Multidimensional Fourier Transform Processing

Abstract: It is often desirable in modern signal processing applications to perform two-dimensional or three-dimensional Fourier transforms. Until the advent of VLSI it was not possible to think about one chip implementation of such processes. In this paper several methods for implementing the multidimensional Fourier transform together with the VLSI computational model are reviewed and discussed. We show that the lower bound for the computation of the multidimensional transform is O(n2 log2 n). Existing nonoptimal architectures suitable for implementing the 2-D transform, the RAM array transposer, mesh connected systolic array, and the linear systolic matrix vector multiplier are discussed for area time tradeoff. For achieving a higher degree of concurrency we suggest the use of rotators for permutation of data. With ``hybrid designs'' comprised of a rotator and one-dimensional arrays which compute the one-dimensional Fourier transform we propose two methods for implementation of multidimensional Fourier transform. One design uses the perfect shuffle for rotations and achieves an AT2 p of O(n2 log2 n· log2 N). An optimal architecture for calculation of multidimensional Fourier transform is proposed in this paper. It is based on arrays of processors computing one-dimensional Fourier transforms and a rotation network or rotation array. This architecture realizes the AT2 p lower bound for the multidimensional FT processing.

Transform and Hybrid Transform/DPCM Coding of Images Using Pyramid Vector Quantization

Abstract: The transform and hybrid transform/DPCM methods of image coding are generalized to allow pyramid vector quantization of the transform coefficients. An asymptotic mean-squared error performance expression is derived for the pyramid vector quantizer and used to determine the optimum rate assignment for encoding the various transform coefficients. Coding simulations for two images at average rates of 0.5-1 bit/pixel demonstrate a 1-3 dB improvement in signal-to-noise ratio for the vector quantization approach in the hybrid coding, with more modest improvements in signal-to-noise ratio in the transform coding. However, this improvement is quite noticeable in image quality, particularly in reducing "blockiness" in the low bit rate encoded images.

A new approach to recursive Fourier transform

Abstract: In the recursive Fourier transform, the data window can be chosen such that the number of computations required to update the transform at each frequency upon reception of a new data sample is independent of the transform block length.

Transform amplitude sharpening: a new method of image enhancement

Abstract: A new frequency-domain based technique is proposed. In the proposed method, the magnitude of the Fourier transform of the image is modified using a noval amplitude change function with the phase kept invariant. The inverse transform of the new 2D transform results in an enhanced image. The amplitude change function used is the Tukey's twicing function ( Exploratory Data Analysis , Addison-Wesley, Reading, MA, 1977). In many applications, multiple use of the twicing function is shown to yield better results. The proposed method is somewhat similar to the alpha-rooting method but does not suffer from certain objectionable artifacts associated with the latter and also exhibits less degradation due to noise. A postprocessing of the enhanced image generated using the proposed transform amplitude method via histogram modification has been found to improve the picture quality. A number of image enhancement examples are included illustrating the effectiveness of the proposed method.

A separable Hartley-like transform in two or more dimensions

Abstract: This letter introduces a discrete, separable, real-to-real transform, called the cas-cas transform. Theorems for the two-dimensional (2-D) case are presented, and the cas-cas transform is compared to the Hartley transform as an alternative way to convolve 2-D arrays and compute 2-D power spectra.

Selection of the Transformation Variable in the Laplace Transform Method of Estimation

Abstract: Summary The work of this paper is based on the innovative approach of Feigin et al. (1983), who estimate parameters of lifetime distributions by equating empirical and theoretical Laplace transforms. We show that the optimal choice of the transform variable depends critically upon the number of sampling times, the way they are spaced, and how the empirical transform is formed. Two new approaches for choosing the transform variable, viz. using cross-validation or constrained optimisation, are introduced and shown to have potential for wide-ranging use.

Orthogonal transformation coding system

Abstract: PURPOSE: To realize high encoding efficiency in spite of the state of an image, by selecting an orthogonal transform data of minimum differential quantity by an arithmetic means, and coding the differential signal. CONSTITUTION: By taking a difference between the orthogonal transform data and plural data by differentiators 103∼106, and selecting the data with the highest efficiency by a selector 108 based on prescribed reference, coding as a differential data is applied. In other words, plural data are the orthogonal transform data of the same block of all of the frames, the orthogonal transform data of the partial block of a present frame, the orthogonal transform data of a background image consisting of a temporally integrated background image or an image block at a specific time, and the orthogonal transform data at the specific time. Thus, by using the orthogonal transform data consisting of the temporally integrated background image or the image block at the specific time, the differential data goes to a very small value when a certain image part is returned to its original position in the reciprocal movement of the certain image part, then, it is possible to improve the coding efficiency more remarkably than the orthogonal transform data at the same position of all of the frames. COPYRIGHT: (C)1988,JPO&Japio

Reconstruction of complex-valued propagating wave fields using the Hilbert–Hankel transform

Abstract: In this paper the theory of the unilateral inverse Fourier transform and the unilateral Hankel transform is developed. The consistency between each transform and its bilateral version leads to an approximate real-part sufficiency condition for complex-valued one-dimensional even signals and two-dimensional circularly symmetric signals. The two-dimensional result is used in a reconstruction algorithm that is applied to synthetic -and experimental underwater acoustic fields.

Comparative study of time efficiency of several algorithms for discrete W transform and discrete Hartley transform

Abstract: Subroutines for several algorithms for the computation of the discrete W transform and the discrete Hartley transform are implemented in a YNC-M240D computer for testing of their time efficiency. Results show that the subroutines for the fast W transform algorithm reported recently are more efficient than subroutines for radix-2, radix-4 and the split radix fast Hartley transform algorithms.

A new image data compression method–extrapolative prediction–discrete sine transform coding (in the case of one–dimensional coding)

Abstract: This paper proposes the extrapolative prediction-discrete sine transform as a new highly efficient coding for the gray-level image In the proposed method, an extrapolative prediction is made from the immediately preceding pixel to the present pixel block, and the prediction error signal is encoded by the orthogonal transform Assuming that the information source for the image is a stationary first-order Markov process in the wide sense, it is shown that the orthogonal transform which decorrelates the prediction error signal can be approximated by a certain kind of sine transform An algorithm is presented for the high-speed execution of this data The rate-distortion characteristic is discussed for the case of one-dimensional coding, and it is shown theoretically that the coding efficiency of the proposed method is nearly the same as those of the discrete 16-pixel cosine transform with block length of 4 pixels and the 8-pixel fast Karhunen-Loeve transform Comparing the coding complexities of those methods, the proposed method is shown to be especially advantageous in the hardware realization Computer simulations were made for actual images using the fixed-rate coding and variable-rate coding (entropy coding), and the result supports the idea

Transform coding of synthetic aperture radar (SAR) images

Abstract: Transform Coding is a type of source coding that is used to compress the data required for images without substantial loss of fidelity. Transform Coding has been studied by many authors for optical images and the results have shown favorable compression ratios on the order of 10 to 1 without noticeable loss of picture quality. This is due to the highly correlated nature of typical images. Observable autocorrelation lags for SAR imagery seldom occur past lags of 3 or 4. However, since correlation exists, a reduction of the data can be achieved. The approach taken in this paper was to achieve data compression on SAR images by the use of Karhunen-Loeve, Walsh and Cosine Transform coding. All coefficients of each transform were allocated a variable number of bits using the Huang and Schultheiss [1] approach followed by the Lloyd-Max quantizer [2,3]. Experiments were done with several variations of the basic transform coding scheme.

A new VLSI architecture for image data rate discrete cosine transform processor

Abstract: The Discrete Cosine Transform (DCT) [1] is presently the best known transform image encoder that performs closest to the theoretically optimal karhunen-loeve transform [1]. The kernel of DCT has both periodicity and symmetry properties. The most efficient DCT implementation todate is due to B.G.Lee [2]. His Fast Cosine Transform algorithm [2] is based on a decimation in time scheme resulting in butterfly structural units with some similarity to Fast Fourier Transform [FFT]. In this paper [3] a new approach of direct sample by sample DCT has been adopted. Using distributed arithmetic [4] multipliers has been replaced by adders, and the memory requirements has been significantly reduced by exploiting the symmetry and periodicity of the DCT kernel.

Two-Dimensional Hybrid Image Coding And Transmission

Abstract: Image data compression is achieved through the use of a two-dimensional (2-D) transform operation on the gray-level pixels within an image subsection followed by 2-D DPCM encoding of common transform coefficients from disjoint image subsections. Earlier results for this 2-D hybrid scheme employing the Discrete Cosine Transform (DCT) indicate an overall improvement in image source coding gain vis-a-vis conventional 2-D transform coding. Hybrid system performance dependence on transform block size is demonstrated along with the rank-ordering of the relative performance obtained when using the Haar, Walsh, Slant and DCT 2-D orthogonal transforms. It is shown that performance gains over conventional block 2-D transform coding are realized for transforms which are less efficient than the DCT. This hybrid system will provide a means of substantially improving existing hardware transform coding systems with a minimal increase in hardware complexity.

A dynamic spectral transform and its statistical characteristics

Abstract: A generalized spectral transform is defined by extending the kernel of the conventional sectionalized Fourier transform (SFT). The generalized transform accumulates signal energy along narrow dynamic spectral channels which may be made to conform to the instantaneous frequency dynamics of a given signal. This property may be used to achieve optimum detection of a deterministically known signal, or to estimate the spectral dynamics of an unknown signal over the temporal limits of the transform. As an initial step toward achieving the general spectral transform, the canted spectral transform (CST) is defined by using a quadratic phase kernel. The statistical properties of the CST are derived and compared with those of the conventional SFT. Statistical distributions of the peak cant variable for simulated signals in Gaussian noise provide a basis for determining the performance of the CST in practical applications.