Showing papers on "Discrete cosine transform published in 1990"

Discrete Cosine Transform: Algorithms, Advantages, Applications

Abstract: Discrete Cosine Transform. Definitions and General Properties. DCT and Its Relations to the Karhunen-Loeve Transform. Fast Algorithms for DCT-II. Two Dimensional DCT Algorithms. Performance of the DCT. Applications of the DCT. Appendices. References. Index.

Lapped transforms for efficient transform/subband coding

Abstract: Two lapped transforms for subband/transform coding of signals are introduced: a version of the lapped orthogonal transform (LOT), which can be efficiently computed for any transform length; and the modulated lapped transform (MLT), which is based on a modulated quadrature mirror (QMF) bank. The MLT can also be efficiently computed by means of a type-IV discrete sine transform (DST-IV). The LOT and the MLT are both asymptotically optimal lapped transforms for coding an AR(1) signal with a high intersample correlation coefficient. The coding gains of the LOT and MLT of length M are higher than that of the discrete cosine transform (DCT) of the same length; they are actually close to the coding gains obtained with a DCT of length 2M. An MLT-based adaptive transform coder (ACT) for speech signals is simulated; the code is essentially free from frame rate noise and has a better spectral resolution that DCT-based ATC systems. >

Chapter 1 – discrete cosine transform

Abstract: Publisher Summary This chapter presents discrete cosine transform. The development of fast algorithms for efficient implementation of the discrete Fourier transform (DFT) by Cooley and Tukey in 1965 has led to phenomenal growth in its applications in digital signal processing (DSP). The discovery of the discrete cosine transform (DCT) in 1974 has provided a significant impact in the DSP field. While the original DCT algorithm is based on the FFT, a real arithmetic and recursive algorithm, developed by Chen, Smith, and Fralick in 1977, was the major breakthrough in the efficient implementation of the DCT. A less well-known but equally efficient algorithm was developed by Corrington. Subsequently, other algorithms, such as the decimation-in-time (DIT),decimation-in-frequency (DIF), split radix, DCT via other discrete transforms such as the discrete Hartley transform (DHT) or the Walsh-Hadamard transform (WHT), prime factor algorithm (PFA), a fast recursive algorithm, and planar rotations, which concentrate on reducing the computational complexity and/or improving the structural simplicity, have been developed. The dramatic development of DCT-based DSP is by no means an accident.

Low bit rate transform coder, decoder and encoder/decoder for high-quality audio

Abstract: A low bit-rate (192 kBits per second) transform encoder/decoder system (44.1 kHz or 48 kHz sampling rate) for high-quality music applications employs short time-domain sample blocks (128 samples/block) so that the system signal propagation delay is short enough for real-time aural feedback to a human operator. Carefully designed pairs of analysis/synthesis windows are used to achieve sufficient transform frequency selectivity despite the use of short sample blocks. A synthesis window in the decoder has characteristics such that the product of its response and that of an analysis window in the encoder produces a composite response which sums to unity for two adjacent overlapped sample blocks. Adjacent time-domain signal samples blocks are overlapped and added to cancel the effects of the analysis and synthesis windows. A technique is provided for deriving suitable analysis/synthesis window pairs. In the encoder, a discrete transform having a function equivalent to the alternate application of a modified Discrete Cosine Transform and a modified Discrete Sine Transform according to the Time Domain Aliasing Cancellation technique or, alternatively, a Discrete Fourier Transform is used to generate frequency-domain transform coefficients. The transform coefficients are nonuniformly quantized by assigning a fixed number of bits and a variable number of bits determined adaptively based on psychoacoustic masking. A technique is described for assigning the fixed bit and adaptive bit allocations. The transmission of side information regarding adaptively allocated bits is not required. Error codes and protected data may be scattered throughout formatted frame outputs from the encoder in order to reduce sensitivity to noise bursts.

Human visual weighted progressive image transmission

Abstract: A progressive image transmission scheme which combines transform coding with the human visual system (HVS) model is developed. The adaptive transform coding of W.H. Chen and C.H. Smith (1977) is utilized to classify an image into four equally populated subblocks based on their AC energies. The modulation transfer function (MTF) of the HVS model is obtained experimentally, based on processing a number of test images. A simplified technique for incorporating the MTF into the discrete cosine transform (DCT) domain is utilized. In the hierarchical image buildup, the image is first reconstructed from the DC coefficients of all subblocks. Further transmission hierarchy of transform coefficients and consequent image buildup are dependent on their HVS weighted variances. The HVS weighted reconstructed images are compared to the ones without any weighting at several stages. The HVS weighted progressive image transmission results in perceptually higher quality images compared to the unweighted scheme. >

Polynomial transform computation of the 2-D DCT

Abstract: A 2-D DCT (discrete cosine transform) algorithm based on a direct polynomial approach is presented. The resulting algorithm reduces the number of both multiplications and additions compared to previous algorithms. It is shown that, although being mathematically involved, it possesses a clean, butterfly-based structure. Tables comparing the number of operations are provided, as well as flowgraphs. >

Image data processing apparatus

Abstract: An image data processing apparatus includes a converter for subjecting each block to a discrete cosine transform (DCT) to convert blocks into DCT coefficients, a first memory for temporarily storing the DCT coefficients, a second memory for storing threshold values of a quantization matrix which is used for quantizing the DCT coefficients, a quantizing part for quantizing the DCT coefficients, a differential part for obtaining a difference in D.C. components of quantized DCT coefficients related to present and previous blocks, a zero detector for detecting whether or not A.C. components of the quantized DCT coefficient are zero coefficients, a counter for counting a number of successive zero coefficients of the A.C. components, a coder for subjecting the D.C. and A.C. components to a Huffman coding to output a coded D.C. and A.C. components, a first register for storing an address of an arbitrary DCT coefficient, a comparator for comparing an address where the DCT coefficient is stored in the first memory and the address in the first register, and a second register for holding the DCT coefficient output from the converter when the two compared addresses match.

Digital compression method and system with improved coding efficiency

Abstract: In a method for creating a scan sequence for a single chip color camera an analysis of typical images, captured through a color filter array, is performed to determine an optimal scan sequence for the particular array and/or the typical images. The images, after being digitally captured, are separated into red, green and a blue image databases and the color databases are processed separately. A Discrete Cosine Transform is performed on blocks of the image data and the average RMS values for the coefficients of the images are determined. The RMS values are sorted in descending order to produce a descending scan sequence that optimizes the performance of run length coding schemes. The scan sequence can be stored in a hardware, firmware or software lookup table as a list of block coordinates or indices and used by the camera system to convert two dimensional blocks of coefficients into one dimensional lists of coefficients suitable for run length coding. The block coefficients are used to convert the decoded coefficients into image blocks before presentation on a color CRT of before producing a color print. By incorporating the method into an image capture system an adaptive system which will optimize coding for different image environments and/or different color filter arrays suitable for the different environments is produced.

DCT algorithms for VLSI parallel implementations

Abstract: Two algorithms are presented for computing the discrete cosine transform (DCT) on existing VLSI structures. First, it is shown that the N-point DCT can be implemented on the existing systolic architecture for the N-point discrete Fourier transform (DFT) by introducing some modifications. Second, a new prime factor DCT algorithm is presented for the class of DCTs of length N=N/sub 1/*N/sub 2/, where N/sub 1/ and N/sub 2/ are relatively prime and odd numbers. It is shown that the proposed algorithm can be implemented on the already existing VLSI structures for prime factor DFT. The number of multipliers required is comparable to that required for the other fast DCT algorithms. It is shown that the discrete sine transform (DST) can be computed by the same structure. >

A fast recursive algorithm for the discrete sine transform

Abstract: A fast recursive algorithm for the discrete sine transform (DST) is developed. An N-point DST can be generated from two identical N/2-point DSTs. Besides being recursive, this algorithm requires fewer multipliers and adders than other DST algorithms. It can be considered as a generalization of the Cooley-Tukey FFT (fast Fourier transform) algorithm. The structure of the algorithm is suitable for VLSI implementation. >

Direct methods for computing discrete sinusoidal transforms

Abstract: According to Wang, there are four different types of DCT (discrete cosine transform) and DST (discrete sine transform) and the computation of these sinusoidal transforms can be reduced to the computation of the type-IV DCT. As the algorithms involve different sizes of transforms at different stages they are not so regular in structure. Lee has developed a fast cosine transform (FCT) algorithm for DCT-III similar to the decimation-in-time (DIT) Cooley–Tukey fast Fourier transform (FFT) with a regular structure. A disadvantage of this algorithm is that it involves the division of the trigonometric coefficients and may be numerically unstable. Recently, Hou has developed an algorithm for DCT-II which is similar to a decimation-in-frequency (DIF) algorithm and is numerically stable. However, an index mapping is needed to transform the DCT to a phase-modulated discrete Fourier transform (DFT), which may not be performed in-place. In the paper, a variant of Hou's algorithm is presented which is both in-place and numerically stable. The method is then generalised to compute the entire class of discrete sinusoidal transforms. By making use of the DIT and DIF concepts and the orthogonal properties of the DCTs, it is shown that simple algebraic formulations of these algorithms can readily be obtained. The resulting algorithms are regular in structure and are more stable than and have fewer arithmetic operations than similar algorithms proposed by Yip and Rao. By means of the Kronecker matrix product representation, the 1-D algorithms introduced in the paper can readily be generalised to compute transforms of higher dimensions. These algorithms, which can be viewed as the vector-radix generalisation of the present algorithms, share the in-place and regular structure of their 1-D counterparts.

Systolic architectures for the computation of the discrete Hartley and the discrete cosine transforms based on prime factor decomposition

Abstract: Two-dimensional systolic array implementations for computing the discrete Hartley transform (DHT) and the discrete cosine transform (DCT) when the transform size N is decomposable into mutually prime factors are proposed. The existing two-dimensional formulations for DHT and DCT are modified, and the corresponding algorithms are mapped into two-dimensional systolic arrays. The resulting architecture is fully pipelined with no control units. The hardware design is based on bit serial left to right MSB (most significant bit) to LSB (least significant bit) binary arithmetic. >

Clinical evaluation of irreversible image compression: analysis of chest imaging with computed radiography.

Abstract: To implement a picture archiving and communication system, clinical evaluation of irreversible image compression with a newly developed modified two-dimensional discrete cosine transform (DCT) and bit-allocation technique was performed for chest images with computed radiography (CR). CR images were observed on a cathode-ray-tube monitor in a 1,024 X 1,536 matrix. One original and five reconstructed versions of the same images with compression ratios of 3:1, 6:1, 13:1, 19:1, and 31:1 were ranked according to quality. Test images with higher spatial frequency were ranked better than those with lower spatial frequency and the acceptable upper limit of the compression ratio was 19:1. In studies of receiver operating characteristics for scoring the presence or absence of nodules and linear shadows, the images with a compression ratio of 25:1 showed a statistical difference as compared with the other images with a compression ratio of 20:1 or less. Both studies show that plain CR chest images with a compression...

Discrete cosine transform filtering

Abstract: Circular convolution-multiplication relationships for the discrete cosine transform (DCT) that are similar to those for the discrete Fourier transform (DFT) are developed. The relations are valid if the filter frequency response is real and even. Two fairly simple relations are developed. The multiplication of the DCT of signal sequence and the DFT of filter sequence results in circular convolution of the folded signal sequence and the filter sequence. Thus, it can be used to filter an image in the frequency domain as an approximation of circular convolution in the spatial domain. >

DCT/DST alternate-transform image coding

Abstract: An image coding method for low bit rates is proposed. It is based on alternate use of the discrete cosine transform (DCT) and the discrete sine transform (DST) on image blocks. This procedure achieves the removal of redundancies in the correlation between neighboring blocks as well as the preservation of continuity across the block boundaries. An outline of the mathematical justification of the method, assuming a certain first-order Gauss-Markov model, is given. The resulting coding method is then adapted to nonstationary real images by locally adapting the model parameters and improving the block classification technique. Simulation results are shown and compared with the performance of related previous methods, namely adaptive DCT and fast Karhunen-Loeve transform (FKLT). >

Visual telephony as an ISDN application

Abstract: The key factors deterring the use of visual telephony are identified, and an overview of a typical system architecture is given. The video signal formats and video and audio coding algorithms used are described. Video codec implementation is considered, and an implementation based on application-specific integrated circuits is presented. In particular, three key signal processing modules in the video codec are examined: a discrete cosine transform chip, a motion estimation chip, and a variable-length codec chip. Standardization activities in the video coding area are discussed. >

Method and apparatus for performing image compression using discrete cosine transform

Abstract: A method and apparatus for performing data compression is disclosed that does not require interpolation of pixel data in order to define image blocks. More specifically, the present invention provides spatially interleaved image blocks composed of high frequency image components by sampling the high frequency image components at a pitch or spatial sample frequency equal to that of the low frequency image components. The present invention provides the added advantage of reducing the number of image blocks that must be defined in order to perform data compression.

Optimal block cosine transform image coding for noisy channels

Abstract: A method is presented for the joint source-channel coding optimization of a scheme based on the two-dimensional block cosine transform when the output of the encoder is to be transmitted via a memoryless binary symmetric channel. The authors' approach involves an iterative algorithm for the design of the quantizers (in the presence of channel errors) used for encoding the transform coefficients. This algorithm produces a set of locally optimum (in the mean-squared error sense) quantizers and the corresponding binary codeword assignment for the assumed transform coefficient statistics. To determine the optimum bit assignment among the transform coefficients, the authors have used an algorithm based on the steepest descent method, which, under certain convexity conditions on the performance of the channel-optimized quantizers, yields the optimal bit allocation. Simulation results for the performance of this locally optimum system over noisy channels have been obtained, and appropriate comparisons with a reference system designed for no channel errors have been made. It is shown that substantial performance improvements can be obtained by using this scheme. Furthermore, theoretically predicted results and rate distortion-theoretic bounds for an assumed two-dimensional image model are provided. >

Fast scaled-DCT algorithm

Abstract: The Discrete Cosine Transform (DCT) followed by scaling and quantiza.tion is an ml- portant operation in image processing. Because of the scaling, the DCT itself need not he computed, but rather a scalar mu]tiple of the DCT might do, with appropriate compensationincorporated into the scaling. We present a fast method for computing such scaled output ofthe 2-dimensional DCT on 8 x 8 points. We also present a similar algorithm for the inversescaled DCT.1. INTRODUCTIONThe discrete cosine transform (DCT) plays an important role in digital image processing.Of particular interest is the two-dimensional DCT followed by scaling and quantiza.tion. This has applications in data compression of continuous tone images [1, 11]. Because the DCT is so often used, research into fast algorithms for its implementation has been rather active[3, 4, 5, 7, 8, 9, 10, 12, 13, 14, 15].Given an array y(k) , 0 k  K — 1, of input data, its one-dimensional DCT output is K—i (irn(2k+1)\ y(n) = c(n) cost i y(),

Transform coding using coefficient prediction techniques

Abstract: A system and method for improving the quality of decoded images, without any cost to compression efficiency, in both progressive still frame and motion video applications wherein the images are coded with intraframe transform based coding techniques, such as Discrete Cosine Transform (DCT) coding. Prediction of the AC components is utilized and operations are performed on the AC coefficient prediction in the decoder portions of the system in combination with a thresholding technique. Input images are subdivided into blocks of pixels, which are changed into blocks of coefficients by forward transform coding resulting in DC coefficients, representative of the average value in a block of pixels, and AC coefficients, representative of harmonic frequencies in a block of pixels. AC coefficient prediction is performed using both DC and AC coefficients from the block, whereupon the predicted coefficient values are thresholded and the thresholded coefficient values are added to their corresponding transform coefficient values for the given block. These steps are repeated for all of the blocks of the image and the image representation is recovered by applying an inverse transform operation to the results of all of the additions for all of the blocks of the image.

DigiCipher-all digital, channel compatible, HDTV broadcast system

Abstract: DigiCipher, an all-digital HDTV (high-definition television) system, with transmission over a single 6 MHz VHF or UHF channel, is described. It provides full HDTV performance with virtually no visible transmission impairments due to noise, multipath, and interference. It offers high picture quality, while the complexity of the decoder is low. Furthermore, low transmitting power can be used, making it ideal for simulcast HDTV transmission using unused or prohibited channels. DigiCipher can also be used for cable and satellite transmission of HDTV. There is no satellite receive dish size penalty (compared to FM-NTSC) in the satellite delivery of DigiCipher HDTV. To achieve the full HDTV performance in a single 6 MHz bandwidth, a highly efficient unique compression algorithm based on DCT (discrete cosine transform) transform coding is used. Through the extensive use of computer simulation, the compression algorithm has been refined and optimized. Computer simulation results show excellent video quality for a variety of HDTV material. For error-free transmission of the digital data, power error correction coding combined with adaptive equalization is used. At a carrier-to-noise ratio of above 19 dB, essentially error-free reception can be achieved. >

Discrete cosine transform processing system

Abstract: A three dimensional (3D) discrete cosine transform (DCT) uses one dimensional DCT networks for transforming and inverse-transforming blocks of data, such as image data. The 3D DCT configuration uses DCT transform coding to remove both the spatial and temporal redundancy of a sequence of image frames to achieve high bandwidth compression.

Coded picture information decoding apparatus having means for improving picture distortion

Abstract: A coded picture information decoding apparatus includes a decoder part for decoding a code word corresponding to a serious of transfer coefficients obtained by carrying out a discrete cosine transform for picture information to be transmitted in a block unit obtained by dividing the picture information on a coder side and for reproducing the series of transfer coefficients, and an inverse transform part for carrying out an inverse discrete cosine transform for the series of transfer coefficients reproduced by the decoder part in the block unit and for outputting reproduced picture information. The apparatus also includes a prediction part for predicting, in the block unit, whether or not a picture distortion will occur on the basis of the transfer coefficients obtained in the block unit and for outputting a prediction result obtained in the block unit. Further, the apparatus includes an image processing unit for carrying out a predetermined image process of preventing the occurrence of the picture distortion for the reproduced picture information related to a block indicated by the prediction result showing that the occurrence of the picture distortion is predicted.

A chip set core for image compression

Abstract: Two components for image compression which provide almost all the computational power required by today's efficient codecs for full motion image compression are presented. The first component computes 8*8 discrete-cosine transform and zigzag conversion of coefficient scanning for a pixel rate up to 27 MHz. The second component computes full-search motion estimation for a pixel rate up to 18 MHz. System implementation for image compression is discussed. >

Variable block-size transform image coder

Abstract: A discrete cosine transform image coding scheme based on adaptive block size is proposed and demonstrated. The scheme adaptively optimizes the block sizes according to some local activity indexes of the image scenes. The optimization is achieved by applying the technique from graph theory. Nine rectangular block sizes are used, corresponding to all combinations of 8, 16, and 32 pixels per side. This approach reduces interblock correlation between coefficients, and increases the energy compaction in the transform domain. Experimental results are presented and compared to results obtained by an identical coder using a fixed block size. >

Adaptive cosine transform image coding with constant block distortion

Abstract: An adaptive block discrete-cosine transform (DCT) coding scheme is implemented with the same average distortion designated for each block. This constant distortion designation not only has perceptual advantages, but also allows the rate to vary, adjusting to the changing spectral characteristics among the blocks. The successful execution of this scheme requires a different spectral estimate for each block. To keep overhead and computation within limits, a novel technique is introduced by which a two-dimensional block spectrum is characterized by a one-dimensional autoregressive model. Simulations with images of natural scenes and medical radiology provide reconstructions with nearly uniform block distortion and very high visual and measurable quality at low rates. >

High fidelity audio transform coding with vector quantization

Abstract: Multi-stage tree-structured vector quantization (MSTVQ) is examined as an alternative to entropy constrained scalar quantization (ECSQ) in transform coding of high fidelity audio signals with a simultaneous masking model for distortion control. Discrete-cosine-transform coefficients are normalized by an interpolated spectral power envelope and groups of adjacent coefficients are vector coded with variable rate to achieve distortion-masking. With the current coder configuration, high fidelity quality for a sampling rate of 32 kHz is achievable with data rates below 64 kbps for some transform and masking model, preliminary results show that MSTVO and ECSQ have a similar rate-distortion performance. >

Interpolation using type I discrete cosine transform

Abstract: A novel interpolation method, using the type I discrete cosine transform (DCT-I), is introduced. The original definition of the DCT-I has been modified to suit this application. Three options for the modified DCT-I are proposed.

The stability of the sine and cosine functional equations

Abstract: In this work the stability of the functional equations describing the addition theorems for sine and cosine is proved.