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Topic: Transform coding

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	Transform Coding
		Transform coding is used to convert spatial image pixel values to transform coefficient values.
		The lapped orthogonal transforms are a special case in which the coefficients' influence is confined to a few adjacent blocks, with a tapering-off influence toward the edges.
		A portion of a sine wave coded with a Fourier transform has all the energy concentrated at the same frequency coefficients regardless of the phase of the sinusoid (although the energy will be apportioned differently between the sine and cosine components).
	www.bretl.com /mpeghtml/xfrmcode.HTM (567 words)

	Transform coding - Wikipedia, the free encyclopedia
		Transform coding is a type of data compression for "natural" data like audio signals or photographic images.
		In transform coding, knowledge of the application is used to choose information to discard, thereby lowering its bandwidth.
		The common JPEG image format is an example of a transform coding, one that examines small blocks of the image and "averages out" the color using a discrete cosine transform to form an image with far fewer colors in total.
	en.wikipedia.org /wiki/Transform_coding (426 words)

	Dynamic bit allocation subband excited transform coding method and apparatus - Patent 5235671
		A speech coding system as claimed in claim 1 wherein the means for determining iteratively estimates distortion and computes for each distortion estimate a bit allocation across the spectrum to allocate a predetermined number of bits.
		A speech coding system as claimed in claim 4 wherein the means for determining tunes the computed bit allocation toward the number of available bits by adding bits to higher energy subbands or subtracting bits from lower energy subbands.
		A speech coding system as claimed in claim 1, further comprising a power spectrum means for estimating spectral power density of each subband of coefficients, wherein the means for determining a quantizer determines each quantizer based upon the spectral power density of the subbands of coefficients.
	www.freepatentsonline.com /5235671.html (4710 words)

	Image Compression - from DCT to Wavelets : A Review
		Transform coding, on the other hand, first transforms the image from its spatial domain representation to a different type of representation using some well-known transform and then codes the transformed values (coefficients).
		The construction is based on writing a wavelet transform in terms of lifting, which is a flexible technique that has been applied to the construction of wavelets through an iterative process of updating a subband from an appropriate linear combination of the other subbands.
		Interaction of harmonic analysis with data compression, joint source-channel coding, image coding based on models of human perception, scalability, robustness, error resilience, and complexity are a few of the many outstanding challenges in image coding to be fully resolved and may affect image data compression performance in the years to come.
	www.acm.org /crossroads/xrds6-3/sahaimgcoding.html (5361 words)

	Fast Lossless Transform Coding: (Site not responding. Last check: 2007-09-10)
		Transform coding is commonly used in many different source coding schemes, but is generally applied in a lossy fashion.
		Furthermore, transforms in finite fields have an advantage over integer transforms in that the result of a transform in a finite field is bounded to within a much smaller range than that of similar integer transforms.
		Therefore, a potential class of transforms to use for lossless coding is transforms in a finite field.
	www.eecs.umich.edu /~holtk/reports/ffwavelet (2689 words)

	whoop de doo
		The general idea behind transform coding is to pack the energy of an image into fewer pixels.
		In the transform domain the pixels with large values are represented with many bits and the ones with small values with fewer bits.
		Requires three inputs: the wavelet transform to be quantized, a "quantization vector", and the filename to write to.
	www.owlnet.rice.edu /~elec539/Projects99/NSJS/project1 (950 words)

	ATRAC: Adaptive Transform Acoustic Coding for MiniDisc
		Transform coefficients are grouped into nonuniform bands to reflect the human auditory system, and then quantized on the basis of dynamic sensitivity and masking characteristics.
		The goal of many audio coding systems [1-6] is to control the time-frequency distribution of this noise in such a way as to render it inaudible to the human ear.
		Using a combination of subband coding and transform coding techniques, the input signal is analyzed in nonuniform frequency divisions which emphasize the important low-frequency regions.
	www.minidisc.org /aes_atrac.html (2390 words)

	Transform coding versus Subband Coding - Hydrogenaudio Forums
		With subband coding, the quantization noise is constrained within the channels, with transform coding the quantization noise is smeared in the time domain.
		In subband image coding, esp. using wavelets, coarse quantisation of the high frequency subbands leads to 'ringing' in the edges, thus the distortion is somewhat localised.
		Basically what they found was that both transform coding in the Fourier domain and subband coding, the quadratic error decreases proportionately as 1/M for linear approximations.
	www.hydrogenaudio.org /forums/index.php?showtopic=4895 (946 words)

	Wyner-Ziv Coding of Video
		A model was proposed to predict the average received picture quality delivered by the SLEP system as a function of the encoding bit rates of the primary and redundant descriptions, the bit rate of the parity symbols transmitted in the Wyner-Ziv bit stream, and the probability with which packets are lost during transmission [Rane_PCS2006].
		The theoretical study of linear transforms shows that, under certain conditions, the Karhunen-Loeve transform of the source vector is determined by its expected conditional covariance given the side information, which is approximated by the DCT for conditionally stationary processes.
		Applying conventional run-length coding on the high frequency coefficients of a frame and using these coefficients to perform motion estimation at the decoder is effective in generating reliable side information for the Wyner-Ziv encoded low frequencies.
	ivms.stanford.edu /~dsc/wzcodingvideo (3531 words)

	The Wavelet Digest :: View topic - Thesis: Beyond Traditional Transform Coding
		transform coding, the original signal is mapped to an intermediary
		scalar quantization of the intermediary and entropy coding.
		Transform coding is normally used solely for source coding.
	www.wavelet.org /phpBB2/viewtopic.php?t=4927 (285 words)

	Decompression of standard ADCT-compressed images - Patent 5379122
		A method as described in claim 1, wherein the forward transform coding operation using the frequency space transform operation is a discrete cosine transform.
		A method as described in claim 6, wherein the forward transform coding operation using the frequency space transform operation is a discrete cosine transform.
		This statistical coding is performed in a lossless way and the only loss introduced in the compression is the one generated by the quantization of the DCT coefficients using the Q-Table.
	www.freepatentsonline.com /5379122.html (5473 words)

	Priority coding of transform coefficients (US4751742)
		Another disclosed aspect relates to the transmission of transform domain coefficients for an image which is undergoing change with time, and applies to any transform for which transform domain coefficients can be organized in a hierarchial manner in multiple bands, regardless of the manner in which the transform process actually proceeds.
		Identical transform coefficient models are maintained at both the transmitter and the receiver.
		The transmitter identifies transform coefficient changes necessary to cause a transform coefficient model to completely represent the most current image, prioritizes the change data, and selects a subset of said change data consistent with the limitation of a fixed rate transmission channel.
	www.delphion.com /details?pn10=US04751742 (508 words)

	Digital Image Processing: Block Transform Coding -- from Mathematica Information Center
		Transform methods are typically used in filtering, compression, and image texture analysis.
		Transform coding compresses image data by representing the original signal with a small number of transform coefficients.
		Transform coding is an integral part of the Joint Photographic Experts Group (JPEG) standard for lossy image compression.
	library.wolfram.com /infocenter/Demos/397 (156 words)

	Sign Coding in an Embedded Wavelet Image Coder (Site not responding. Last check: 2007-09-10)
		While promising algorithms exist for efficiently coding the transform magnitudes, current wavelet image coding algorithms are not efficient at coding the sign of the transform coefficients.
		However the wavelet transform coefficients themselves are not restricted as such, and are defined by both a magnitude and a sign.
		The ability of a wavelet transform to compact the energy of an image into a small fraction of the transform coefficients says nothing about the nature of the signs of these coefficients, but rather only speaks of their magnitudes.
	foulard.ee.cornell.edu /adeever/sc.html (564 words)

	Lossless Transform Coding of Audio Signals - Purat, Liebchen, Noll (ResearchIndex) (Site not responding. Last check: 2007-09-10)
		Transform coding, however, hasn't been investigated so far, although it seems to be more adapted to the harmonic structure of most audio signals.
		Using a codebook with different entropy codes for the transform...
		This approach is very similar in nature to the linear prediction approach as it utilizes a transform coder to produce a lossy...
	citeseer.ist.psu.edu /323479.html (472 words)

	Lapped Biorthogonal Transforms for the Transform Coding with Reduced Blocking and Ringing Artifacts (Site not responding. Last check: 2007-09-10)
		Two new lapped transforms are introduced: the LBT (lapped biorthogonal transform) and the HLBT (hierarchical lapped biorthogonal transform).
		The LBT and HLBT have a transform coding gain that is typically between 0.5 and 2.5 dB higher than that of the DCT.
		Image coding examples using JPEG and embedded zerotree coders demonstrate the better performance of the LBT and HLBT.
	research.microsoft.com /Pubs/view.aspx?pubid=56 (206 words)

	TransProbModel (Site not responding. Last check: 2007-09-10)
		Maximum likelihood estimation of the parameters of the model (component priors, means qa, the transform W, the number of grid markings along the different grid axes) proceeds by the EM algorithm.
		One of the byproducts of the construction is the derivation of new orthogonal transforms W that, unlike previous transforms, are explicitly designed to minimize coding distortion.
		The mixture model and the coding algorithm derived from it, as well as a short summary of results, are in Archer and Leen "From Mixtures of Mixtures, to Adaptive Transform Codes" in Advances in Neural Information Processing Systems 14, 2001.
	www.cse.ogi.edu /~tleen/Research/TransProbModel.html (442 words)

	A simple transform coding example (Site not responding. Last check: 2007-09-10)
		Take top left pixel as the base value for the block, pixel A. Calculate three other transformed values by taking the difference between these (respective) pixels and pixel A, i.e.
		The above transform scheme may be used to compress data by exploiting redundancy in the data:
		Fourier Transform and (more commonly) Discrete Cosine Transforms (DCT) compression techniques fall into this category.
	www.cs.cf.ac.uk /Dave/MM/OLD_BSC/node210.html (280 words)

	Geoff Davis's Home Page
		We describe a new type of non-linearity for use in constructing non-linear transforms: a set of linear predictors that are chosen adaptively using a non-linear selection function.
		We motivate the use of transform coding in practical settings, and describe the properties of various decorrelating transforms.
		We motivate the use of the wavelet transform in coding using rate-distortion considerations as well as approximation-theoretic considerations.
	www.geoffdavis.net (1452 words)

	AUDIO CODING
		To appreciate the importance of coding digital audio efficiently and with quality which is essentially indistinguishable from that of an original CD, consider the bit rate that current CD's use to code audio.
		Current state-of-the-art coding algorithms, such as the Perceptual Audio Coder or PAC developed at ATandT Bell Labs, are capable of coding 2 channels of digital audio at a total bit rate of 128 kbps with essentially no loss in quality from that of the original CD coding [6,2].
		Frequency domain coding offers a more direct way than predictive coding for noise shaping and suppression of frequency components that needs not to be transmitted.
	www.umiacs.umd.edu /users/desin/Speech/node13.html (575 words)

	Bibliography: Transform coding
		Comparative performance of SVD and adaptive cosine transform in coding images.
		Block distortion in orthogonal transform coding - analysis, minimization, and distortion measure.
		Performance evaluation for transform coding using a nonseparable covariance model.
	cnls.lanl.gov /~brendt/bibliographies/html/transform_coding.html (573 words)

	H.261 Video Coding (Site not responding. Last check: 2007-09-10)
		H.261 is video coding standard published by the ITU (International Telecom Union) in 1990.
		The coding algorithm is a hybrid of inter-picture prediction, transform coding, and motion compensation.
		The datarate of the coding algorithm was designed to be able to be set to between 40 Kbits/s and 2 Mbits/s.
	rice.ecs.soton.ac.uk /peter/h261/h261.html (299 words)

	(WO/1989/011718) IMPROVED ADAPTIVE TRANSFORM CODING (Site not responding. Last check: 2007-09-10)
		Dividing the signal into blocks using a window (52) is followed by dynamic scaling (54) used to conserve necessary processing for the discrete cosine transform (64) and the use of LPC coefficients (68) for pitch generation (82) and bit allocation (108).
		Consequently, the transformed information (64), pitch (106), and bit allocation (108) are utilized for accurate quantization (66) of the speech signal.
		Dynamic scaling (54), pitch (97), and quantization (66 and 80) information are then converted to a standard format (116) for transmission and subsequent decoding.
	www.wipo.int /pctdb/en/wo.jsp?WO=1989/11718 (282 words)

	Keith Price Bibliography Transform Coding -- General
		See also Image Coding by Linear Transformations and Block Quantization.
		Diamantaras, K.I. Strintzis, M.G. Optimal Transform Coding in the Presence of Quantization Noise,
		0208Adaptive coding of transform in block based compression.
	iris.usc.edu /Vision-Notes/bibliography/image-proc156.html (822 words)

	Keith Price Bibliography Vector Quantization with other Transform Coding Methods
		Classified wavelet transform coding of images using two-channel conjugate vector quantization,
		Mohdyusof, Z. Fischer, T.R. An Entropy-Coded Lattice Vector Quantizer for Transform and Subband Image-Coding,
		Wavelet packet coding with jointly optimized lattice vector quantization and data rate allocation,
	iris.usc.edu /Vision-Notes/bibliography/image-proc151.html (914 words)

	A Unified Rate-Distortion Analysis Framework for Transform Coding
		A Unified Rate-Distortion Analysis Framework for Transform Coding
		transform coding systems, such as EZW, SPIHT and JPEG image
		R-D functions and robustly control the output bit rate or picture
	www-iplab.ece.ucsb.edu /publications/01CSVTHe.htm (132 words)

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