| M. Vetterli and J. Kovacevi'c, Wavelets and Subband Coding. Prentice Hall, 1995. |
....can be unambiguously extracted for subjective measurement. In addition, a similarity measurement is taken for objective test as well. Wavelet theory has emerged as an effect means of representing image signals in terms of a multiresolution structure [11] Based on multiresolution representation [12 13], a signal is divided into a number of components, each corresponding to different frequency bands. Since each component has a better frequency and time localization, the multiresolution decomposed signal can be processed much more easily than its original representation. Multiresolution ....
....embedding and extracting approaches. Section 5 summarizes the experimental results. Conclusions are finally made in Section 6. 2. WAVELET DECOMPOSITION Wavelet transforms have received extensive attention owing to their feasibility for many important signal and image processing applications [12 13]. The wavelet transform attempts to hierarchically decompose an input signal into a series of successively lower resolution reference signals and their associated detail signals. The reference signal and its associated detail signal contain the necessary information to construct the reference ....
M. Vetterli and J. Kovacevic, Wavelets and Subband Coding, Prentice Hall, 1995.
....of the image statistics. Table I shows that coefficient variance in the original image is not sensitive to shifts, unlike for the compressed image, where the variance is very shift dependent. This phenomenon arises because the maximally decimated wavelet transform is not shiftinvariant [3]. As a result, wavelet compression introduces cyclostationarity into the image, resulting in the ringing effects visible around the image discontinuities. To reduce or remove these artifacts, we propose to address the cyclostationarity introduced into the image by compression. Our objective is to ....
M. Vetterli and J. Kovacevic, Wavelets and subband coding. Prentice Hall, 1995.
....us. Being defined pathwise, they are random variables. 2. 2 Scaling of Wavelet Coe#cients The discrete wavelet transform represents a 1 d process Y (t) in terms of shifted and dilated versions of a prototype bandpass wavelet function #(t) and shifted versions of a low pass scaling function #(t) [23, 106]. Made precise in the vocabulary of Hilbert spaces: For special choices of the wavelet and scaling functions, the atoms # j,k (t) 2 , # j,k (t) 2 , j, k Z (2.6) form an orthonormal basis and we have the representations [23, 106] Y (t) D J 0 ,k # J 0 ,k (t) ....
....of a low pass scaling function #(t) 23, 106] Made precise in the vocabulary of Hilbert spaces: For special choices of the wavelet and scaling functions, the atoms # j,k (t) 2 , # j,k (t) 2 , j, k Z (2. 6) form an orthonormal basis and we have the representations [23, 106] Y (t) D J 0 ,k # J 0 ,k (t) j=J 0 C j,k j,k (t) 2.7) with C j,k : Y (t) j,k (t) dt, D j,k : Y (t) # j,k (t) dt. 2.8) For a wavelet (t) centered at time zero and frequency f 0 , the wavelet coe#cient C j,k measures the signal content around time 2 j k and frequency 2 ....
M. Vetterli and J. Kovacevic. Wavelets and subband coding. Prentice-Hall, Englewood Cli#s, NJ, 1995.
....describes the extrema representation and how the spline wavelet based decomposition can be used to reconstruct the wavelet representation. The concluding sections deal with specific experiments, simulations and conclusions. 2 The Multiresolution Decomposition The notation here largely follows [1,2] etc. The multiresolution approach can be used to effectively link subband decomposition and wavelets. We state here for completeness the following definition. Definition 1. A multiresolution analysis consists of a sequence of embedded closed subspaces : V 2 ae V 1 ae V 0 ae V 1 : such ....
....by essentially normalising the spline basis. For the experiments in this work, we construct the biorthogonal wavelet transform. The properties of this transform are explained in the next section. We review the notation for B splines below. Notation in this section largely follows [6] and [2]. Definition 3. The normalised B spline of order k for the knot sequence t is denoted by B i;k;t and is defined by B i;k;t = t i k Gamma t i ) t i ; t i k ] Gamma x) 8x 2 R The placeholder notation ( indicates that the k th divided difference of the function (t Gamma ....
M. Vetterli and J. Kovacevic. Wavelets and Subband Coding. Prentice Hall, 1995.
....play the central role in the timedomain pre post processing across block boundaries. It can be easily veri ed that the determinant of the polyphase matrix E(z) in (2) 3) is a monomial, i.e. jE(z)j = z n 2 Z , hence one can obtain FIR perfect reconstruction by simply choosing R(z) E (z) [4], 5] 6] The z transforms of the analysis lters and synthesis lters in matrix notation are H 0 (z) H 1 (z) HM 1 (z) E(z 1 z z F 0 (z) F 1 (z) FM 1 (z) 1 z z (M 1) R(z ) The structure of the pre lter P in (1) ensures that all analysis ....
....solution space, the coding gain only decreases slightly. A. f1,2g Regular 4 Band 8 tap Filter Bank Fig. 4 presents a 4 band 8 tap f1,2g regular system via the 4 point DCT and 4 point pre post ltering. The 2 2 matrix V is parameterized with 2 free parameters under the constrain V[1 3] [4 4] . The smoothness in the synthesis bank is evident from the synthesis scaling and the three wavelet functions. 0.05 0.15 0.2 0.25 0.35 0.4 0.45 40 35 30 25 20 15 10 0 5 DC Att. 406.0206 dB Stopband Att. 10.0226 Cod. Gain 8.606 Response (dB) 0.05 0.1 0.15 0.25 0.3 0.35 0.4 ....
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M. Vetterli and J. Kovacevic, Wavelets and Subband Coding, Prentice Hall, Englewood Clis, NJ, 1995.
....are provided by investigating the possible use of the on board DMA. Keywords: wavelet, lifting scheme, filter bank, JPEG2000, DSP This work was partially developed under the Texas Instruments Elite program 1 Introduction A huge number of applications use the discrete wavelet transform (DWT) [1] as a means to extract relevant features from signals. Examples are reported in the fields of mathematics, physics, numerical computing, and engineering, including image classification, feature detection, image denoising, image registration, and image compression, just to mention a few. Especially ....
.... 9] In this paper we focus on the study of the DSP based implementation of a wavelet kernel; the target application is image coding with JPEG2000, with its extension to intraframe video coding (Motion JPEG2000) Until recently, DWT implementations were based on the so called filter bank scheme [1], which computes the DWT of a signal by iterating a sequence of highand lowpass filtering steps, followed by downsampling. In 1997 Sweldens proposed a new scheme, called lifting scheme (LS) as an alternative way to compute the DWT [10] The LS has immediately obtained a noteworthy success, as it ....
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M. Vetterli, J. Kovacevic, "Wavelets and subband coding", Prentice Hall PTR, Englewood Cliffs, New Jersey, 1995
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M. Vetterli and J. Kovacevi'c, Wavelets and Subband Coding, Prentice Hall, Englewood Cliffs, NJ, 1995.
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M. Vetterli and J. Kovacevi'c, Wavelets and Subband Coding, Prentice Hall, Englewood Cliffs, NJ, 1995.
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M. Vetterli and J. Kovacevi'c, Wavelets and Subband Coding, Prentice Hall, Englewood Cliffs, NJ, 1995.
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M. Vetterli and J. Kovacevi'c, Wavelets and Subband Coding, Prentice Hall, 1995.
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M. Vetterli and J. Kovacevic. Wavelets and Subband Coding. Prentice-Hall, Englewood Cli#s, NJ, 1995.
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M. Vetterli and J. Kovacevi'c. Wavelets and Subband Coding. Prentice-Hall, Englewood Cliffs, NJ, 1995.
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M.Vetterli and J. Kovacevi'c, Wavelets and Subband Coding, Prentice Hall, 1995.
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M.Vetterli and J. Kovacevi'c, Wavelets and Subband Coding, Prentice Hall, 1995. -0.4 -0.2 0
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M.Vetterli and J. Kovacevic, Wavelets and Subband Coding, Prentice Hall, 1995.
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M. Vetterli and J. Kovacevic. Wavelets and Subband Coding. Prentice-Hall, Englewood Cliffs, NJ, 1995.
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M. Vetterli and J. Kovacevic, Wavelets and Subband Coding, Prentice-Hall, Englewood Cliffs, NJ, 1995.
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M. Vetterli and J. Kovacevic. Wavelets and Subband Coding. Prentice-Hall, 1995.
....bank. The two output sequences are then separately quantized and sent over two different erasure channels. We suppose that the channels are independent, that they have the same erasure probability and that R 1 = R 2 . For convenience we will formulate our problem in the polyphase domain [26] [31]. In this case the analysis stage can be equivalently represented by the block scheme shown in Fig. 3. 2 2 2 Q x[n] 1 0 H (w) H (w) 0 G G (w) Fig. 2. Two channel filter bank. First we move the quantization step before the transform and approximate our continuous polyphase ....
.... in l 2 (Z) The discrete transform is a perfectly invertible operator that converts quantized sequences into quantized sequences [4] 17] 37] synthesis polyphase matrix G( is uniquely defined (up to a phase factor) In fact G( must be such that the condition G( H( I is satisfied [31]. Now, assume that the target central distortion is D 0 and that both channels are coded independently. Since y 1 [n] y 2 [n] are stationary Gaussian sources and quantization is fine, the minimum bit rates necessary to scalar code the two sequences is [3] 6 ) 49) In case we do not ....
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M. Vetterli and J. Kovacevi'c. Wavelets and Subband Coding. Prentice-Hall, Englewood Cliffs, NJ, 1995.
....used in quantum theory. The theorem was also proved in [28] A. Digression: Frame Interpretation of Filter Banks Fig. 1 depicts a signal processing structure called a filter bank. It has been used extensively in compression as well as communications (with analysis and synthesis banks reversed) [33]. Early work in filter banks concentrated on trying to provide perfect reconstruction, that is, ensure that the output signal is only a shifted and possibly scaled version of the input signal. As the field matured, it was recognized that the filter bank implements a particular, structured linear ....
....work in filter banks concentrated on trying to provide perfect reconstruction, that is, ensure that the output signal is only a shifted and possibly scaled version of the input signal. As the field matured, it was recognized that the filter bank implements a particular, structured linear transform [33]. Most of the research concentrated on critically sampled filter banks, those with M = N , in which the filter impulse responses are basis functions from an orthogonal or a biorthogonal basis of 2 (Z) Some researchers, however, tried to overcome certain critical sampling restrictions by ....
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M. Vetterli and J. Kovacevi'c. Wavelets and Subband Coding. Signal Processing. Prentice Hall, Englewood Cliffs, NJ, 1995.
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M. Vetterli and J. Kovacevi'c, Wavelets and Subband Coding. Prentice Hall, 1995.
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M. Vetterli and J. Kovacevi'c, Wavelets and Subband Coding, Prentice-Hall, Englewood Cliffs, NJ, 1995.
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VETTERLI, M., AND KOVACEVIC, J. Wavelets and Subband coding. Prentice Hall, New Jersey, 1995.
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M. Vetterli and J. Kovacevic. Wavelets and Subband coding. Prentice Hall, New Jersey, 1995.
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M. Vetterli and J. Kovacevic. Wavelets and Subband Coding. Prentice-Hall, Englewood Cliffs, NJ, 1995.
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M. Vetterli and J. Kovacevic. Wavelets and Subband Coding. Prentice Hall, Englewood Cli#s, New Jersey, 1995. 36
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M. Vetterli and J. Kovacevic, Wavelets and Subband Coding (Prentice Hall, 1995).
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M. Vetterli and J. Kovacevic, Wavelets and Subband Coding, Prentice-Hall, Englewood Cli#s, NJ, 1995.
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M. Vetterli and J. Kovacevic, Wavelets and Subband Coding, Prentice Hall, Englewood Cli#s, New Jersey, 1995.
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Vetterli M. and Kovacevic J., Wavelets and Subband Coding. Prentice Hall, 1995.
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M. Vetterli and J. Kovacevic, Wavelets and Subband Coding, Prentice Hall, 1995.
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M. Vetterli, and J. Kovacevic, "Wavelets and Subband Coding," NJ, USA: Prentice Hall, 1995.
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M. Vetterli and J. Kovacevic. Wavelets and Subband Coding. Prentice Hall, 1995.
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M. Vetterli and J. Kovacevic. Wavelets and Subband Coding. Prentice Hall, 1995.
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M. Vetterli and J. Kovacevic. Wavelets and Subband Coding. Prentice Hall, Englewood Cli#s NJ, 1995.
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M. Vetterli, J. Kovacevic, Wavelets and Subband Coding, Prentice Hall, 1995.
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M. Vetterli and J. Kovacevic. Wavelets and subband coding. Prentice-Hall, 1995.
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M. Vetterli and J. Kovacevic. Wavelets and Subband Coding. Prentice Hall, Englewood Cli#s, NJ, 1995.
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M. Vetterli and J. Kovacevic. Wavelets and Subband coding. Prentice Hall, New Jersey, 1995.
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M. Vetterli and J. Kovacevic, Wavelets and Subband Coding, Prentice Hall, New Jersey, 1995.
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M. Vetterli and J. Kovacevic, Wavelets and Subband Coding, 1995.
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M. Vetterli, J. Kovacevic, Wavelets and Subband Coding, Prentice Hall, 1995.
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M. Vetterli and J. Kova cevic, Wavelets and Subband Coding, 1995.
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Vetterli, M. and J. Kovacevic: 1995, Wavelets and Subband Coding. PrenticeHall.
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M. Vetterli and J. Kovacevic. Wavelets and subband coding. Prentice Hall, 1995.
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M. Vetterli and J. Kovacevic, Wavelets and Subband Coding, Prentice Hall, Englewood Cli#s, NJ, 1995.
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M. Vetterli and J. Kovacevi'c. Wavelets and Subband Coding. PrenticeHall, 1995.
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M. Vetterli and J. Kovacevi'c. Wavelets and Subband Coding, Prentice Hall, 1995.
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M. Vetterli and J. Kovacevi'c, "Wavelets and Subband Coding," Prentice Hall, Englewood Cliffs, N.J., 1995.
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M. Vetterli and J. Kovacevi'c, Wavelets and Subband Coding, Prentice Hall, Englewood Cliffs, NJ, 1995.
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