TY - JOUR
T1 - A Generalized Lloyd-Type Algorithm for Adaptive Transform Coder Design
AU - Archer, Cynthia
AU - Leen, Todd K.
N1 - Funding Information:
Manuscript received July 1, 2002; revised March 12, 2003. This work was supported in part by National Science Foundation under Grant ECS-9976452. The associate editor coordinating the review of this paper and approving it for publication was Prof. Sheila S. Hemami.
PY - 2004/1
Y1 - 2004/1
N2 - In this paper, we establish a probabilistic framework for adaptive transform coding that leads to a generalized Lloyd type algorithm for transform coder design. Transform coders are often constructed by concatenating an ad hoc choice of transform with suboptimal bit allocation and quantizer design. Instead, we start from a probabilistic latent variable model in the form of a mixture of constrained Gaussian mixtures. From this model, we derive an transform coder design algorithm, which integrates optimization of all transform coder parameters. An essential part this algorithm is our introduction of a new transform basis - the coding optimal transform - which, unlike commonly used transforms, minimizes compression distortion. Adaptive transform coders can be effective for compressing databases of related imagery since the high overhead associated with these coders can be amortized over the entire database. For this work, we performed compression experiments on a database of synthetic aperture radar images. Our results show that adaptive coders improve compressed signal-to-noise ratio (SNR) by approximately 0.5 dB compared with global coders. Coders that incorporated the coding optimal transform had the best SNRs on the images used to develop the coder. However, coders that incorporated the discrete cosine transform generalized better to' new images.
AB - In this paper, we establish a probabilistic framework for adaptive transform coding that leads to a generalized Lloyd type algorithm for transform coder design. Transform coders are often constructed by concatenating an ad hoc choice of transform with suboptimal bit allocation and quantizer design. Instead, we start from a probabilistic latent variable model in the form of a mixture of constrained Gaussian mixtures. From this model, we derive an transform coder design algorithm, which integrates optimization of all transform coder parameters. An essential part this algorithm is our introduction of a new transform basis - the coding optimal transform - which, unlike commonly used transforms, minimizes compression distortion. Adaptive transform coders can be effective for compressing databases of related imagery since the high overhead associated with these coders can be amortized over the entire database. For this work, we performed compression experiments on a database of synthetic aperture radar images. Our results show that adaptive coders improve compressed signal-to-noise ratio (SNR) by approximately 0.5 dB compared with global coders. Coders that incorporated the coding optimal transform had the best SNRs on the images used to develop the coder. However, coders that incorporated the discrete cosine transform generalized better to' new images.
KW - Adaptive transform coding
KW - Compression
KW - Entropy-constrained quantization
KW - Expectation-maximization
KW - Gaussian mixtures
KW - Generalized Lloyd algorithms
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U2 - 10.1109/TSP.2003.819980
DO - 10.1109/TSP.2003.819980
M3 - Article
AN - SCOPUS:0347603363
SN - 1053-587X
VL - 52
SP - 255
EP - 264
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 1
ER -