{"062e3a09a2b460e0fcc4b8ad3c8a9875thomasrichter":{"DOI":"10.1117/12.890513","ISBN":"9780819487452","ISSN":"","URL":"http://spie.org/Publications/Proceedings/Paper/10.1117/12.890513","abstract":"Equal-Expectation Magnitude Quantization (EEM) aims at minimizing the distortion of a quantizer with defined reconstruction points by shifting the deadzone parameter such that the expectation value of the signal equals the reconstructed value. While intuitively clear, this argument is not sufficient to prove rate-distortion optimality. In this work, it is show that the EEM quantizer is rate-distortion optimal up to third order in an expansion in powers of the quantization bucket size in the high-bitrate appoximation, and the approximating series for the optimal quantizer is computed. This result is compared to an even simpler quantization strategy based on the LLoyd-Max quantizer which selectively sets coefficients to zero. It is shown that both strategies lead to the same asymptotic expansion for the threshold parameter, but zeroing coefficients provides optimality in one additional order in the quantization bucket size.","annote":"","author":[{"family":"Richter","given":"Thomas"}],"citation-label":"richter2011quantization","collection-editor":[{"family":"Tescher","given":"Andrew G."}],"collection-title":"","container-author":[{"family":"Tescher","given":"Andrew G."}],"container-title":"Applications of Digital Image Processing XXXIV","documents":[],"edition":"","editor":[{"family":"Tescher","given":"Andrew G."}],"event-date":{"date-parts":[["2011","sep"]],"literal":"2011"},"event-place":"","id":"062e3a09a2b460e0fcc4b8ad3c8a9875thomasrichter","interhash":"5749c603f43f68dfbc74022088ffb6a1","intrahash":"062e3a09a2b460e0fcc4b8ad3c8a9875","issue":"","issued":{"date-parts":[["2011","sep"]],"literal":"2011"},"keyword":"myown quantization","misc":{"isbn":"9780819487452","doi":"10.1117/12.890513"},"note":"","number":"","page":"","page-first":"","publisher":"SPIE","publisher-place":"","status":"","title":"EEM quantization revisited: asymptotic optimality for variable rate coding","type":"paper-conference","username":"thomasrichter","version":"","volume":"8135"},"aff6f09c8d42df4861ce6c90540d2ba8thomasrichter":{"DOI":"10.1109/DCC.2011.78","ISBN":"978-1-61284-279-0","ISSN":"","URL":"http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=5749531","abstract":"Similar to the JPEG image compression standard, the JPEG XR image\ncompression solely controls the image quality loss and hence the output rate\nby means of the quantizer bucket sizes; a precise rate control mechanism\nlike the EBCOT rate allocation algorithm in JPEG 2000 is not specified, and\nhence rate-distortion optimality of the quantizer is, in general, not given.\n\nIn this work, a simple rate-control mechanism for JPEG XR is introduced that\nallows an efficient control of the quantizer towards rate-distortion\noptimality. One possibility to implement this quantizer control would be to\nuse the spatial variable quantization feature of JPEG XR, but it was seen in\nan earlier work that the additional side information required to transmit\nthe quantization setting almost compensates the PSNR gain of variable\nquantization and complicates the rate allocation process by requiring an\nadditional quantizer allocation step.\n\nHowever, while JPEG XR defines the image reconstruction process completely,\nan encoder still has the freedom to select the deadzone size of the\nquantizer; this mechanism has the additional advantage that no additional\nside information needs to be transmitted and that the deadzone size is not,\nunlike the quantizer bucket size, constrained to a set of pre-defined\nvalues specified in the standard.\n\nIt is found that the image quality of JPEG XR can be improved by about 0.2\nto 0.4 dB by performing a rate-distortion optimal selection of the deadzone;\nthis gain is seen to be comparable to the PSNR loss of a JPEG 2000 codec\nwhere, for experimental reasons, EBCOT rate control has been turned off.","annote":"","author":[{"family":"Richter","given":"Thomas"}],"citation-label":"richter2011deadzone","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Data Compression Conference (DCC), 2011","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2011","mar"]],"literal":"2011"},"event-place":"Snowbird, UT","id":"aff6f09c8d42df4861ce6c90540d2ba8thomasrichter","interhash":"95c1969b1a1b6bdc1d7a31ca7c6eecc1","intrahash":"aff6f09c8d42df4861ce6c90540d2ba8","issue":"","issued":{"date-parts":[["2011","mar"]],"literal":"2011"},"keyword":"JPEG Optimal Quantization Quantization, Rate-Distortion XR!!,","misc":{"isbn":"978-1-61284-279-0","doi":"10.1109/DCC.2011.78"},"note":"","number":"","page":"474","page-first":"474","publisher":"IEEE","publisher-place":"Snowbird, UT","status":"","title":"Deadzone Based Rate Allocation for JPEG XR","type":"paper-conference","username":"thomasrichter","version":"","volume":""},"129ef12bf4cd76de2771395baf389fb4thomasrichter":{"DOI":"10.1109/DCC.2009.16","ISBN":"","ISSN":"1068-0314","URL":"http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=4976475","abstract":"We introduce a novel universal refinable trellis quantization scheme (URTCQ) that is suitable for bitplane coding with many reconstruction stages. Existing refinable trellis quantizers either require excessive codebook training and are outperformed by scalar quantization for more than two stages (MS-TCQ, E-TCQ), require a huge computational burden (SR-TCQ) or achieve a good rate distortion performance in the last stage only (UTCQ). The presented quantization technique is a mixture of a scalar quantizer and an improved version of the E-TCQ. For all supported sources only one time training to an i.i.d. uniform source is required and its incremental bitrate is not more than 1 bps for each stage. The complexity is proportional to the number of stages and the number of trellis states. We compare the rate distortion performance of our work on generalized Gaussian i.i.d. sources with the quantizers deployed in JPEG2000 (USDZQ, UTCQ). It turns out that it is in no stage worse than the scalar quantizer and usually outperforms the UTCQ except for the last stage.","annote":"","author":[{"family":"Steger","given":"S."},{"family":"Richter","given":"T."}],"citation-label":"steger2009universal","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Data Compression Conference, 2009. DCC '09.","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2009","mar"]],"literal":"2009"},"event-place":"","id":"129ef12bf4cd76de2771395baf389fb4thomasrichter","interhash":"35306931e0653b50d572d8534660dde9","intrahash":"129ef12bf4cd76de2771395baf389fb4","issue":"","issued":{"date-parts":[["2009","mar"]],"literal":"2009"},"keyword":"(signal);trellis coded codes;bitplane coding;Image coding;codebook coding;embedded coding;progressive coding;residual compression;Decoding;Distortion distortion measurement;Image performance;scalar quantisation quantization quantization;Bit quantization;universal quantizer;trellis rate;Data reconstruction;Quantization;Rate refinable theory;Rate-distortion;Transform training;rate trellis","misc":{"issn":"1068-0314","doi":"10.1109/DCC.2009.16"},"note":"","number":"","number-of-pages":"9","page":"312-321","page-first":"312","publisher":"","publisher-place":"","status":"","title":"Universal Refinable Trellis Coded Quantization","type":"paper-conference","username":"thomasrichter","version":"","volume":""}}