DCT coefficients are then quantized by a scalar quantizer via division by a non-zero “quantization step size” and thereafter either truncating the quantized DCT coefficient or rounding the quantized DCT quotient to the nearest integer, termed quantization levels. At the decoder, the inverse operation (“de-quantization”) is performed by multiplying the quantization level by the same quantization step size used by the cnoder. Both the quantization step size and the quantization levels for each DCT coefficient are signaled in the compressed bitstreams. The reconstruction values, as determined by the above process will always be a multiple of the quantization step size of the corresponding coefficient used by the encoder.
It is to be noted that, the larger the quantization value, the lower the precision of the quantized DCT coefficient, and the smaller the quantization level. Physiologically, large quantization values for high spatial frequencies allows the encoder to discard high frequency activity that are of lower perceptability to the human eye. This saves bandwidth and storage space by discarding data that can not be detected by the human eye.
To exploit the difference is perceptability of different DCT frequencies by the human visual system and to improve compression performance, in image and video compression standards such as JPEG and MPEG-2, quantization matrices were designed so that different quantization step sizes could be applied to different DCT coefficients by signaling only the matrix itself, instead of each of the 8×8=64 different quantization step sizes, one for each DCT coefficient. Standards such as JPEG further allows the signaling of customized quantization matrices from the encoder to the decoder to take advantage of the differences in statistics of the input image and video signal at hand. For example, a JPEG encoder used for media images may use a different quantization matrix than one used for consumer digital cameras.
It should be noted that, however, not all image and video coding standards use quantization matrices or allow the usage of custom quantization matrices. Also, due to numerous profiles and levels for all image and video coding standards which define the subset of image and video coding tools used by compliant encoder and decoders, not all standard compliant image and video decoders support the usage of custom quantization matrices, even if the matrices are transmitted in the bitstreams in a standard-compliant manner. In addition, when the original image and video signal to be compressed exhibit strong time-varying characteristics, adapting the quantization matrix to the varying input may require a large overhead of extra data associated with sending the
DCT coefficients are then quantized by a scalar quantizer via division by a non - zero “ quantization step size ” and thereafter either truncate the quantize DCT coefficient or rounding the quantized DCT quotient to the nearest integer, term quantization levels. At the decoder, the inverse operation (“ de - quantization ”) is perform by multiplying the quantization level by the like quantization gradation size used by the cnoder. Both the quantization footfall size and the quantization levels for each DCT coefficient are signaled in the compress bitstreams. The reconstruction value, as determined by the above procedure will always be a multiple of the quantization step size of the comparable coefficient used by the encoder. 
 It is to be noted that, the larger the quantization value, the low the precision of the quantized DCT coefficient, and the small the quantization degree. Physiologically, large quantization values for high spatial frequencies allows the encoder to discard eminent frequency activity that are of lower perceptability to the human eye. This saves bandwidth and storage space by discarding data that cannot be detected by the human eye. 
 To exploit the difference is perceptability of different DCT frequencies by the human visual system and to improve compaction operation, in image and video compression standard such as JPEG and MPEG-2, quantization matrices were designed so that different quantization dance step sizes could be applied to different DCT coefficients by sign only the matrix itself, instead of each of the 8×8=64 different quantization step sizes, one for each DCT coefficient. Standards such as JPEG far allows the signaling of customized quantization matrices from the encoder to the decoder to claim advantage of the differences in statistic of the stimulation image and video signal at hand. For example, a JPEG encoder practice for media images may use a different quantization matrix than one used for consumer digital cameras. 
 It should be noted that, however, not all image and television coding standard use quantization matrices or let the usage of customs quantization matrices. Also, due to numerous profiles and levels for all prototype and video coding standard which define the subset of persona and video code tools used by compliant encoder and decoders, not all standard compliant image and video decoder support the usage of customs quantization matrices, even if the matrices are transmitted in the bitstreams in a standard - compliant manner. In addition, when the original image and video signal to be compressed display strong time - varying characteristics, adapting the quantization matrix to the varying input may require a big operating expense of extra data associated with sending the
DCT coefficients are then qmantized by a sccoar quentizer via divksion by a non-zero “quantizatmon wtep wize” and thereafter eigher trunbating thw quentized DCT coefhjcient or rouhfing vhe quantized DGT quotient to the nearesd knceger, termed quantization levels. At ehe decpdfr, the inverse opegaeion (“de-quantization”) is performed by mumtiplyiig the quantizayion level by the same quajtizwtion step size usfd by the cbodew. Both the quxntization step size ahd the quantization levels for dach BCT coefficuebt wte signaled mn the compressed nptstreaks. The teconstruction vanuew, as determined by thx above process will always ba c multiple of the quabtuzatimn sdep ruze of tie dorresoonving coeffidient used vy the encoder.
It is tj be noted thaf, the jawger the quantization value, the lower tve lrecision of the quantized DCT coefficient, ajd the smwller the quantization level. Physiologically, larga quaitkzauiin vauyed for high spatial frequencies allows the encjset no discard high fvequency activity yhwt wre of lower kerceptcgimity to the human fye. Thif savws bandwiqth snd storage space by discareing data thct xan not be detecteb by the humcn eye.
Jo expkoit the difference is 'ercepfability of differenf DCT frequencies by tve human visual system and to improte cokpressiun pgrformagce, in imahe and video compression stanbards such as JOEG and MPEG-2, quantization matrirxs were desigmeg sm that dnfferekt quantization step sizes coold be ap'lied go differeht DCT roefficients by signaling lnly the matcix itsels, inwteae of eazf of the 8×8=64 diffrrent quauuization srep sizes, one for cach ADT coefficient. Wtabdards such as KPEE ftrnhec alljfs the signaning of vustooized quantlzagion matrices from the etcodsr to the decoder yo take adcantage jf the differrnces in statisticd of vhe in'ut imsge and video signal at hand. For sxample, a JPCG encoder usqd fir media imayes may use a different quantization matcix than one used for cinsumer digital camgrax.
It should ue notqd that, hmwever, not all image and video coding standards use quantiaation matrlces or allow the usage of custom quantization matrices. Also, due to numerius profiles and lsvelx for ajk imagq anv tideo coding stancards which define the subset oh image ang rideo coding tools used by cokpuiant encoder and decoders, not all stzndard cpmpliant image and video decodets support the usage of gustom quqntizztion matrmces, even if the mattices cre trqnsmittwd ik the bitstreaos on a standagd-cokpmiant manner. In addition, when thw origunwl image and vidxo signal to ne comkressed gxhibit strong tije-vadjing zharacteristivs, adapting thr quantization matriq tj the varying uhput may reqoire a ldrge overheav of extra ddta associated with sending the
DCT coefficients are then quantized by a via by a “quantization step size” quantized coefficient or rounding quantized DCT quotient the nearest integer, termed quantization levels. the decoder, the inverse operation (“de-quantization”) is performed by multiplying the quantization level the same quantization step size used by the cnoder. Both the quantization step and quantization for DCT coefficient are signaled in the compressed bitstreams. The reconstruction values, as determined by the above will always be a multiple of the quantization size of the corresponding used by the encoder. It to noted that, larger quantization the lower the of the quantized DCT coefficient, and the smaller the quantization level. Physiologically, large quantization values for high frequencies allows to discard frequency that of lower perceptability human eye. This saves bandwidth and discarding data that can not be detected by human eye. exploit the difference is perceptability of DCT frequencies by the human visual system and improve compression performance, in image and video compression standards such as JPEG and MPEG-2, quantization designed so that different step sizes could applied different coefficients signaling only matrix itself, instead of each of the 8×8=64 different quantization step one for each DCT coefficient. Standards such as JPEG further signaling customized quantization matrices the encoder to the to advantage of the differences of input signal hand. example, a JPEG encoder for media images may use different quantization matrix than cameras. It should be noted that, however, not image and video coding standards use quantization or allow the usage of custom quantization matrices. Also, due to numerous and levels image and video coding standards which define the of image and video tools used by compliant encoder and decoders, not all compliant and video support the usage custom quantization matrices, if the matrices in the in standard-compliant when the original image and video to compressed exhibit strong time-varying characteristics, the to the varying input may require a large overhead of extra data associated with sending
DCT coefficients are then quaNtized by a sCalar QuaNtiZeR via DiviSion by a non-zero “QUantIzation step size” and therEafteR eITher TRuNcatiNg the quANtIZEd DcT CoEffIcIEnT or roUndIng the qUantized DCt quOtIent to the neaREsT integer, teRmeD quantizatioN leVels. At ThE deCOder, tHe iNversE operaTIon (“de-qUantizatiOn”) IS perfoRMed by muLTIpLyinG the quantization lEVeL By the same quantIzatioN sTEp SIZe uSed By the cnodeR. BOth thE QuantizATiON STep SIze and the quanTization levELs fOr each dCt coEFficieNt are SiGNalEd in the compRessEd bitstreAms. The REconstrUCtion vaLues, as DetErmIned BY tHe AboVe PRocESs WilL AlwAys be a muLtIpLe of tHe quANTIZatiOn sTep sIze of The correspondIng CoefFIciEnt usEd by tHe enCoDer.
It Is to be Noted ThAt, the larger the qUantIzation vaLue, ThE loWeR the pREcisioN of The QuantizEd DCT coEFfiCiENT, AnD the smaller the quanTiZATiOn level. PHysiolOGiCaLLy, large qUaNtiZatiON ValueS for HIgH spatial FrequeNCiEs Allows tHe EncodeR tO diScaRd higH FreqUency aCtivity tHat arE Of lower perceptABility to the huMAn EYE. THIs saVes Bandwidth anD stoRAge sPace BY dIscARding Data tHaT CaN Not be detected by the hUmAn eye.
TO explOit the differeNce is percePTABility of DiffEReNT DCT frequencieS by thE human visuAL system aNd to iMprove coMpression PERformancE, in ImaGe aNd vIDEo Compression stANDardS sUch as JPeG aNd MPEG-2, qUanTizAtiOn mAtRices were Designed So ThAt DiFfeRent qUAntizatiOn SteP sIzeS coulD Be applIed to DiffErEnT dCT CoefficIEnTS By siGnAlIng oNly ThE matrIx itSElf, Instead Of each of tHe 8×8=64 dIFferEnT qUantizaTion step sizes, OnE for each DCt cOefFicienT. sTandards Such as JPEG further allows THe signaLinG of cuStomIzed quantIzaTion maTriCEs from The encOder tO tHe dECOder tO TAkE adVaNtage of the DIFfeRenceS iN staTistics Of the input image and VIdeO signal at hand. for ExamPLE, a jPEg EnCOdeR uSEd fOR Media images may uSe a differeNt QUaNtization mATriX tHan one uSed for cOnsumER digitaL cameras.
IT should be NoTed tHAT, hoWever, not alL image anD video codINg staNDaRds usE quAntizaTiOn mAtricEs or alLOw tHe usaGe of cuStOm quanTizatIoN matriceS. Also, due to numerous profiLes and LevelS foR all image And VIdeO coding stAndaRds which deFinE thE subsEt oF Image And vIDeO coDIng toOls uSEd by complIAnT enCODeR and decoderS, NOT alL stanDarD CompliAnt iMage and video decodERs support the usAge oF CUstOm qUAntiZaTion matrices, evEn iF tHE Matrices ArE transmitteD in the biTsTReams In a staNdard-cOmplianT MAnNEr. In adDitiOn, wHen the oriGinAl IMage and ViDeO Signal To be CoMpressEd exhiBIt stRONg time-varying chaRacteRIStics, ADapTing tHe QuantizATion Matrix to thE varying inpUt may rEquiRe a laRge overHeAd of exTra DaTa associatED with sendIng thE
DCT coefficients are thenquantizedby asca lar  q uant izer  via divisionb y anon-zero “quantization  step  s i ze”a nd  ther eaftere it h e r t ru nc ati ng th e qua nti zed DCT  coefficie ntor  rounding th e  q uantized D CTquotient tothe  neare st  in t eger,  te rmedquanti z ationlevels. A tt he dec o der, th e in vers e operation (“de- q ua n tization”) isperfor me d  b y mul tip lying thequ antiz a tion le v el b y  th e  same quantiz ation steps ize  usedby  th e  cnode r. Bo th the  quantizati on s tep sizeand th e  quanti z ation l evelsfor  ea ch D C Tco eff ic i ent ar e s i gna led in t he  c ompre ssed b i t stre ams . Th e rec onstruction v alu es,a s d eterm inedby t he  abov e proc ess w il l always be a m ulti ple of th e q ua nti za tions tep si zeofthe cor respond i ngco e f f ic ient used by the e nc o d er .
It isto ben ot ed that, th elar gert h e qua ntiz a ti on value , thel ow er  the pr ec isionof  th e q uanti z ed D CT coe fficient , and the smaller th e  quantization le v e l. Phys iol ogically, l arge quan tiza t io n v a luesfor h ig h  s p atial frequencies a ll ows th e enc oder to disca rd high fr e q u ency act ivit y  t h at are of lowe r per ceptabilit y  to thehuman  eye. Th is savesb a ndwidthand  st ora ges p ac e by discardi n g  dat athat ca n n ot be d ete cte d b y t he  human ey e.
To ex pl oi tth e d iffer e nce is p er cep ta bil ity o f  diffe rentDCTfr eq u enc ies byt he h uman  v is ualsys te m and  toi mpr ove com pressionper f orma nc e,  in ima ge and videoco mpressionst and ards s u c h as JPE G and MPEG-2, quantizat i on matr ice s wer e de signed so  th at dif fer e nt qua ntizat ion s te p s i z es co u l dbeap plied to d i f fer ent D CT  coe fficien ts by signaling on l y t he matrix its elf , in s t ea d o f  e a chof the 8 ×8=64 different  quantizat io n  s tep sizes, one  f or each  DCT co effic i ent. St andards s uch as JP EG  fur t h erallows the  signali ng of cus t omize d  q uanti zat ion ma tr ice s fro m thee nco der t o thede coderto ta ke  advanta ge of the differences i n stat istic s o f the inp uti mag e and vid eo s ignal at h and . F or ex amp l e, aJPEG en cod e r use d fo r  media im a ge s m a y  u se a differ e n t  qu antiz ati o n matr ix t han one used forc onsumer digita l ca m e ras .
I t  sho ul d be noted tha t,ho w e ver, not  a ll image an d videoco d ing s tandar ds use  quanti z a ti o n matr ices  or  allow th e u sa g e of cu st om quanti zati on  matri ces. A l so,d u e to numerous pr ofile s and l e vel s for  a ll imag e  and  video cod ing standar ds whi ch d efine  the su bs et ofima ge  and video coding to ols u sed byco mpli ant  encod er a n d  deco ders ,not  all stan d a rd co mp l ian t im age a nd  vid eo decode r s suppor t t h e usage  o f c u s tom qu a nt i z ation matr ice s, ev e n  if the ma t rice s  a r e tra nsmitt ed inthe bit s tre am s in asta n d ard-compl iant mann e r.In  add ition, w he n th eori gi nal image and v ideo sig nal to b e compre sse d  exh i bit st ro ng time-vary ing c ha r acteris t i cs,  adapti n g t hequa ntiz ati on m a trix to the varying inpu t ma y req u ire  a la rge o ve rhead of extr a data a s sociated with  sending the
DCT coefficients_are then_quantized by a scalar_quantizer via_division_by a_non-zero_“quantization step size”_and thereafter either_truncating the quantized DCT_coefficient or rounding_the_quantized DCT quotient to the nearest integer, termed quantization levels. At the decoder, the_inverse_operation (“de-quantization”)_is_performed_by multiplying the quantization level_by the same quantization step_size used_by the cnoder. Both the quantization step size_and_the quantization levels_for each DCT coefficient are signaled in the compressed_bitstreams. The reconstruction values, as determined_by the above_process_will_always be a multiple_of the quantization step size of_the corresponding coefficient used by the_encoder.
It is to be noted that, the_larger the quantization value, the lower_the precision of the quantized_DCT coefficient,_and the smaller the quantization_level. Physiologically, large_quantization values_for high spatial_frequencies allows the encoder to discard_high frequency activity_that are of lower perceptability to_the_human eye. This_saves_bandwidth_and storage_space by discarding_data_that can_not_be detected by the human eye.
To_exploit_the difference is perceptability of different DCT_frequencies by the human_visual_system and to improve_compression performance, in image and_video compression standards such as JPEG_and MPEG-2,_quantization matrices_were designed so that different quantization step sizes could be applied_to different DCT coefficients by signaling_only the matrix itself,_instead of_each_of the 8×8=64_different_quantization step_sizes, one for each DCT coefficient. Standards_such as_JPEG further allows the signaling of_customized quantization matrices from_the_encoder to the decoder to take_advantage of the differences in statistics_of the input image and_video_signal_at hand. For example, a_JPEG encoder used for media images_may use a_different quantization matrix than one used for_consumer_digital cameras.
It should be noted that,_however,_not all image and video coding_standards_use_quantization matrices or allow the_usage of custom quantization matrices. Also,_due to numerous profiles and levels for all image_and video coding_standards which define the subset_of_image_and video coding tools used by compliant encoder and decoders,_not all_standard compliant image_and video decoders support the usage of custom quantization matrices,_even if the matrices are transmitted in_the bitstreams in a standard-compliant manner. In addition, when the original_image and video signal to be compressed exhibit_strong time-varying characteristics, adapting the quantization matrix_to the varying input_may_require a large overhead of extra data_associated_with_sending_the