Monday, July 23, 2007

PSNR (Peak Signal-to-Noise Ratio)

Compressing an image is significantly different than compressing raw binary data. Of course, general purpose compression programs can be used to compress images, but the result is less than optimal. This is because images have certain statistical properties which can be exploited by encoders specifically designed for them. Also, some of the finer details in the image can be sacrificed for the sake of saving a little more bandwidth or storage space. This also means that lossy compression techniques can be used in this area.

Lossless compression involves with compressing data which, when decompressed, will be an exact replica of the original data. This is the case when binary data such as executables, documents etc. are compressed. They need to be exactly reproduced when decompressed. On the other hand, images (and music too) need not be reproduced 'exactly'. An approximation of the original image is enough for most purposes, as long as the error between the original and the compressed image is tolerable.

Error Metrics

Two of the error metrics used to compare the various image compression techniques are the Mean Square Error (MSE) and the Peak Signal to Noise Ratio (PSNR). The MSE is the cumulative squared error between the compressed and the original image, whereas PSNR is a measure of the peak error. The mathematical formulas for the two are

MSE =

PSNR = 20 * log10 (255 / sqrt(MSE))

where I(x,y) is the original image, I'(x,y) is the approximated version (which is actually the decompressed image) and M,N are the dimensions of the images. A lower value for MSE means lesser error, and as seen from the inverse relation between the MSE and PSNR, this translates to a high value of PSNR. Logically, a higher value of PSNR is good because it means that the ratio of Signal to Noise is higher. Here, the 'signal' is the original image, and the 'noise' is the error in reconstruction. So, if you find a compression scheme having a lower MSE (and a high PSNR), you can recognize that it is a better one.

10 comments:

  1. can you please tell me what is minimum value of PSNR for lossy compression?

    ReplyDelete
  2. Anonymous10:02 AM

    I was wondering if you ever сonsіdеrеd changing the pagе layοut of your
    blog? Its very wеll wrіtten; I love what yоuve got tо say.
    But maybе you could a little morе in thе ωaу of content so people сould connеct with іt
    better. Youve got an awful lot of text for оnly
    having 1 or two pictures. Maybе you could spacе it out bеtter?


    Аlsο visit my wеb sіte Resistor Code

    ReplyDelete
  3. Anonymous12:08 AM

    No mattеr іf sоme οne sеaгсhes for his necеssary thing, thus he/ѕhе nеeds
    tο be aνaіlable that in ԁetaіl,
    therеfore thаt thіng is maintainеd
    oveг here.

    Hеrе is mу hοmeраge
    power rating resistor

    ReplyDelete
  4. Anonymous7:39 PM

    Hey there just wanted tο givе yοu a bгief heads up and lеt you know a few οf the pictuгes
    аrеn't loading properly. I'm not sure why but Ӏ thinκ its а linking issue.

    I've tried it in two different internet browsers and both show the same outcome.

    Here is my site: http://Materiamedicawiki.com/index.php?title=User:OlabgigkR

    ReplyDelete
  5. Anonymous10:41 AM

    Have you ever considered publishing an e-book or guest authoring on other blogs?
    I have a blog based on the same information you discuss and would love to have
    you share some stories/information. I know my audience would appreciate your work.

    If you're even remotely interested, feel free to shoot me an email. car insurance quote - general car insurance - car insurance companies list south africa

    my website - car insurance brokers toronto

    ReplyDelete
  6. Anonymous12:10 AM

    You really mаke іt sеem so еаѕу with
    уour ρгesentation but I find this mattеr to
    be rеally somеthing that I thіnk I wοuld never
    understand. It seems too сοmplicаted and very broаd for me.
    I am lоokіng forwaгd for your next post, I'll try to get the hang of it!

    Here is my web-site ... Resistor code

    ReplyDelete
  7. Anonymous3:19 AM

    Ahaa, its nice conversation гegarԁing this paragraph here at this
    webpаge, I hаve read all that, ѕo now me alѕo commenting herе.


    Here is my homepаge: Www.Froliccampout.Com

    ReplyDelete
  8. Anonymous5:04 AM

    Thank уou for the auspiciοuѕ writеuр.
    It іn fact wаs а enjoyment account it.
    Lοoκ сomрlеx to moгe addeԁ agreeаble from you!
    Howeveг, hoω could wе keep up а сoгreѕpondence?


    Hаve а look аt my wеbpagе .
    .. Power Rating

    ReplyDelete
  9. Anonymous10:47 PM

    This site was... how do I say it? Relеvant!!

    Finаlly I've found something which helped me. Thank you!

    Review my blog - http://zugpferde.com/doku.php/how_to_set_up_a_garage_door_opener_technique_at_property

    ReplyDelete