among everyone this is a of lossy compression on a lossy compression on a set for hyperspectral and all spectral
images
that's a joint work with and they are about the not a button you the university of C N
so first give some motivation apart one but was a compression and the a specific problems
i will describe the proposed compression algorithm then a provide some experimental results on
i spectral and out for spectral images and
finally draw some calm
um
i spectral images are a collection of pictures taken at seven different wave of the same scene
quite a lot of data but when it comes to compress those data on were set to like we're faced
with the problem that
we don't have many computational resources to actually do
impressions so
first that the need is some low complexity um
that's quite different from compression on the ground our car idle is
the second but it thing is that unlike typical consumer digital cameras where there is a two dimensional
detector are rate to
picture
for hyperspectral images to we just have one um
a signal one dimensional array
that takes one a line of the image with all it's
a spectral channels all the different wavelength
the i-th the lines of the images or the image are for by the motion of the aircraft or set
light
so it they are taken at time
so that what use in table is that's we to the compression we don't have the whole image available but
just a few lines of the image with all the spectral channel so
we need to do compression using a a we will about one
so that's do we want to compress
good as we can so we want to have state-of-the-art compression efficiency
and for hyperspectral applications we need to cover a range of bit which is relatively large
to be from around zero point five two
three three or four bit
a pixel
that should be compared with a a sensor be that is typically between twelve and
uh sixteen bits per se
so we have to cover
a a little bit rate and high bit rate
fashion and finally
we need some error containment uh those uh
compressed data packets are down only uh use a communication channel
which is subject to occasional back loss and we don't want
that's a the signal back to these disrupts the reconstruction of the whole
so
uh there are several of all buttons for performing compression of two dimensional images like
and hyperspectral or on for spectral images
a most popular approach uses three dimensional tile from coding
for each sample jpeg two thousand we part two with that of course a multi component transformation
where you can use
you the spectral wavelet transform or an arbitrary spectral transformation
and then the light jpeg two thousand on each of the transform
a a spectral chan
we we can use a way list we use the couple nonlinear transforms whatever
this
uh uh was very well at low rates of the problem of this approach
the high complex
complexity comes from the top for but you know or or from the coding and rate distortion
use a shouldn't G
a thousand where you had to
uh
do we
i i coding all you links and then post compression rate distortion
ascension so that
mass too complex for on more
that it does work well for
archive
hmmm
the second thing is that if we want to use J two thousand well then a for compression we don't
have a whole image available
so our spatial transformations
we have just to take that
on a few lines of that image at a time
which is that
a possible with J
a thousand using be line based transformation
but then that start from them a shouldn't can be done in a global way more are
you has to be done and a lot of weight just a few lines at that time and there's a
big performance pen
or that
oh to be
a a global optimal rate distortion
age
the you the also approach is to use of prediction techniques using three dimensional spatial and spectral prediction
but action has been used for a time
for the last this compression
yeah was this compression used to to go for high quality applications where you want the maximum absolute error between
the decoder in an original image to be a by
a a user select value
so that works very well i high rates
i it doesn't work well as well the little bit rate
and then uh
a two dimensional prediction is usually a couple of colour this station an on how one i entropy coding
have a a clear that we don't go below one
pixel
the short course
a code word
but how one on can provide is just one
so
uh that's a problem
to go below one
so uh what we propose for a compression is based on a a approach where use three dimensional
spatial and spectral predictor or which keeps us a low complexity that need
a compression
but then we're faced with the problem of improving performance of a low bit
existing schemes
the just don't them
so that we don't know how do them is she's we don't really need to perform you was let's compression
move to
truly lasting compression
all the prediction residuals
and so in order to do that we improve quantisation stage
we don't use a simple scalar want either
and we a rate distortion optimization the whole ski
so
uh
this is how we do it
uh the prediction stage you use
therefore forms the prediction independently on sixteen by sixteen blocks of samples
so the speech or shows uh and in which dividing in four sixteen by sixteen blocks
and uh uh of for every we look at a all channels and the court look blocks in the the
different spectral channels so looking
what where the wavelet to mention
we probably right
from the curve at decoding block the bleeding spectral chan
so this is quite different from the kind of prediction that is usually uh and blowing in hyperspectral image compression
pixel by pixel
and not a lot by block prediction
but as will see is a loss as to a very efficient to start from
i
so essentially what we do is uh that are would need to in the next slide that we calculate a
linear predictor that use the previous well
but it be current law
then we calculate
the position the prediction residual and i think about this is that it provides a spatial error containment in that
it some compressed where one is lot
should
that we have set the next blocks in the
uh the the the the block in the same spatial position in the next wave lines but it not affect
and now their spatial loss
which
so the prediction is actually quite seen but we got X
the vector of samples of the current sixteen by six
in lexical that ring
are the vector of samples of the reference plot which is as i said
but score okay at decoder block in previous spectral channel
and then we calculate at least mean square predictor or with which is defined by two parameters are are fine
and and
and is the mean value of the current block and i'll wise at least means square parameter that
pretty P
current uh one
probably principal
alright
so uh the first uh the other thing to move formula
lossy compression quantisation
uh uh
technical near lossless compression of less quantisation
which is almost a do not at high bit but far from optimal a low bit
so for a bit rate compression its customary to use one with that some which creates long sequences of zeros
that are back to the effectively by and three coders
is is the optimal at lower rates
not i rates
and to find some that works well at all rates we decide to you
a a kind of quantizer which is called uniform threshold quantizer or or you Q
which is slightly more complex than E
in form quantizer
but dead zone
but is the or not at all
yeah O you do you
is actually
very simple
it's
i
i i there in which every interval what decision you of rows are all the same size
so calculating the court were is done much the same way
classical
colour you from quantizer
the difference lies in the fact that that construction there is not taken as the midpoint point of the quantization
interval but rather the sense
as H
so uh since we are a blank these to the prediction was walls we make use some so that the
position was you those
for a two dimensional
a a two sided exponentially decreasing distribution lower plot distribution
and so we calculate the
uh
actually actual construct and that used as a it's using these
is to be
and what happens is that if should look at this speech or
so we you can see here are are are the different quantization interval
the getting but of the point of the interval that you know a construction put by a a or for
one times are
a seems we use this uh we make this some some of distribution their out that the way that is
of the prediction that or or more be then the high values
so uh what we do is we add the collection term to the the construction but
account for that
so that by is that construction to works a little bit
so much so as the uh quantisation indexes low so close to
so that
uh
the or from your last
and the second and was the most important one is rate distortion optimization
and this is where really helps to use
a square blocks for the prediction
so the eight yeah here is
uh essentially similar to the skip mode be the compression
sometimes we find certain sixteen by sixteen or that can be pretty to really very well from the you reference
blah
and in that case we don't in the prediction a so we are other keep the encoding of the prediction
or
so that we save a lot it's in the process and just signal to the decoder
that the decoded signal on this case we just the pretty
that the decoder can
a couple
in particular
we actually
prediction
we calculate the variance of the prediction and D
and he can they're this variance for the special
and if D X is the threshold that
it means that the predictor is not a good enough for speech in the current block so we don't the
classical and encoding of the prediction or
i rice
if
the D is below a actual
we simply to that and prediction parameters for a lot of the file but no prediction that so
so that
the the would will be a a to uh mean the petition parameter
from the file
calculate a pretty or in use the predictor as coding
entropy coding all B
but addition was used was is done using a a power of two call
this is a a very typical become uh thing in uh compression for set like imaging
because goal of two codes are much see there than any other
a a cool especially arithmetic medical
so
uh there not was powerful but that that's of a good compromise
performance and complexity
and calculate
the best coding parameter
every sample
based on the of magnitude of on my prediction residual of a window of thirty two
so it's not done a lot
well
a sample by sent
right
so here are some results for the proposed algorithm
a a tried that on a different images all show results for
images from two different data
well as i've is i have this is an images
using spectrum there
long
which is flown on the aircraft
and these images are
had it they have two hundred fifty four spectral channels and the spatial signs
six and an at times five hundred and twelve images
um
and the is a the right images as are where by this
they have no calibration whatsoever no of corporations and not with really image
it is taken by
i've of is
used for
so that classification of
locations and
oh
the second image isn't a in image from the years and
some the which is operated by the not
which is used for a static of studies
these images have a a a a a much less piece spatially
just one hundred and thirty five times ninety pixels
but they have a a spectral channel signal can hundred one spec
is a quality metric we look at the P peak signal noise ratio and and we compare the performance of
the proposed algorithm with two other algorithms
well i he's jpeg two thousand part with the spectral
discrete wavelet transformation
in this case we do not perform the three dimensional a rate distortion optimization we're not doing any
line based comes from so that is also be shown for J
a thousand or and i'm realistic and
one would be actually run the set
a sort of upper bound of the
or of J
and the second algorithm is near lossless compression
use exactly the same predictor
and it to be colder
and not using the U G Q quantizer or nor the latest store
just a or
a by E D P C and we discard uniform quantization and entropy coding of the prediction was
are the results
the curve here
july two thousand to the wavelet transformation
and a continuous list compression algorithm
it is no you assess compression is better and transform coding at high bit-rates and you can see that here
will performance difference with respect to jpeg two thousand speech large over two bit per sample
but that were try this this is not a as good uh so essentially for two reasons
one is related to the fact that
the like to the quantization step size
and the were is the quality of the reference signal for the prediction so these points
this brings the
performance style
and low bit
but then and this i have is not able to achieve a rates be more one bit
a pixel because we're using a
got a call was mean got were like this one
there's just no way to go below that
the proposed algorithm seems to bring the best of both worlds here
better then a job but two thousand and and are a bit rate is larger than then point three or
do you point thirty five percent so
you and that's bit rates the rate distortion optimization works pretty nice here
and it's for for its performance tends to the performance of the yeah lost this compression at high rates and
that's
reasonable about because at high bit-rates
that it is a shall never select the skip model for any block the image and a uniform threshold quantizer
tense this colour one
so
the two algorithms essentially become pretty much the same
we have similar
you a results for the it's image
sort of a yes
do a two thousand as a little bit better or sometimes are performs by a small market
proposed algorithm some but is not quite as good
essentially
you know a comparable performance
and and that's pretty much the same you some near as compression is not a as low bit rates is
become pretty high bit
so this is still a a a a lot of jpeg two thousand for this image but jpeg two thousand
you and recall
is using a um the from a three dimensional very from
as a so
if we use the line based on from no one
so
um
alright right so uh the this is an example of visual quality and this is just essentially sensually goes to
show that we all the were using a block based pretty or we we don't have any hard
here
so this is a
uh a patch from one the end of every as your original signal
and this is not a construct signal by the proposed algorithm at zero one forty bit per piece so it's
is
you know one of the
oh well as
bit rates at the output but in can achieve
and as can be seen that i mean the artifacts
but no not not to science
what's that
the is is that a lot not the facts
uh come from the quantisation the transform from the a some from the coupling of one position
first transformation
where i is in this case where using a block based pretty but the quantisation used and independently of the
signal send
pretty
and what not
so this is what would have a job but for example
which creates you know a a lot
here just which essentially keeps the text or
alright right
so
uh
you can can an uh the proposed is essentially
uh a a a and you by for compression of
a a hyperspectral image where we achieve lower complexity by use
a prediction based approach
which uh uh forms
uh
is known as or better than the state-of-the-art of the art three dimensional for coding with really feature
distortion for optimization
so that seems to be a nice way for for on what compression of set images
complex in memory requirements are significantly lower than jpeg thousand
a it's difficult to compare the complexity of different algorithms by top to sign this working on J two thousand
and seems like the proposed approach to be like and man two
fewer operations than J
for a to the same
on this
uh but used in room for improvement
we're not using any or i've made calling but that and certainly have the coding efficiency apartment coding
what most are as by some margin
we might use
know and of the ring
that is using for a reference uh spectrum channel for the prediction not just a three spectral channel
a the spectral channel but use more correlated with the colour channel
so this is especially on is that provides the nice performance
uh this algorithm is people proposed to the european space efficiency is in is of a mission for the spectral
image image or these it on the is i X amount for
is going to fly to mars
you
that
do have any questions
i can you
can make any comment in regards to um
have the compression technique might affect processing that would occur after
uh the images uh
transmitted for example
yeah end member extraction or some sort of classification task
yeah
uh that's something that wouldn't propose lossy compression to a remote sensing device the re scared about the potential negative
effects of lossy compression so
uh we we were that experiments in the past with that's
and my feeling is that if the mean square error so you have several quality metrics cd can
to measure that not just mean square error the maximum air
spectral and will and and a lot of the matrix but
my experience with that
a if the mean square error is low in a a small have then everything we were very nice
and it's uh in
for for this kind of missions you definitely want to uh to keep the is got a sufficiently small
uh for not a hyperspectral image but for a spectral uh says i'll um
existing since C systems actually use a compression
spurt five does use lossy compression
at a bit of
well i think a three per pixel from paid
and the can a set of in just lossy compression so
uh uh the government agencies which are using problem funding they don't really not care about a lot of compression
but people
that the private companies they they care of what's so my feeling is that
compression is not a big deal
uh are exceptions obviously if the mean square error is is small enough run problem uh comes for example from
applications like a novelty detection
where a a large at so the one on one single pixel can actually by the result of a normally
detection so one has to be
to have a in some ways but for classification
my feeling is that a more less goes we the mean square error if the means got is low
we have time for a a question
quick
"'cause" take a speaker