Learning Better Lossless Compression · 2020. 6. 17. · Fabian Mentzer Luc Van Gool Michael...

Learning Better Lossless Compression Using Lossy CompressionFabian Mentzer Luc Van Gool Michael Tschannen

What and Why

BPG xl Residual x – xl

Residual is centered closely around 0 →

Encode residual of lossy image compression algorithm BPG to do lossless compression.

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

BPG x

Background: Arithmetic Coding

~ p

Setup: Finite set of symbols, the probability of a symbol occurring is given by the probability distribution p.

We can encode a stream of symbols losslessly to a bistream with Arithmetic Coding.

, ,

Set of symbols:


i.i.d. ~ p

This is an example stream. p( ) is higher, so we want to use fewer bits when encoding a banana symbol! That’s what arithmetic coding does.

Set of symbols:

~ p, ,



Stream of symbols:


bitstream

Stream of symbols:

i.i.d. ~ p arithmetic encoder

Arithmetic coding assigns a bit-sequence to each symbol, such that more likely symbols get shorter sequences. We encode the stream of symbols into one bitstream.

~ p, ,



Set of symbols:


arithmetic decoder

Decoding recovers the stream

bitstream

Stream of symbols:

i.i.d. ~ p arithmetic encoder

Set of symbols:

~ p, ,




Set of symbols:

~ p, ,

Problem: In general, we don’t know p. So we learn a model p’ for it by minimizing the cross-entropy H(p, p’). This is the same as minimizing the negative log likelihood of p’ over mini-batches.

Lossless Compression

BPG xl Residual x – xlBPG xSo, to encode this residual, all we need is a model p(r).

How

BPG

Bitstream

QCx

xl

Encoding1. Get quality factor Q for BPG from the learned Q-classifier (QC). 2. Encode input x with BPG using that Q, get xl and save to bitstream.

How

RC

BPG

Bitstream

QC

xl

xp(r|xl)

3. Feed xl to the learned Residual Compressor (RC), which predicts the conditional PMF p(r|xl).

Encoding

How

−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

Arithmetic Coding

RC

BPG

Bitstream

QC

xl

x

rp(r|xl)

4. Calculate residual r = x – xl. 5. Encode r using PMF p(r|xl)

with Arithmetic coding.

Encoding

How


Arithmetic Coding

RC RC

BPG

Bitstream

QC

xl

x

rp(r|xl) p(r|xl)

Decoding1. Obtain xl from the bitstream. 2. Feed xl into RC to get PMF

p(r|xl).

xl

r

How


Arithmetic Coding

Arithmetic Coding

RC RC

BPG

Bitstream

QC

xl

x

rp(r|xl) p(r|xl)

xl

3. Decode r from the bitstream, using the PMF p(r|xl) and arithmetic coding.

Decoding

How

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


rArithmetic Coding

Arithmetic Coding

RC RC

BPG

Bitstream

QC

xl

x

r

xp(r|xl) p(r|xl)

xl

4. Obtain x = r + xl.Decoding

Results

0 1 2 3 4

Learned

Non-Learned

+44%

+9.5%

+9.2%

PNG

JPEG2k-LL

WebP-LL

FLIF

L3C

Ours

[Mean Bits Per Sub-Pixel on OpenImages]

+2.8%

+7.2%

State of the Art on Open Images, where we train.

Results

0 1 2 3 4

Lear

ned

Non

-Lea

rned

PNG

JPEG2k-LL

WebP-LL

FLIF

L3C

Ours

CLIC.mobile

Better than previous learned method (L3C) on other datasets

1.5 2.5 3.5 4.5CLIC.pro

1.5 2.5 3.5 4.5DIV2K

+54%

+7.2%

+9.3%

+4.9%

-1.8%

+36%

+2.3%

+2.5%

+0.4%

-5.1%

+38%

+1.6%

+3.2%

+0.5%

-5.5%

Learning Better Lossless Compression · 2020. 6. 17. · Fabian Mentzer Luc Van Gool Michael...

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