A Matlab Playground for JPEG

1
A Matlab Playground for JPEG

• Andy Pekarske
• Nikolay Kolev

2
What is JPEG

• We explored the information flow during
  transformation of images from their basic bitmap
  format to compressed coefficients streams.
• We also undertook the task to construct a JPEG
  decoder which uses the compressed binary
  coefficient sequences and converts them back into
  viewable images.
• This allowed us to analyze better the complete
  cycle of image compression and at the same time
  to be able to understand and explore the complete
  process which is undertaken when compressing,
  storing, transmitting and rebuilding an image
  with JPEG.

3
Improvement Possibilities

• Adhering to the standards original scheme, we
  wanted to explore and implement various
  self-contained techniques that could lead to
  better image quality and higher compression
  ratio.
• We wanted to verify that DCT (Discrete Cosine
  Transform) is the best choice for image
  energy/frequency compaction transform.
  Theoretically FFT (Fast Fourier Transform) is
  also an acceptable (actually the first) method
  for frequency analysis of time and space signals,
  although our conclusion was that DCT is a better
  choice.
• The lossy compression portion of JPEG achieved
  through block coefficient quantization could be
  made less lossy and more efficient at the same
  time by choosing in a more sophisticated way
  which coefficients should be stripped of
  precision and which retained with high precision
  at this stage of the overall image compression.
• Theoretically it could be shown that Arithmetic
  Encoding could be a better and more efficient
  technique for lossless compression than Huffman
  Encoding.

4
Designing the Huffman Decoder

• Having a JPEG encoder initially, we had to design
  a decoder in order to make the process useful.
• It was interesting to learn that the reverse
  process (decoding) of Huffman coding is quite
  more computationally intensive than the encoding
  portion of this lossless compression technique.

5
DCT vs. FFT

• At first sight FFT should be a good substitute
  for DCT, as both take as input nxn blocks and
  produce nxn coefficient blocks and both feature
  perfect reconstruction.
• We could not prove that assumption in our
  project. FFT gives a very blurry result for any
  image processed with FFT.

6
Optimizing Quantization

• We believe that the lossless portion of JPEG
  could be less lossy if a more sophisticated
  method for coefficient quantization is utilized.
• Our test program allows for experimenting with
  this parameter of JPEG and we implemented portion
  of selective algorithm that allows for
  compression level choice.

7
Implementing Arithmetic Encoding

• We had to construct a complementary coding pair
  Arithmetic Encoder/Decoder in order to be able to
  compare Arithmetic with Huffman coding.
• We utilized two Matlab functions arithmenco( )
  and artithmdeco( ) to implement this feature.
• We realized that is quite challenging to come up
  with a good encoding scheme and to design an
  efficient interface so that there is a robust
  coupling between encoder and decoder

8
Visual Results
Original 64x64 128x128
DCT, Huffman
DCT, Arithmetic
Here default quantization is used
9
Visual Results
Original 64x64 128x128
DCT, Huffman
DCT, Arithmetic
Here adaptive (higher in the case) quantization
is used
10
Conclusions

• Switching an image encoder/decoder to use
  different types of Frequency Domain transforms is
  not a trivial task
• Quantization matrix choice is very important for
  achieving good compression ratio without loss of
  quality
• As expected, images processed by Arithmetic
  encoding are identical to images undergone
  Huffman lossless compression
• Arithmetic encoding could be a better scheme for
  lossless compression but requires a much more
  sophisticated algorithm than that in Huffman
  method in order to make this hold in practice.

11
Demonstration and Questions

• Demonstration of Matlab code and conducted
  experiments
• Audience chance to experiment with Matlab program
• Questions