An Adaptation of EPCA to Image Compression and Reconstruction

1
An Adaptation of EPCA to Image Compression and
Reconstruction

• Xin LI, Zhili Wu, Xiaofeng Zhang
• Dept. of Computer Science
• Hong Kong
  Baptist University

2
Outline

• Problem Review
• Background on Dimension Reduction and Image
  Compression
• Background on EPCA
• Our Modified Method
• Function deduction
• Experimental Results
• Open Problems

3
Introduction

• Dimension Reduction
• Try to find the accurate low-dimensional
  representation for original high-dimensional data
• Linear Nonlinear compression e.g. PCA, LLE,
  Exponential-PCA
• Application area e.g. machine learning, signal
  processing, image processing
• Image Compression

Swiss Roll
4
Motivation

• Belief Compression
• Proposed by N. Roy, G. Gordon and Thrun (2005)
• Due to the sparse belief space occurred in the
  some real world POMDP problem such as Robot
  Navigation Problem.
• To find a low-dimensional subspace embedded in
  the original high-dimensional space of belief
  state.
• Image Compression
• Sparse images?
• Find a accurate low-dimensional description for
  Sparseimages?

5
Motivation

• Belief Compression
• Proposed by N. Roy, G. Gordon and Thrun (2005)
• Due to the sparse belief space occurred in the
  some real world POMDP problem such as Robot
  Navigation Problem.
• To find a low-dimensional subspace embedded in
  the original high-dimensional space of belief
  state.
• Image Compression
• Sparse images?
• Find a accurate low-dimensional description for
  Sparseimages?

6
Motivation

• Belief Compression
• Proposed by N. Roy, G. Gordon and Thrun (2005)
• Due to the sparse belief space occurred in the
  some real world POMDP problem such as Robot
  Navigation Problem.
• To find a low-dimensional subspace embedded in
  the original high-dimensional space of belief
  state.
• Image Compression
• Sparse images?
• Find a accurate low-dimensional description for
  Sparseimages?

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EPCA - The Compression Tool
In what degree
(High-D)
(High-D)

• General function
• Loss Function
• Using the exponential function as the link
  function
• Advantages
• Guarantee all the reconstructed data with all
  positive elements
• Loss function derived from the exponential link
  function has been proven to be an unnormalized
  Kullbach-Leibler (KL) divergence

f, U
(Low-D)
Particularly,
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Newton Method for EPCA and Its Simplification
Loss Function
Minimize Loss Iteratively solving with Newton
method
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Our proposed simplification for E-PCA
Original iterative function
Modified function
Our simplification makes the updating simpler by
only requiring to calculate U one time for all j
in each iteration
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Distinction of E-PCA
Comparison with PCA
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Comparison with SVD
Its clearly the reconstruction using E-PCA is
better!!
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E-PCA and Block E-PCA on Image Compression

• Standard Lenna image of 512 by 512 gray pixels to
  test.
• Make an comparison between E-PCA and Block E-PCA
• E-PCA is better in reconstruction, but the Block
  E-PCA has fast computation

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Denoise Behavior Comparison with SVD

• To test a 27 by 418 image
• added Poisson noise.
• E-PCA is better!!

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Open problem

• Further simplification for E-PCA
• Extend E family for E-PCA
• Better link function for image compression?
• Link functions for image family respectively?
• To achieve more efficient and compact
  low-dimensional representation

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• The end

QA