40 research outputs found
Image Compression by Wavelet Transform.
Digital images are widely used in computer applications. Uncompressed digital images require considerable storage capacity and transmission bandwidth. Efficient image compression solutions are becoming more critical with the recent growth of data intensive, multimedia-based web applications.
This thesis studies image compression with wavelet transforms. As a necessary background, the basic concepts of graphical image storage and currently used compression algorithms are discussed. The mathematical properties of several types of wavelets, including Haar, Daubechies, and biorthogonal spline wavelets are covered and the Enbedded Zerotree Wavelet (EZW) coding algorithm is introduced. The last part of the thesis analyzes the compression results to compare the wavelet types
An Analysis of Stockwell Transforms, with Applications to Image Processing
Time-frequency analysis is a powerful tool for signal analysis and processing. The Fourier transform and wavelet transforms are used extensively as is the Short-Time Fourier Transform (or Gabor transform). In 1996 the Stockwell transform was introduced to maintain the phase of the Fourier transform, while also providing the progressive resolution of the wavelet transform. The discrete orthonormal Stockwell transform is a more efficient, less redundant transform with the same properties.
There has been little work on mathematical properties of the Stockwell transform, particularly how it behaves under operations such as translation and modulation. Previous results do discuss a resolution of the identity, as well as some of the function spaces that may be associated with it [2]. We extend the resolution of the identity results, and behaviour under translation, modulation, convolution and differentiation. boundedness and continuity properties are also developed, but the function spaces associated with the transform are unrelated to the focus of this thesis.
There has been some work on image processing using the Stockwell transform and discrete orthonormal Stockwell transform. The tests were quite preliminary. In this thesis, we explore some of the mathematics of the Stockwell transform, examining properties, and applying it to various continuous examples. The discrete orthonormal Stockwell transform is compared directly with Newland’s harmonic wavelet transform, and we extend the definition to include varitions, as well as develop the discrete cosine based Stockwell transform. All of these discrete transforms are tested against current methods for image compression
A family of stereoscopic image compression algorithms using wavelet transforms
With the standardization of JPEG-2000, wavelet-based image and video
compression technologies are gradually replacing the popular DCT-based methods. In
parallel to this, recent developments in autostereoscopic display technology is now
threatening to revolutionize the way in which consumers are used to enjoying the
traditional 2D display based electronic media such as television, computer and
movies. However, due to the two-fold bandwidth/storage space requirement of
stereoscopic imaging, an essential requirement of a stereo imaging system is efficient
data compression.
In this thesis, seven wavelet-based stereo image compression algorithms are
proposed, to take advantage of the higher data compaction capability and better
flexibility of wavelets. In the proposed CODEC I, block-based disparity
estimation/compensation (DE/DC) is performed in pixel domain. However, this
results in an inefficiency when DWT is applied on the whole predictive error image
that results from the DE process. This is because of the existence of artificial block
boundaries between error blocks in the predictive error image. To overcome this
problem, in the remaining proposed CODECs, DE/DC is performed in the wavelet
domain. Due to the multiresolution nature of the wavelet domain, two methods of
disparity estimation and compensation have been proposed. The first method is
performing DEJDC in each subband of the lowest/coarsest resolution level and then
propagating the disparity vectors obtained to the corresponding subbands of
higher/finer resolution. Note that DE is not performed in every subband due to the
high overhead bits that could be required for the coding of disparity vectors of all
subbands. This method is being used in CODEC II. In the second method, DEJDC is
performed m the wavelet-block domain. This enables disparity estimation to be
performed m all subbands simultaneously without increasing the overhead bits
required for the coding disparity vectors. This method is used by CODEC III.
However, performing disparity estimation/compensation in all subbands would result
in a significant improvement of CODEC III. To further improve the performance of
CODEC ill, pioneering wavelet-block search technique is implemented in CODEC
IV. The pioneering wavelet-block search technique enables the right/predicted image
to be reconstructed at the decoder end without the need of transmitting the disparity
vectors. In proposed CODEC V, pioneering block search is performed in all subbands
of DWT decomposition which results in an improvement of its performance. Further,
the CODEC IV and V are able to perform at very low bit rates(< 0.15 bpp). In
CODEC VI and CODEC VII, Overlapped Block Disparity Compensation (OBDC) is
used with & without the need of coding disparity vector. Our experiment results
showed that no significant coding gains could be obtained for these CODECs over
CODEC IV & V.
All proposed CODECs m this thesis are wavelet-based stereo image coding
algorithms that maximise the flexibility and benefits offered by wavelet transform
technology when applied to stereo imaging. In addition the use of a baseline-JPEG
coding architecture would enable the easy adaptation of the proposed algorithms
within systems originally built for DCT-based coding. This is an important feature
that would be useful during an era where DCT-based technology is only slowly being
phased out to give way for DWT based compression technology.
In addition, this thesis proposed a stereo image coding algorithm that uses JPEG-2000
technology as the basic compression engine. The proposed CODEC, named RASTER
is a rate scalable stereo image CODEC that has a unique ability to preserve the image
quality at binocular depth boundaries, which is an important requirement in the design
of stereo image CODEC. The experimental results have shown that the proposed
CODEC is able to achieve PSNR gains of up to 3.7 dB as compared to directly
transmitting the right frame using JPEG-2000
Time Frequency Analysis of Wavelet and Fourier Transform
Signal processing has long been dominated by the Fourier transform. However, there is an alternate transform that has gained popularity recently and that is the wavelet transform. The wavelet transform has a long history starting in 1910 when Alfred Haar created it as an alternative to the Fourier transform. In 1940 Norman Ricker created the first continuous wavelet and proposed the term wavelet. Work in the field has proceeded in fits and starts across many different disciplines, until the 1990’s when the discrete wavelet transform was developed by Ingrid Daubechies. While the Fourier transform creates a representation of the signal in the frequency domain, the wavelet transform creates a representation of the signal in both the time and frequency domain, thereby allowing efficient access of localized information about the signal