Wavelet-Based Image Compression
In Chapter 3, we studied how the discrete cosine transform (DCT) is used
for the compression of images. The basic properties of getting a higher com-
pression ratio include energy compaction and the de-correlation property of
the DCT. The JPEG lossy image compression standard that uses DCT suffers
through artifacts like blockiness and ringing, which degrade the quality of
the decompressed image.
In this chapter, we are going to study another transform called the
wavelet transform, which possesses properties like energy compaction and
de-correlation and is used in image compression, reducing an effect of block-
iness artifact. The wavelet is the most popular transform in the eld of signal
processing and is used in a number of applications. The concept of wavelets,
continuous and discrete wavelets and their properties, and wavelet-based
multiresolution analysis (MRA), which is used for image compression, are
described in this chapter. The wavelet-based compression is used in JPEG
2000 or the J2K image compression standard.
4.2 The Short-Time Fourier Transform
The Fourier transform has long been used for signal analysis. The Fourier
transform provides information about the frequency spectrum of the sig-
nal. It presents the frequencies and their amplitudes present in the signal.
The Fourier transform only presents the signal frequencies and not the time
instance at which a particular frequency occurs. Another drawback of the
Fourier transform is that it works better with stationary signals.
This frequency localization problem is overcome by the short-time Fourier
transform (STFT) in which the signal is analyzed in a particular time inter-
val, taking the Fourier transform in that interval. For analysis of the low-
frequency signal, the time interval should be large, and for a high-frequency