Wavelet Compression/Reconstruction and Visualization of Pulmonary X-Ray Images for Achieving of Asbestosis Infected Patients Data - Visual Computing: Scientific Visualization and Imaging Systems - page 117

Wavelets in biomedical applications were covered in [ 16 ]. Considerable efforts
were performed from 1990s till this day to apply wavelets for radiological
imaging. Fidelity of reconstructed radiographic images was discussed in [ 17 ],
where wavelet transform and JPEG coding were used. Wavelets were introduced
in DICOM standard for image compression, because of fidelity [ 17 , 18 ]. Fidelity
for different wavelets and compression ratios (CR) was checked in [ 12 ].
This chapter deals with wavelet compression of the pulmonary X-rays with
important condition—reconstructed images must provide the original medical
information. Furthermore, suspicious areas in the reconstructed images should be
emphasized to make easier diagnostics.
Benefits are in monitoring of health condition, prevention of disease, early
diagnostics, more reliable diagnostics, and saving space for achieving medical
data. Therefore, contribution to saving and/or prolonging human lives is the most
important benefit of the proposed algorithm.
The chapter is organized as follows. In the following sections, theoretical back-
ground, proposed algorithm, results, and conclusions will be presented, respectively.

6.2 Theoretical Background

Image compression, is one of the most outstanding applications of wavelets [ 16 ,
19 , 20 ]. Powerful compression possibilities of wavelets have been exploited in
many applications, off and online, for single images and for image sequences [ 21 ].
Wavelets are incorporated in JPEG-2000 standard as well and security [ 22 - 24 ].
Their ability in denoising and compression often depend on thresholding. In the
proposed algorithm (in the next heading), thresholding is avoided.
The basic idea of an integral representation is to describe a signal x ð t Þ , that is
integrable in Lebesque sense and closed on L 2 ð R Þ , via its density X ð s Þ with respect
to arbitrary kernel u t ; ð :
x ð t Þ ¼ Z

X ð s Þ u ð t ; s Þ dst 2 T L 2 ð R Þ ð 6 : 1 Þ

S

The wavelet transform W ð a ; b Þ of a continuous-time signal x ð t Þ is defined as:
W ð a ; b Þ ¼ jj 2 Z

þ1

x ð t Þ w ð t a
b

Þ dt ð 6 : 2 Þ

1

where b is scaling parameter, a translation parameter, and w ð t Þ wavelet. Thus, the
wavelet transform can be computed as the inner product of x ð t Þ and translated and
scaled versions of the wavelet. If w ð t Þ is considered to be a bandpass impulse
response, then the wavelet analysis can be understood as a bandpass analysis.
Time and frequency resolution of WT depends of b. For high analysis frequen-
cies, good time localization but poor frequency resolution can be achieved. When