Thresholding in a calculation algorithm for fast approximation of wavelet transform

Charles C. Chang; Jyh-Charn S. Liu; Andrew K. Chan

doi:10.1117/12.292807

30 October 1997 Thresholding in a calculation algorithm for fast approximation of wavelet transform

Charles C. Chang, Jyh-Charn S. Liu, Andrew K. Chan

Proceedings Volume 3169, Wavelet Applications in Signal and Image Processing V; (1997) https://doi.org/10.1117/12.292807
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

Abstract

Wavelet transform has been widely used in many signal and image processing applications such as edge detection and data compression. For applications that tolerate a slight compromise in accuracy for faster speed, a fast approximation of wavelet transform is favorable. In this paper we propose a simple yet effective algorithm for fast wavelet transform. The use of fixed point numbers simplifies the hardware design and computational complexity than the use of a floating point arithmetic unit. Calculations are further reduced using our thresholding-in-calculation (TIC) technique to omit calculations of small terms that are negligible to the accumulated sum. The TIC technique basically determines whether a multiplication followed by an addition shall be executed using a look-up table with the quantized magnitude of multiplication operands as input parameters. Knowing the levels of quantization, any combination of the quantized multiplication operands can approximate the product and be compared to a predetermined threshold value. If the approximated product is greater than or equal to the threshold value, the corresponding entry in the look-up table is marked for multiplication; otherwise, no multiplication will be executed. Our simulation results show that our approximation algorithm is effective for wavelet transform of audio signals. In addition, when our algorithm is applied to a simple wavelet based edge detection algorithm, the detection result is almost the same as the one using precise calculation of the wavelet transform.

Citation Download Citation

Charles C. Chang, Jyh-Charn S. Liu, and Andrew K. Chan "Thresholding in a calculation algorithm for fast approximation of wavelet transform", Proc. SPIE 3169, Wavelet Applications in Signal and Image Processing V, (30 October 1997); https://doi.org/10.1117/12.292807

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available

Members: $17.00

Non-members: $21.00 ADD TO CART

PROCEEDINGS
8 PAGES

DOWNLOAD PAPER SAVE TO MY LIBRARY

GET CITATION

RIGHTS & PERMISSIONS

Get copyright permission Get copyright permission on Copyright Marketplace

KEYWORDS

Wavelet transforms

Detection and tracking algorithms

Edge detection

Toxic industrial chemicals

Computer simulations

Data compression

Fast wavelet transforms

Show All Keywords

Keywords/Phrases

Search In:

Publication Years