On the Design of Fast Wavelet Transform Algorithms With Low Memory Requirements

• Published in: IEEE transactions on circuits and systems for video technology Vol. 18; no. 2; pp. 237 - 248
• Main Authors: Oliver, J., Perez Malumbres, M.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Algorithms; Applied sciences; Circuit properties; Coding, codes; Detection, estimation, filtering, equalization, prediction; Devices; Digital cameras; Discrete cosine transforms; Discrete wavelet transforms; Electric, optical and optoelectronic circuits; Electronic circuits; Electronics; Encoders; Energy resolution; Exact sciences and technology; Frequency filters; Image coding; Image processing; Information, signal and communications theory; optimization methods; PDA; Personal digital assistants; Proposals; run length codecs; Signal and communications theory; Signal convertors; Signal, noise; Studies; Synchronism; Telecommunications and information theory; wavelet transform computation; Wavelet transforms; Wavelet transform computation; optimization methods; image coding; run length codecs; Personal digital assistant; Performance evaluation; Mobile phone; State of the art; Image processing; Data compression; Wireless telecommunication; Implementation; Optimization; wavelet transform computation; Image coding; Codec; Filter bank; Fast algorithm; Mobile radiocommunication; Coding circuit; Image compression; Two dimensional model; Synchronization; Wavelet transformation; Recursive method; Signal processing; Numerical simulation
• ISSN: 1051-8215; 1558-2205
• DOI: 10.1109/TCSVT.2007.913962

In this paper, a new algorithm to efficiently compute the two-dimensional wavelet transform is presented. This algorithm aims at low memory consumption and reduced complexity, meeting these requirements by means of line-by-line processing. In this proposal, we use recursion to automatically place the order in which the wavelet transform is computed. This way, we solve some synchronization problems that have not been tackled by previous proposals. Furthermore, unlike other similar proposals, our proposal can be straightforwardly implemented from the algorithm description. To this end, a general algorithm is given which is further detailed to allow its implementation with a simple filter bank or using the more efficient lifting scheme. We also include a new fast run-length encoder to be used along with the proposed wavelet transform for fast image compression and reduced memory consumption. When a 5-megapixel image is transformed, experimental results show that the proposed wavelet transform requires 200 times less memory and is five times faster than the regular one. If we consider the whole coding system, numerical results show that it achieves state-of-the-art performance with very low memory requirements and fast execution, becoming an interesting solution for resource-constrained devices such as mobile phones, digital cameras, and PDAs.