Fast search for best representations in multitree dictionaries.

Area of Science:

• Signal Processing
• Computer Vision
• Data Compression

Background:

• The best representation problem seeks to find the optimal way to represent a signal from a given dictionary to minimize a cost function.
• Existing dictionary frameworks have limitations in efficiently solving the best representation problem for complex signals.

Purpose of the Study:

• To introduce a novel framework of multitree dictionaries for solving the best representation problem.
• To develop an efficient algorithm for finding the best representation within this new framework.
• To demonstrate the effectiveness of the proposed framework in practical applications like image coding.

Main Methods:

• Development of the multitree dictionary framework, encompassing prior dictionary structures.
• Implementation of a recursive tree-pruning algorithm for efficient best representation search.
• Application and evaluation of the framework in a novel block image coder.

Main Results:

• The proposed recursive tree-pruning algorithm efficiently finds the best representation in multitree dictionaries.
• The novel block image coder significantly outperforms standard JPEG and quadtree-based methods.
• Performance of the new coder is comparable to advanced embedded coders like JPEG2000 and SPIHT.

Conclusions:

• The multitree dictionary framework provides an efficient and effective solution to the best representation problem.
• This framework offers significant advantages for signal processing tasks, particularly in image compression.
• The developed algorithm and coder represent a substantial advancement in data representation and compression technology.