The investigator and his colleague study the problem how to use tight wavelet frames for image/data compression. They have related the problem to many useful equivalent problems such as compressed sensing, cryptography, error correcting codes, in-painting or recovery of lost data, and consistent recovery from quantized expansions so that the ideas and mathematical techniques from the equivalent problems can be borrowed to study the image/data compression based on tight wavelet frames. They will use the method of virtual components, finite state machine, new variations of orthogonal greedy algorithm, lp optimization with p between 0 and 1, and harmonic frames to tackle the data compression problem. Preliminary results show that they are very promising. An ultimate goal of the proposed research is to build flexible methods for constructing multivariate tight wavelet frames with required properties for data compression and make them available for applications.
Images and data compression is absolutely necessary for internet, multimedia communication, and data storage/transmission. Fifteen years ago, FBI established a standard using a wavelet function to compress all finger prints for storage and processing. Tight wavelet frames are more flexible to construct than orthonormal wavelet functions. The investigator and his colleague will study how to use tight wavelet frames for image and data compression. The expected scientific results will enable better understanding how to find the most sparse representation of data in redundant linear systems. The results will have immediate impact on the modern design of communication systems like mobile telephony, digital camera, and digital broadcasting as well as on the methods of multimedia data compact representation.
