# Improved Image Compression Via Evolvable Wavelets.

## Institution

Murray State University

## Faculty Advisor/ Mentor

James Hereford

## Abstract

This research describes a new approach to image and signal compression based on “evolvable” wavelet filters. Wavelet filters are used in many practical applications such as FBI fingerprint compression and the JPEG 2000 standard. In this research we want to find the wavelet filter which gives the best overall signal-to-noise ratio for a given compression ratio. To do this, a genetic algorithm is used to find the optimal wavelet for a given image. A genetic algorithm applies some of the principles of biological evolution to find the optimal solution to a problem. First, a population, or set of solutions, is selected. The best solutions are statistically selected and “mated” to form a new population of solutions. New solutions are also added at random via mutation. In our case, the mutation occurs by randomly changing bits of data. This new population of solutions is then tested and the cycle repeats. The idea is similar to the “survival of the fittest” concept with each generation (iteration) the population average gets better and eventually converges to the best solution. Thus, the optimal wavelet “evolves” over many generations to the strongest solution. What has made wavelets difficult to optimize in the past is that the wavelet coefficients must satisfy some specific constraints. We overcome this difficulty by using a recently discovered parameterized representation of wavelets. The results from the optimal wavelet found from the genetic algorithm will be compared against the results from the wavelet filter used by the FBI.

Improved Image Compression Via Evolvable Wavelets.

This research describes a new approach to image and signal compression based on “evolvable” wavelet filters. Wavelet filters are used in many practical applications such as FBI fingerprint compression and the JPEG 2000 standard. In this research we want to find the wavelet filter which gives the best overall signal-to-noise ratio for a given compression ratio. To do this, a genetic algorithm is used to find the optimal wavelet for a given image. A genetic algorithm applies some of the principles of biological evolution to find the optimal solution to a problem. First, a population, or set of solutions, is selected. The best solutions are statistically selected and “mated” to form a new population of solutions. New solutions are also added at random via mutation. In our case, the mutation occurs by randomly changing bits of data. This new population of solutions is then tested and the cycle repeats. The idea is similar to the “survival of the fittest” concept with each generation (iteration) the population average gets better and eventually converges to the best solution. Thus, the optimal wavelet “evolves” over many generations to the strongest solution. What has made wavelets difficult to optimize in the past is that the wavelet coefficients must satisfy some specific constraints. We overcome this difficulty by using a recently discovered parameterized representation of wavelets. The results from the optimal wavelet found from the genetic algorithm will be compared against the results from the wavelet filter used by the FBI.