Keywords: polarimetric matched filter, genetic algorithm, SAR
Abstracts
The optimal use of polarimetric scattering information provided by fully polarimetric synthetic aperture radar (SAR) is useful for discriminating between different terrain covers. Conventionally, eigenanalysis is used to synthesize a polarimetric matched filter (PMF) image that maximizes the contrast between the features of interest, but it involves many algebraic operations and can get one contrast ratio for any two classes at one time. This paper describes the application of genetic algorithm (GA) to the contrast enhancement. It obtains all contrast ratios characterizing the best discrimination for any two among all possible classes simultaneously. After using an L-band fully polarimetric SAR image as a test data, it shows that the proposed method is very effective and promising.
1. Introduction
Remote sensing imagery data are known for their high degree of complexity and irregularity, especially for SAR image. Moreover, there are usually many natural and man-made targets resulting in extremely difficult in the task of segmentation, classification, and detection. The problem of optimization of polarimetric contrast enhancement has been attracting attention in recent years [1-7]. The main purpose is to choose the polarization states that enhances the desired target versus the undesired target (clutter). What we can control is the polarization states of the transmitter and the receiver. For example, Teti et al. [3] used polarimetric matched filter (PMF) technique based on eigenanalysis to enhance image contrast in selected regions to improve detection and classification of flooded regions. Yang et al. [4] developed a numerical method for solving the optimal problem of contrast enhancement. However, the polarimetric techniques reported abovementioned for target discrimination have been limited to the special case of two targets because of the complex nature of the optimization problem. In reality, there are more than two possible targets of interest involving the discrimination process. This motivates us to use stochastic-base search method to handle problems with targets more than two so as to enhance the operation efficiency and yet remain effective.
Two stochastic-base optimization procedures that can deal a large number of discrete parameters are simulated annealing and genetic algorithm (GA). In recent years, applications of GA to a variety of optimization problems in electromagnetics have been successfully demonstrated [7-11]. It's optimization is global in the sense that it has random components that test for solutions outside the current minimum, while the algorithm converges. In particular, GA is much better at dealing with solution spaces having discontinuities, constrained parameters, and/or a large number of dimensions with many local maxima.
Traditional optimization algorithms search for the best solution, using gradients and/or random guesses. Gradient methods have the disadvantages of getting stuck in local minimum, requiring gradient calculations, working on only continuous parameters, and being limited to optimizing a few parameters. Random-search methods do not require gradient calculations, but being a blind-search and tend to be slow. In addition, GA is easy to program and is able avoid the mathematical rigor of traditional optimization methods.
In this paper, we utilize GA to search for a pair of optimal polarimetric states so that at these polarization states the contrast ratio between two classes in SAR image is maximmum. Besides, it can get all contrast ratios for any two classes simultaneously subject to the sum of all individual contrast ratios being maximum. The results also provide an excellent preprocess for subsequent image classification, if desired.
2. Genetic Algorithm
This section begins with a brief overview of GA, followed by a description of a step-by-step implementation. More details on GA can be found in [9][11][12] and references cited there. The goal of the GA is essentially to find a set of parameters that maximize (or minimize) the output of a function (or process). A typical flow diagram of a simple GA optimizer is presented in Figure 1.
2.1 Parameters Encoding
Encoding is a transformation from the parameter space (also called phenotype) to the gene space (also called genotype). Genes in the chromosome represent the coded parameters. Usually, a binary coding is utilized. For example, if the chromosome has three parameters (said var1, var2, var3) to be optimized and use three bits for each parameter, then the chromosome might be written as
Chromosome
1 1 0
0 0 1
1 0 0
Parameters
var1 var2 var3
2.2 Population Initialization
If there are M populations in a generation, 1 or 0 is randomly selected for each bit to form a chromosome and consequently construct M chromosomes that represent possible solution of var1, var2, and var3. This randomness guarantees the diversity of population of possible solutions.
Chromosome 1
1
1
0
0
0
1
1
0
0
Chromosome 2
0
1
1
1
1
1
0
1
0
Chromosome M
1
0
0
0
1
1
1
0
1
2.3 Fitness Calculation
Each chromosome has a cost value, founded by evaluating a fitness function, or object function. Fitness evaluation involves decoding of the chromosomes to produce the parameters that are associated with the individual. If a GA tool is available, the good fitness function is the only portion that a user must provide and in general the most difficult part of the whole processes. The fitness value in this example can be expressed as
fitness = f(var1, var2, var3) (1)
2.4 Reproduction
Reproduction, also called selection, shows the influence of the fitness value to GA. Although, fitness is the merit of goodness of an individual, reproduction cannot be executed only by selecting the best individual, because the best individual may not be very close to the optimal solution, especially in the very early generation. In order to avoid the problem of premature convergence, some individuals with relative low fitness value must be preserved to ensure that genes possessed by these individuals are not lost prematurely. The selection operator can either be stochastic or deterministic.
2.5 Crossover
The most productive step in GA before convergence is crossover. It stems from the idea that by exchanging information between two chromosomes may produce a new better chromosome. One-point and two-point crossover methods are the most popular.The probability of individuals chosen to attend crossover during each generation is specified by the parameter pcrossover(typically 0.6---1.0). After crossover, the total number of chromosomes remains constant.
| parent 1 |
|
1 1 0 0 0 |
|
1 1 0 0 |
| parent 2 |
|
0 1 1 1 1 |
|
1 0 1 0 |
| offspring 1 |
|
1 1 0 0 0 |
|
1 0 1 0 |
| offspring 2 |
|
0 1 1 1 1 |
|
1 1 0 0 |
