dctandidct.java

用java实现二维dct变换及其idct逆变换

public class 二维dct变换及idct变化 {

	/**
	 * @param args
	 * 可以考虑用一个子程序实现dct与idct，就像dft与idft那样
	 */
	
	final static int 维数 = 8;
	public static void main(String[] args) {
		// TODO 自动生成方法存根
		int i, j;
		二维dct变换及idct变化 ob = new 二维dct变换及idct变化();
		int[][] x = {{89,101,114,125,126,115,105,95},
				{97,115,131,147,149,135,123,113},
				{114,134,159,178,175,164,149,137},
				{121,143,177,196,201,189,165,150},
				{119,141,175,201,207,186,162,144},
				{107,130,165,189,192,171,144,125},
				{97, 119,149,171,172,145,117,92 },
				{88, 107,136,156,155,129,97,75}};
		//double[][] x_double = {{}{}{}{}{}{}{}{}{}{}};
		int[][] y = new int[维数][维数];		
		y = ob.dct(x);
		System.out.println("dct变换");
		for(i = 0; i < 维数; i++){
			for(j = 0; j < 维数; j++){
				System.out.print(y[i][j] +  "   ");
			}
			System.out.println();
		}
		
		
		System.out.println("idct变换");

		x = ob.idct(y);
		for(i = 0; i < 维数; i++){
			for(j = 0; j < 维数; j++){
				System.out.print(x[i][j] +  "   ");
			}
			System.out.println();
		}
	}
	
	//接收int型的x[][]，得到int型的y[][]
//	
	public int[][] dct(int[][] x_int){		
		int i, j;
		double[][] x_double = new double[维数][维数];
		double[][] y_double = new double[维数][维数];
		double[][] c = new double[维数][维数];
		double[][] c转置 = new double[维数][维数];
		int[][] y_int = new int[维数][维数];
		for(i = 0; i < 维数; i++)
			for(j = 0; j < 维数; j++){
				if(i == 0)
					c[i][j] = 1 / Math.sqrt(8);
				else
					c[i][j] = 1 / 2.0 * Math.cos(i * (2 * j + 1) * Math.PI / 16);
				c转置[j][i] = c[i][j];
				
//				为了减少误差，函数矩阵乘法是接收double型参数的，故将x[][]double化
				x_double[i][j] = (double) x_int[i][j];
			}
		
		
		y_double = 矩阵乘法(c, x_double);
		y_double = 矩阵乘法(y_double, c转置);	
		//四舍五入
		for(i = 0; i < 维数; i++)
			for(j = 0; j < 维数; j++){
				y_int[i][j] = (int) (y_double[i][j] + 0.5);
			}
		return y_int;
	}
	

	//接收int型的y[][]，得到int型的x[][]
	public int[][] idct(int[][] y_int){
		int i, j;
		
		double[][] x_double = new double[维数][维数];
		double[][] y_double = new double[维数][维数];
		int[][] x_int = new int[维数][维数];
		double[][] c = new double[维数][维数];
		double[][] c转置 = new double[维数][维数];
		for(i = 0; i < 维数; i++)
			for(j = 0; j < 维数; j++){
				if(i == 0)
					c[i][j] = 1 / Math.sqrt(8);
				else
					c[i][j] = 1 / 2.0 * Math.cos(i * (2 * j + 1) * Math.PI / 16);
				c转置[j][i] = c[i][j];
				
				
//				为了减少误差，函数矩阵乘法是接收double型参数的，故将y[][]double化
				y_double[i][j] = (double) y_int[i][j];
			}
		
		x_double = 矩阵乘法(c转置, y_double);
		x_double = 矩阵乘法(x_double, c);		
		//四舍五入
		for(i = 0; i < 维数; i++)
			for(j = 0; j < 维数; j++){
				x_int[i][j] = (int) (x_double[i][j] + 0.5);
			}
		return x_int;
	}

	
	//重载 y[][] = a[][] * b[][]
	public double[][] 矩阵乘法(double[][] a, double[][] b){
		if(a[0].length != b.length)
			System.out.println("出错了");
		int i, j, k,len_x,len_y;
		int len = b.length;//即a的列数 ，b的行数
		len_x = a.length;//a的行数。
		len_y = b[0].length;//b的列数
		double[][] y = new double[len_x][len_y];
		for(i = 0; i < len_x; i++)
			for(j = 0; j < len_y; j++){
				//y[i][j] = 0;因为初始化时y[][] = 0
				for(k = 0; k < len; k++)
					y[i][j] += a[i][k] * b[k][j];  
			}
		return y;
	}
	
}