idct2

2-D inverse discrete cosine transform

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Syntax

B = idct2(A)
B = idct2(A,m,n)
B = idct2(A,[m n])

Description

example

B = idct2(A) returns the two-dimensional inverse discrete cosine transform (DCT) of A.

B = idct2(A,m,n) and

B = idct2(A,[m n]) pads A with 0s to size m-by-n before applying the inverse transformation. If m or n is smaller than the corresponding dimension of A, then idct2 crops A before the transformation.

Examples

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Open Live Script

Read an image into the workspace, then convert the image to grayscale.

RGB = imread('autumn.tif');
I = im2gray(RGB);

Perform a 2-D DCT of the grayscale image using the dct2 function.

J = dct2(I);

Display the transformed image using a logarithmic scale. Notice that most of the energy is in the upper left corner.

imshow(log(abs(J)),[])
colormap parula
colorbar

Set values less than magnitude 10 in the DCT matrix to zero.

J(abs(J) < 10) = 0;

Reconstruct the image using the inverse DCT function idct2. Rescale the values to the range [0, 1] expected of images of data type double.

K = idct2(J);
K = rescale(K);

Display the original grayscale image alongside the processed image. The processed image has fewer high frequency details, such as in the texture of the trees.

montage({I,K})
title('Original Grayscale Image (Left) and Processed Image (Right)');

Input Arguments

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Input matrix, specified as a 2-D numeric matrix.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Number of image rows, specified as a positive integer. idct2 pads image A with 0s or truncates image A so that it has m rows. By default, m is equal to size(A,1).

Number of image columns, specified as a positive integer. idct2 pads image A with 0s or truncates image A so that it has n columns. By default, n is equal to size(A,2)

Output Arguments

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Transformed matrix using a two-dimensional discrete cosine transform, returned as an m-by-n numeric matrix.

Data Types: double

Tips

  • For any matrix A, idct2(dct2(A)) equals A to within round-off error.

Algorithms

idct2 computes the two-dimensional inverse DCT using:

Amn=∑p=0M−1∑q=0N−1αpαqBpqcosπ(2m+1)p2Mcosπ(2n+1)q2N, 0≤m≤M−10≤n≤N−1,

where

αp={1M, p=0             2M, 1≤p≤M−1

and

αq={1N, q=0            2N, 1≤q≤N−1.

References

[1] Jain, A. K., Fundamentals of Digital Image Processing, Englewood Cliffs, NJ, Prentice Hall, 1989, pp. 150-153.

[2] Pennebaker, W. B., and J. L. Mitchell, JPEG: Still Image Data Compression Standard, New York, Van Nostrand Reinhold, 1993.

See Also

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Introduced before R2006a

Image Processing Toolbox Documentation

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