2-D inverse discrete cosine transform



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.


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This example shows how to remove high frequencies from an image using the two-dimensional discrete cosine transfer (DCT).

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

RGB = imread('autumn.tif');
I = rgb2gray(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.


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.

K = idct2(J);

Display the original grayscale image alongside the processed image.

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


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


idct2 computes the two-dimensional inverse DCT using:

Amn=p=0M1q=0N1αpαqBpqcosπ(2m+1)p2Mcosπ(2n+1)q2N, 0mM10nN1,


αp={1M, p=0             2M, 1pM1


αq={1N, q=0            2N, 1qN1.


[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