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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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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.

colormap parula

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.

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