idct2

2-D inverse discrete cosine transform

Syntax

B = idct2(A)

B = idct2(A,m,n)

B = idct2(A,[m n])

Description

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]) zero-pads or crops the matrix A to size m-by-n before applying the inverse transformation.

Examples

Remove High Frequencies in Image using 2-D DCT

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

A — Input matrix

2-D numeric matrix

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

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

m — Number of image rows

size(A,1) (default) | positive integer

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).

n — Number of image columns

size(A,2) (default) | positive integer

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

B — Transformed matrix

m-by-n numeric matrix

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:

$$A_m{}_n={\displaystyle \sum _{p=0}^{M-1}{\displaystyle \sum _{q=0}^{N-1}{\alpha }_p}}{\alpha }_q{B}_{pq}\cos \frac{\pi (2m+1)p}{2M}\cos \frac{\pi (2n+1)q}{2N},\begin{array}{c}0\le m\le M-1\\ 0\le n\le N-1\end{array},$$

where

$${\alpha }_p=\{\begin{array}{c}\frac{1}{\sqrt{M}},p=0\\ \sqrt{\frac{2}{M}},1\le p\le M-1\end{array}$$

and

$${\alpha }_q=\{\begin{array}{c}\frac{1}{\sqrt{N}},q=0\\ \sqrt{\frac{2}{N}},1\le q\le N-1\end{array}.$$

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.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

idct2 supports the generation of C code (requires MATLAB^® Coder™). For more information, see Code Generation for Image Processing.

Version History

Introduced before R2006a

R2023b: Support for C code generation

idct2 now supports the generation of C code (requires MATLAB Coder).