# Documentation

### This is machine translation

Translated by
Mouseover text to see original. Click the button below to return to the English version of the page.

# 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)` pads `A` with 0's to size `m`-by-`n` before transforming. If `[m n]` < `size(A)`, `idct2` crops `A` before transforming.

`B = idct2(A,[m n])` same as above.

For any `A`, `idct2(dct2(A))` equals `A` to within roundoff error.

## Class Support

The input matrix `A` can be of class `double` or of any numeric class. The output matrix `B` is of class `double`.

## Examples

collapse all

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.

```figure imshow(log(abs(J)),[]) colormap(gca,jet(64)) 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`.

`K = idct2(J);`

Display the original grayscale image alongside the processed image.

```figure imshowpair(I,K,'montage') title('Original Grayscale Image (Left) and Processed Image (Right)');```

## Algorithms

`idct2` computes the two-dimensional inverse DCT using:

where

and

## 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.