# 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

Create a DCT matrix.

```RGB = imread('autumn.tif'); I = rgb2gray(RGB); J = dct2(I); imshow(log(abs(J)),[]), colormap(jet), colorbar```

Set values less than magnitude 10 in the DCT matrix to zero, then reconstruct the image using the inverse DCT function `idct2`.

```J(abs(J)<10) = 0; K = idct2(J); figure, imshow(I) figure, imshow(K,[0 255])```

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### 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.