Image Transforms: DCT

It is well known that LSI operators may be implemented in the Fourier transform domain, leading to computational efficiencies. The energy compaction property of transforms, such as the discrete Fourier transform (DFT), discrete cosine transform (DCT), and discrete wavelet transform (DWT), plays an important role in many image/video compression techniques. Here we demonstrate image compression using the DCT transform.

Here we load the package.

Here we load an example image.

Here we take the block cosine transform of the example image. The blocks are non-overlapping, with dimensions 8 x 8.

Here we show a fragment of the example image and the DCT coefficients.

We now retain cosine coefficients located in a low-frequency zone of each block. We then use the inverse DCT to calculate an approximation to the original image. Here is a typical zonal mask.

This reconstructs an approximation of the original.

Here is the processed image and the approximation error.

The compression capabilities of the DCT are clearly visible. Using only 23% of the image's total energy, the reconstructed image (left) is a reasonable approximation of the original. The error signal is shown on the right. The approximation is guaranteed to improve as the number of coefficients is increased.