Introduction to Image Compression:-

Image compression is an application of data compression. It is used for reducing the redundancy in the image, that is nothing but avoiding the duplicate data. It also reduces the required storage area to store an image. It can be lossy or lossless. There are several techniques for image compression such as DCT (discrete cosine transform), DWT (discrete wavelet transform), PCA (principal component analysis) etc.

Figure below depicts the general flow of image compression and decompression.

dct2

Discrete Cosine Transformation:-

The Discrete Cosine Transformation is used for most compression applications. DCT is a technique to convert signal into elementary frequency component. It transforms digital image data from spatial domain to frequency domain. DCT is a fast transform. DCT has excellent compaction for highly correlated data. It gives good compromise between information packing ability and computational complexity.

Methodology:-

The discrete cosine transform helps to separate the image into parts or spectral sub bands of differing importance with respect to the images visual quality.

The general equation for a 1D (N data items) DCT is defined by the following equation:

The general equation for a 2D (N by M image) DCT is defined by the following equation:

dct3

dct4

Quantization:-

Quantization is the process where actual reduction of image is done. It is a lossy compression technique which basically used in DCT. It is achieved by compressing a range of values to a single quantum value. When the number of discrete symbols in a given stream is reduced, the stream becomes more compressible.

Encoding:-

 In Encoding the results of the quantization are encode. It can be Run Length encoding or Huffman coding. It optimizes the representation of the information to further reduce the bit rate.

Common Applications:-

  • JPEG Format
  • MPEG-1 and MPEG-2
  • MP3
  • Advanced Audio Coding.. etc

Results:-

dct5