**Introduction of 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.

__Discrete wavelet Transformation:- __

Wavelet Transform decomposes a signal into a set of basis functions, these basis functions are called wavelets. Wavelets are mathematical function that separate data into different frequency component with a resolution matched to its scale. . DWT transforms a discrete time signal to a discrete wavelet representation.

**Methodology:**

In equation ѱ is a function called wavelet, a represent another function which measure the degree of compression or scale and b represent translation function which measures the time location of the wavelet.

Discrete wavelet transform in 2D function f(x,y) of size M*N is :

__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:

__Implementation:- __

*I) Compression Procedure***II) Decompression Procedure****Quantization:-**

Quantization is the process where actual reduction of image is done. 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*.***Result :-**

**Conclusion :-**

- It is observed that compression ratio is High, for several images Compression and Decompression by Hybrid Method.