**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.

**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 :

**Implementation:-**

DWT factorize poly-phase matrix of wavelet filter into a sequence of alternating upper and lower triangular matrices and diagonal matrix.

**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*.*

**Applications:-**

- Medical Application
- Image Processing
- Data Compression
- Signal de-noising

**Results:-**

* *