Number of bits required to
represent the information in an image can be minimized by removing the
redundancy present in it

There are three types of
redundancies:

**1. Spatial redundancy**

Which is due to the
correlation or dependence between neighboring pixel values;

**2. Spectral redundancy,**

**3. Temporal redundancy,**

Which is present because of
correlation between different frames in images.

Image compression research
aims to reduce the number of bits required to represent an image by removing
the spatial and spectral redundancies as much as possible. Data redundancy is
of central issue in digital image compression. If n1 and n2 denote the number
of information
carrying units in original and compressed image respectively, then the compression
ratio CR can be defined as

**Block Diagram:**

**Compression:**

**Description:**

1. This compression system is totally based on DCT.

2. This system used for compressing grayscale images.

3. Then DCT is applied to an image.

4. In 5

^{th}block all the DCT coefficients are sorted with sorting algorithm.
5. After sorting algorithm the repeated DCT coefficients are
eliminated so size is reduced.

6. Then image is again rearranged for applying IDCT, and after applying IDCT finally compressed image is
obtained.

In this algorithm for reducing no of DCT coefficients rate
is required. Rate should be less than size of the image.

E.g. if size of the image is 400 row and 400 columns

Then rate should be
In this case rate varies from 1 to 16 because by putting
value of rate from 1 to 16 above condition is true.

**De-Compression:**

Exact Inverse Process is applied at
Receiver or decompression.

**Peak-Signal to Noise Ratio (PSNR)**

The PSNR is most commonly used as a measure of quality of
reconstruction of lossy compression codec’s (e.g., for image compression). The
signal in this case is the original data, and the noise is the error introduced
by compression. When comparing compression codec’s it is used as an
approximation to human perception of reconstruction quality, therefore in some
cases one reconstruction may appear to be closer to the original than another,
even though it has a lower PSNR (a higher PSNR would normally indicate that the
reconstruction is of higher quality). The PSNR is calculated by using following formula.

**MATLAB Implementation:**

**Main GUI figure…****Compressions GUI figure:**

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