# What is Wavelet Based Coding in Details ?

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Introduction:

Wavelet-based coding is a form of compression technology that uses wavelet transforms to reduce the size of digital data. The technology is particularly effective at compressing images and video files while maintaining the quality of the original data. Wavelet-based coding is widely used in digital media, including broadcasting, web streaming, and digital cinema.

In this article, we will explore the working of wavelet-based coding, different types of wavelet transforms, advantages and disadvantages of wavelet-based coding, examples, and other related information.

### How does wavelet-based coding work?

Wavelet-based coding works by dividing digital data into different frequency bands using wavelet transforms. Wavelet transforms are a mathematical tool that allows data to be analyzed and compressed in the frequency domain. Wavelet transforms can be applied to one or more dimensions of a signal, such as time or space, to decompose the signal into a set of wavelet coefficients.

In wavelet-based coding, the digital data is first decomposed into wavelet coefficients using a wavelet transform. The wavelet coefficients are then quantized, and the resulting values are encoded using variable-length codes. The quantization step is critical because it reduces the number of bits required to represent each coefficient. The variable-length codes are used to represent the quantized coefficients in a compact form.

Wavelet-based coding is typically used for compressing image and video data. In image compression, the wavelet transform is applied to the rows and columns of the image to generate a set of wavelet coefficients. In video compression, the wavelet transform is applied to each frame of the video.

### Different types of wavelet transforms:

There are many different types of wavelet transforms that can be used in wavelet-based coding. Some of the most common types include:

1. Haar wavelet: The Haar wavelet is the simplest wavelet transform and is often used as a basis for other wavelet transforms.

2. Daubechies wavelets: The Daubechies wavelets are a family of wavelet transforms that are widely used in image and video compression.

3. Coiflet wavelets: The Coiflet wavelets are another family of wavelet transforms that are commonly used in image and video compression.

4. Symlet wavelets: The Symlet wavelets are a family of wavelet transforms that are similar to the Daubechies wavelets.

1. High compression efficiency: Wavelet-based coding can achieve high compression ratios while maintaining the quality of the original data.

2. Scalability: Wavelet-based coding allows data to be compressed at different levels of detail, making it a flexible compression technology that can be used in a wide range of applications.

3. Robustness: Wavelet-based coding is robust to noise and other forms of distortion, making it ideal for use in environments where data may be corrupted or lost.

1. Complexity: Wavelet-based coding can be computationally intensive and requires significant processing power, which can make it challenging to implement in real-time applications.

2. Lossy compression: Wavelet-based coding is a form of lossy compression, which means that some information is lost during the compression process.

3. Encoding and decoding latency: Wavelet-based coding can introduce a significant amount of encoding and decoding latency, which can be a problem in real-time applications.

### Example of wavelet-based coding:

The JPEG2000 standard is an example of wavelet-based coding. JPEG2000 is a popular image compression standard that uses wavelet transforms to compress images. JPEG2000 can achieve high compression ratios while maintaining the quality of the original image. JPEG2000 also supports progressive transmission, which means that an image can be transmitted in several stages, with each

stage containing more detail than the previous one. This allows users to view an image as it is being transmitted, even if the entire image has not been fully transmitted yet.

### Other applications of wavelet-based coding include:

1. Digital cinema: Wavelet-based coding is used in the Digital Cinema Package (DCP) format, which is the standard format for distributing digital movies to theaters.

2. Broadcast and streaming: Wavelet-based coding is used in broadcasting and streaming applications to compress video data and reduce bandwidth requirements.

3. Medical imaging: Wavelet-based coding is used in medical imaging applications to compress large amounts of image data generated by MRI and CT scanners.

### Conclusion:

Wavelet-based coding is a powerful compression technology that can achieve high compression ratios while maintaining the quality of digital data. The technology is widely used in digital media applications, including broadcasting, web streaming, and digital cinema. Wavelet-based coding works by using wavelet transforms to decompose digital data into a set of wavelet coefficients, which are then quantized and encoded using variable-length codes. While wavelet-based coding has many advantages, including high compression efficiency and scalability, it also has some disadvantages, including complexity and lossy compression. Despite these limitations, wavelet-based coding remains an essential technology in digital media and is likely to continue to be used in a wide range of applications in the future.