Multi-resolution analysis and wavelet transformation-Introduction

The sine function of the basic function of Fourier transformation, while wavelet transformation is based on some small waves called "wavelet", which has a changing frequency and a limited duration. This allows them to provide an equivalent score for the image, not only to clarify the Notes (frequency) to be played, but also to specify when to play. Relatively speaking, the Traditional Fourier transformation only provides the notes or frequency information, and the local information is lost during the transformation process.

Wavelet is the basis of Multi-Resolution theory analysis. The Multi-Resolution Theory is related to signal representation and analysis under multiple resolutions, and has obvious advantages.--Features that cannot be found at a certain resolution can be easily discovered at another resolution. Although there are many ways to interpret wavelet transform from the perspective of multi-resolution, this method can simplify the interpretation process of mathematics and physics.

When observing an image, we usually see areas of the connected texture similar to the gray level. They combine to form objects. If the object size is too small or the contrast is not high, it is usually observed with a higher resolution. If the object size is large or the contrast is very strong, you only need a lower resolution. If the size of an object is large or small, or the contrast is strong or weak at the same time, it will be advantageous to study them at several resolutions.

An effective but simple structure of interpreting images with multiple resolutions is the image pyramid. The image pyramid was originally used for machine vision and image compression. the pyramid of an image is a collection of images that gradually decrease resolution arranged in pyramid shape.

Another important image technology related to multi-resolution analysis is sub-band encoding. In the child band encoding, an image is divided into a series of restricted band components, called Child bands, which can be reorganized together to reconstruct the original image without distortion. Initially developed for voice and image compression, the sub-band can be used for sampling without information loss. The reconstruction of the original image can be completed through interpolation, filtering, and superposition of a single sub.

The last image processing method related to multi-resolution analysis is Hal (Haar. Its importance is reflected in the fact that its base function is well known as the oldest and simplest orthogonal wavelet.

We have introduced three famous image processing technologies, which are used in mathematical multi-resolution analysis (MRA. InMRAMedium, the scale function is used to establish a function or a series of approximate values of an image, and the approximate degree difference between adjacent two approximate values2Times. An additional function called wavelet is used to encode the differences between adjacent approximate values.