用于信号和图像处理的快速Haar小波变换

A new image compression by gradient Haar wavelet

With the development of human communications the usage of Visual Communications has also increased. The advancement of image compression methods is one of the main reasons for the enhancement. This paper first presents main modes of image compression methods such as JPEG and JPEG2000 without mathematical details. Also, the paper describes gradient Haar wavelet transforms in order to construct a preliminary image compression algorithm. Then, a new image compression method is proposed based on the preliminary image compression algorithm that can improve standards of image compression. The new me…

Image Encryption Based On Gradient Haar Wavelet and Rational Order Chaotic Maps

Haar wavelet is one of the best mathematical tools in image cryptography and analysis. Because of the specific structure, this wavelet has the ability which is combined with other mathematical tools such as chaotic maps. The rational order chaotic maps are one of clusters of chaotic maps which their deterministic behaviors have high sensitivity. In this paper, we propose a novel method of gradient Haar wavelet transform for image encryption. This method use linearity properties of the scaling function of the gradient Haar wavelet and deterministic behaviors of rational order chaotic maps in or…

基于Haar小波的图像压缩及质量评价

Haar Wavelet Based Approach for Image Compression and Quality Assessment of Compressed Image

随着技术的不断发展和进入数字时代，我们每次都要处理大量的信息，这往往会带来困难。因此，数字信息必须以高效和有效的方式存储和检索，以便将其投入实际使用。Wavelet提供了一种编码信息的数学方法，其方式是根据细节层次分层。这种分层便于在各个中间阶段进行近似。这些近似值可以使用比原始数据少得多的空间来存储。提出了一种以小波为基函数的低复杂度二维图像压缩方法，并给出了压缩图像质量的度量方法。这里选择和使用的特定小波是最简单的小波形式，即Haar小波。应用二维离散小波变换（DWT），从图像的信息矩阵中估计出细节矩阵。利用小波变换提供的细节矩阵和信息矩阵估计值合成重构图像。通过压缩比、峰值信噪比、平均意见评分、图像质量等级等指标对压缩后的图像质量进行了评价。

Gabor Wavelets in Image Processing

This work shows the use of a two-dimensional Gabor wavelets in image processing. Convolution with such a two-dimensional wavelet can be separated into two series of one-dimensional ones. The key idea of this work is to utilize a Gabor wavelet as a multiscale partial differential operator of a given order. Gabor wavelets are used here to detect edges, corners and blobs. A performance of such an interest point detector is compared to detectors utilizing a Haar wavelet and a derivative of a Gaussian function. The proposed approach may be useful when a fast implementation of the Gabor transform is…

一维语音信号和二维图像的小波多尺度定量分析

Quantitative Multiscale Analysis using Different Wavelets in 1D Voice Signal and 2D Image

多尺度分析代表对信号的多分辨率审查，以改善其信号质量。利用DCT、FFT和不同的小波（如Haar、Deubachies、Morlet、Cauchy、Shannon、Biforthogonal、Symmlet和Coiflet）对一维语音信号和二维图像进行多分辨率分析，并部署基于级联滤波器组的分解和重构。对所选小波进行了定量分析，研究了一维语音信号和二维图像在多尺度第四级的信号质量、均方误差、熵和峰峰值信噪比。此外，在多尺度分析中，2D图像压缩性能在DB-4中为93.00%，在bior-4.4中为93.68%，在Sym-4中为93.18%，在Coif-2中为92.20%。

Wavelet based Watermarking approach in the Compressive Sensing Scenario

Due to the wide distribution and usage of digital media, an important issue is protection of the digital content. There is a number of algorithms and techniques developed for the digital watermarking.In this paper, the invisible image watermark procedure is considered. Watermark is created as a pseudo random sequence, embedded in the certain region of the image, obtained using Haar wavelet decomposition. Generally, the watermarking procedure should be robust to the various attacks-filtering, noise etc. Here we assume the Compressive sensing scenario as a new signal processing technique that ma…