Wavelet Transforms | A Quick Study
Ivan Selesnick · 2007
The wavelet transform has become a useful computational tool for a variety of signal and image processing applications. For example, the wavelet transform is useful for the compression of digital image files; smaller files are important for storing images using less memory and for transmitting images faster and more reliably. The FBI uses wavelet transforms for compressing digitally scanned fingerprint images. NASA’s Mars Rovers used wavelet transforms for compressing images acquired by their 18 cameras. The wavelet-based algorithm implemented in software onboard the Mars Rovers is designed to meet the special requirements of deep-space communication. In addition, JPEG2K (the newer JPEG image file format) is based on wavelet transforms. Wavelet transforms are also useful for ‘cleaning ’ signals and images (reducing unwanted noise and blurring). Some algorithms for processing astronomical images, for example, are based on wavelet and wavelet-like transforms. This Quick Study describes the wavelet transform, illustrates why it is effective for noise reduction, and briefly describes several improvements of the basic wavelet transform and basic noise reduction method used in the illustration. We describe what the wavelet transform is, and we describe algorithms for processing a signal after its wavelet transform has been computed. First we