Wavelet compression is an image-compression technique.
In mathematical terms, a wavelet is a function -- a relationship between two sets that matches each member of the first set with a unique member of the second set -- which, when plotted, fluctuates about the horizontal axis, or x-axis. Wavelet compression is a form of data compression used to compress image data -- in other words, to code it more efficiently, using fewer binary digits, or “bits” -- so that it occupies less storage space.
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A popular form of wavelet compression, known as Discrete Wavelet Transform (DWT), treats an image as a continuous, fluctuating wave, rather than a collection of discrete picture elements, or “pixels”. A pixel is the smallest element of a digital image. In a color image, each pixel consists of red, green and blue subpixels, which contribute to the overall color and brightness of the pixel. DWT actually treats an image as a series of waves, one for each color channel.
DWT centers each wave on zero and measures the amplitude, or displacement from zero, of the wave -- in other words, the peaks and troughs -- at various points along its length. This process produces a set of values, known as wavelet coefficients, which are centered on zero, with very few large values. DWT takes the average of adjacent wavelet coefficients to simplify the wave and compress the image by a factor of two and repeats this process -- known as “decomposition” -- over and over again to produce the final simplified waveform. As decomposition proceeds, it generates progressively simpler, lower-resolution versions of the wave, but retains all the information required to reproduce a detailed version of the wave.
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During decomposition, DWT not only averages adjacent wavelet coefficients, but also records the differences between them. Minor differences between adjacent wavelet coefficients indicates flatter, less significant areas of a wave, which can be simplified, or “smoothed” with adversely affecting the quality of the finished image. Major differences between adjacent waveform coefficients indicate steep peaks or troughs, which typically represent lines, edges or other details in an image and need to be preserved.
In 1997, the Joint Photographic Experts Group (JPEG), applied the principles of wavelet compression to image compression and came up with JPEG 2000, the successor to the previous JPEG standard. JPEG 2000 affords compression about 20 percent better than does conventional JPEG and allows images to be scaled without needing to store redundant, or duplicate, data.
