We have been able to reconstruct the original array. The beauty of what we have done so far lies in the fact that it is completely reversible. All the other entries, the detail coefficients, are close to 0. Repeat this process again and again till you get just one approximation coeff.Īs we can see, the resulting array has only one entry that is big the leftmost one. The last four ones are called detail coefficients. The first four entries are called approximation coefficients. Group the columns in pairs:, ,, Īverage each of these pairs, then replace the four first columns of r with those values and compute 1/2 the difference of each pair, then replace the last four columns of r with those. We will take the following one-dimensional array
Which is based on the idea of decomposing a Its one of the simplest wavelet transforms We are going to use Haar wavelet transform. It can typically be visualized as a "brief oscillation" like one recorded by a seismograph or heart monitor.Įach wavelet measurement (the wavelet transform corresponding to a fixed parameter) tells us something about the temporal extent of the signal, as well as something about the frequency spectrum of the signal.
It also reduces the time required for images to be sent over the Internet or downloaded from Web pages.Ī wavelet is a wave-like oscillation with an amplitude that begins at zero, increases, and then decreases back to zero. The reduction in file size allows more images to be stored in a given amount of disk or memory space. Image compression is minimizing the size in bytes of a graphics file without degrading the quality of the image to an unacceptable level. Image-Compression-using-Wavelet-Transform
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