Dictionary Learning

Authored by: Angshul Majumdar

Compressed Sensing for Engineers

Print publication date:  December  2018
Online publication date:  December  2018

Print ISBN: 9780815365563
eBook ISBN: 9781351261364
Adobe ISBN:


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So far, we have studied the topics where we assumed that the sparsifying basis is known. For example, images are known to be sparse in wavelet, discrete cosine transform (DCT), or curvelet; speech has a sparse representation in short-time Fourier transform; and biomedical signals can be sparsely represented by wavelet or Gabor transform. Such fixed mathematical transforms are generic and, as we can see, applicable to a wide variety of problems. All such transforms are defined for representing signals following some abstract structures, for example, smooth functions, functions with finite number of discontinuities, and piecewise linear functions. Since many natural signals approximately follow such structures, these transforms are popular in compressed sensing.

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