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Sparse Representations

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Digital Signal Processing with Matlab Examples, Volume 3

Part of the book series: Signals and Communication Technology ((SCT))

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Abstract

Sparse representations intend to represent signals with as few as possible significant coefficients. This is important for many applications, like for instance compression. When using wavelets it is frequently noticed that a great compression rate can be obtained, with almost unnoticeable loss of information. Supposing that the signal comes from a sensor, it would be very convenient to have the sensor yielding already compressed information. This is called ‘compressed sensing’. After a preliminary study in section two, the chapter attacks the core of the topic in section three. The next section is devoted to sparse representation in the context of images, including image decomposition in texture+cartoon, or in terms of patches, or by using morphological components. Some more concepts and tools were considered in section five, like for instance diffusion in 2D, or Bregman related algorithms. An almost unexpected field of application that has emerged is matrix completion, which is treated in section six. Finally, the chapter includes some experiments about denoising based on total variation (TV), picture reconstruction, and text removal from images.

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Giron-Sierra, J.M. (2017). Sparse Representations. In: Digital Signal Processing with Matlab Examples, Volume 3. Signals and Communication Technology. Springer, Singapore. https://doi.org/10.1007/978-981-10-2540-2_2

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