Dictionary Learning

Many signals and natural images can be represented as a sparse
linear combination of basis vectors over an overcomplete
dictionary.

Signal samples:


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Dictionary Learning is solving the following problem:


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Where D is an overcomplete dictionary, A is the projection
coefficients of x_i onto the columns of D. It adaptively learns D
from the input signal, and make sure the projection coefficients
are sparse.

Result
Image denoising:


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inpainting:


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