K SVD简述 字典学习 稀疏编码

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K-SVD

Rachel Zhang

 

1. k-SVD introduction

1.     K-SVD usage:

Design/Learn a dictionary adaptively to betterfit the model and achieve sparse signal representations.

2.     Main Problem:

Y = DX

Where Y∈R(n*N), D∈R(n*K), X∈R(k*N), X is a sparse matrix.

N is # of samples;

n is measurement dimension;

K is the length of a coefficient.

 

2. Derivation from K-Means

3.       K-Means:

1)       The sparse representationproblem can be viewed as generalization of the VQ objective. K-SVD can be viewed as generalization of K-Means.

2)       K-Means algorithm for vectorquantization:

Dictionary of VQ codewords is typically trained using K-Means algorithm.

When Dictionary D is given, each signal is represented as its closestcodeword (under l2-norm distance). I.e.

Y_i = Dx_i</