We introduce a new method, called Tree K-SVD, to learn a tree-structured dictionary for sparse representations, as well as a new adaptive sparse coding method, in a context of image compression. Each dictionary at a level in the tree is learned from residuals from the previous level with the K-SVD method. The tree-structured dictionary allows efficient search of the atoms along the tree as well as efficient coding of their indices. Besides, it is scalable in the sense that it can be used, once learned, for several sparsity constraints. We show experimentally on face images that, for a high sparsity, Tree K-SVD offers better rate-distortion performances than state-of-the-art "flat" dictionaries learned by K-SVD or Sparse K-SVD, or than the predetermined overcomplete DCT dictionary. We also show that our adaptive sparse coding method, used on a tree-structured dictionary to adapt the sparsity per level, improves the quality of reconstruction.
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