![]() For example, most natural images may be segmented, and it is probable that dictionary usage will be similar for regions within a particular segment class. In image analysis, there is often additional information that may be exploited when learning dictionaries, with this well suited for Bayesian priors. Exploiting Structure and Compressive Measurements Recent research has demonstrated that an ensemble of representations can be better than a single expansion, with such an ensemble naturally manifested by statistical models of the type described here.ī. An approximation to the full posterior may be manifested via Gibbs sampling, yielding an ensemble of dictionary representations. Furthermore, one may place a prior on the noise or residual variance, with this inferred from the data. ![]() Utilizing nonparametric Bayesian methods like the beta process (BP), , and the Indian buffet process (IBP), , one may, for example, infer the number of factors (dictionary elements) needed to fit the data. To mitigate the aforementioned limitations, dictionary learning has recently been cast as a factor-analysis problem, with the factor loading corresponding to the dictionary elements (atoms). For example, one must often assume access to the noise/residual variance, the size of the dictionary is set a priori or fixed via cross-validation-type techniques, and a single (“point”) estimate is learned. However, many existing algorithms for implementing such ideas also have some restrictions. These methods have demonstrated state-of-the-art performance for denoising, superresolution, interpolation, and inpainting. Many of the existing methods for learning dictionaries are based on solving an optimization problem, , –,, , in which one seeks to match the dictionary to the imagery of interest, while simultaneously encouraging a sparse representation. Most of the denoising, interpolation, and CS literature assume “off-the-shelf” wavelet and DCT bases/dictionaries, but recent research has demonstrated the significant utility of learning an often overcomplete dictionary matched to the signals of interest (e.g., images), ,, , –,, ,,. ![]() All of these applications exploit the fact that images may be sparsely represented in an appropriate dictionary. Recently, there has been significant interest in sparse image representations, in the context of denoising and interpolation, , –,, ,, compressive sensing (CS), , and classification. ![]()
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