We describe a method for learning sparse multiscale image representations using a sparse prior distribution over the basis function coefficients. The prior consists of a mixture of a Gaussian and a Dirac delta function, and thus encourages coefficients to have exact zero values. Coefficients for an image are computed by sampling from the resulting posterior distribution with a Gibbs sampler. Denoising using the learned image model is demonstrated for some standard test images, with results that compare favorably with other denoising methods.

We describe a method for learning sparse multiscale image repre- sentations using a sparse prior distribution over the basis function coe(cid:14)cients. The prior consists of a mixture of a Gaussian and a Dirac delta function, and thus encourages coe(cid:14)cients to have exact zero values. Coe(cid:14)cients for an image are computed by sampling from the resulting posterior distribution with a Gibbs sampler. The learned basis is similar to the Steerable Pyramid basis, and yields slightly higher SNR for the same number of active coe(cid:14)cients. De- noising using the learned image model is demonstrated for some standard test images, with results that compare favorably with other denoising methods.

Recent studies have shown significantly improved branch prediction through the use of branch classification. By separating static branches into groups, or classes, with similar dynamic behavior predictors may be selected that are best suited for each class. Previous methods have classified branches according to taken rate (or bias). We propose a new metric for branch classification: branch transition rate, which is defined as the number of times a branch changes direction between taken and not taken during execution. We show that transition rate is a more appropriate indicator of branch behavior than taken rate for determining predictor performance. When both metrics are combined, an even clearer picture of dynamic branch behavior emerges, in which expected predictor performance for a branch is closely correlated with its combined taken and transition rate class. Using this classification, a small group of branches is identified for which two-level predictors are ineffective.

We show how a wavelet basis may be adapted to best represent natural images in terms of sparse coefficients. The wavelet basis, which may be either complete or overcomplete, is specified by a small number of spatial functions which are repeated across space and combined in a recursive fashion so as to be self-similar across scale. These functions are adapted to minimize the estimated code length under a model that assumes images are composed of a linear superposition of sparse, independent components. When adapted to natural images, the wavelet bases take on different orientations and they evenly tile the orientation domain, in stark contrast to the standard, non-oriented wavelet bases used in image compression. When the basis set is allowed to be overcomplete, it also yields higher coding efficiency than standard wavelet bases.