Sparse Modeling of Grouped Line Spectra

This licentiate thesis focuses on clustered parametric models for estimation of line spectra, when the spectral content of a signal source is assumed to exhibit some form of grouping. Different from previous parametric approaches, which generally require explicit knowledge of the model orders, this thesis exploits sparse modeling, where the orders are implicitly chosen. For line spectra, the non-linear parametric model is approximated by a linear system, containing an overcomplete basis of candidate frequencies, called a dictionary, and a large set of linear response variables that selects and weights the components in the dictionary. Frequency estimates are obtained by solving a convex optimization program, where the sum of squared residuals is minimized. To discourage overfitting and to infer certain structure in the solution, different convex penalty functions are introduced into the optimization. The cost trade-off between fit and penalty is set by some user parameters, as to approximate the true number of spectral lines in the signal, which implies that the response variable will be sparse, i.e., have few non-zero elements. Thus, instead of explicit model orders, the orders are implicitly set by this trade-off. For grouped variables, the dictionary is customized, and appropriate convex penalties selected, so that the solution becomes group sparse, i.e., has few groups with non-zero variables. In an array of sensors, the specific time-delays and attenuations will depend on the source and sensor positions. By modeling this, one may estimate the location of a source. In this thesis, a novel joint location and grouped frequency estimator is proposed, which exploits sparse modeling for both spectral and spatial estimates, showing robustness against sources with overlapping frequency content. For audio signals, this thesis uses two different features for clustering. Pitch is a perceptual property of sound that may be described by the harmonic model, i.e., by a group of spectral lines at integer multiples of a fundamental frequency, which we estimate by exploiting a novel adaptive total variation penalty. The other feature, chroma, is a concept in musical theory, collecting pitches at powers of 2 from each other into groups. Using a chroma dictionary, together with appropriate group sparse penalties, we propose an automatic transcription of the chroma content of a signal

Colorization as a Proxy Task for Visual Understanding

We investigate and improve self-supervision as a drop-in replacement for ImageNet pretraining, focusing on automatic colorization as the proxy task. Self-supervised training has been shown to be more promising for utilizing unlabeled data than other, traditional unsupervised learning methods. We build on this success and evaluate the ability of our self-supervised network in several contexts. On VOC segmentation and classification tasks, we present results that are state-of-the-art among methods not using ImageNet labels for pretraining representations. Moreover, we present the first in-depth analysis of self-supervision via colorization, concluding that formulation of the loss, training details and network architecture play important roles in its effectiveness. This investigation is further expanded by revisiting the ImageNet pretraining paradigm, asking questions such as: How much training data is needed? How many labels are needed? How much do features change when fine-tuned? We relate these questions back to self-supervision by showing that colorization provides a similarly powerful supervisory signal as various flavors of ImageNet pretraining.Comment: CVPR 2017 (Project page: http://people.cs.uchicago.edu/~larsson/color-proxy/