6,703 research outputs found
Oracle-order Recovery Performance of Greedy Pursuits with Replacement against General Perturbations
Applying the theory of compressive sensing in practice always takes different
kinds of perturbations into consideration. In this paper, the recovery
performance of greedy pursuits with replacement for sparse recovery is analyzed
when both the measurement vector and the sensing matrix are contaminated with
additive perturbations. Specifically, greedy pursuits with replacement include
three algorithms, compressive sampling matching pursuit (CoSaMP), subspace
pursuit (SP), and iterative hard thresholding (IHT), where the support
estimation is evaluated and updated in each iteration. Based on restricted
isometry property, a unified form of the error bounds of these recovery
algorithms is derived under general perturbations for compressible signals. The
results reveal that the recovery performance is stable against both
perturbations. In addition, these bounds are compared with that of oracle
recovery--- least squares solution with the locations of some largest entries
in magnitude known a priori. The comparison shows that the error bounds of
these algorithms only differ in coefficients from the lower bound of oracle
recovery for some certain signal and perturbations, as reveals that
oracle-order recovery performance of greedy pursuits with replacement is
guaranteed. Numerical simulations are performed to verify the conclusions.Comment: 27 pages, 4 figures, 5 table
Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms
We consider the problem of detecting a small subset of defective items from a
large set via non-adaptive "random pooling" group tests. We consider both the
case when the measurements are noiseless, and the case when the measurements
are noisy (the outcome of each group test may be independently faulty with
probability q). Order-optimal results for these scenarios are known in the
literature. We give information-theoretic lower bounds on the query complexity
of these problems, and provide corresponding computationally efficient
algorithms that match the lower bounds up to a constant factor. To the best of
our knowledge this work is the first to explicitly estimate such a constant
that characterizes the gap between the upper and lower bounds for these
problems
Reconstructive Sparse Code Transfer for Contour Detection and Semantic Labeling
We frame the task of predicting a semantic labeling as a sparse
reconstruction procedure that applies a target-specific learned transfer
function to a generic deep sparse code representation of an image. This
strategy partitions training into two distinct stages. First, in an
unsupervised manner, we learn a set of generic dictionaries optimized for
sparse coding of image patches. We train a multilayer representation via
recursive sparse dictionary learning on pooled codes output by earlier layers.
Second, we encode all training images with the generic dictionaries and learn a
transfer function that optimizes reconstruction of patches extracted from
annotated ground-truth given the sparse codes of their corresponding image
patches. At test time, we encode a novel image using the generic dictionaries
and then reconstruct using the transfer function. The output reconstruction is
a semantic labeling of the test image.
Applying this strategy to the task of contour detection, we demonstrate
performance competitive with state-of-the-art systems. Unlike almost all prior
work, our approach obviates the need for any form of hand-designed features or
filters. To illustrate general applicability, we also show initial results on
semantic part labeling of human faces.
The effectiveness of our approach opens new avenues for research on deep
sparse representations. Our classifiers utilize this representation in a novel
manner. Rather than acting on nodes in the deepest layer, they attach to nodes
along a slice through multiple layers of the network in order to make
predictions about local patches. Our flexible combination of a generatively
learned sparse representation with discriminatively trained transfer
classifiers extends the notion of sparse reconstruction to encompass arbitrary
semantic labeling tasks.Comment: to appear in Asian Conference on Computer Vision (ACCV), 201
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