5,915 research outputs found
Single image super resolution using compressive K-SVD and fusion of sparse approximation algorithms
Super Resolution based on Compressed Sensing (CS) considers low resolution (LR) image patch as the compressive measurement of its corresponding high resolution (HR) patch. In this paper we propose a single image super resolution scheme with compressive K-SVD algorithm(CKSVD) for dictionary learning incorporating fusion of sparse approximation algorithms to produce better results. The CKSVD algorithm is able to learn a dictionary on a set of training signals using only compressive sensing measurements of them. In the fusion based scheme used for sparse approximation, several CS reconstruction algorithms participate and they are executed in parallel, independently. The final estimate of the underlying sparse signal is derived by fusing the estimates obtained from the participating algorithms. The experimental results show that the proposed scheme demands fewer CS measurements for creating better quality super resolved images in terms of both PSNR and visual perception
Compressive Parameter Estimation for Sparse Translation-Invariant Signals Using Polar Interpolation
We propose new compressive parameter estimation algorithms that make use of
polar interpolation to improve the estimator precision. Our work extends
previous approaches involving polar interpolation for compressive parameter
estimation in two aspects: (i) we extend the formulation from real non-negative
amplitude parameters to arbitrary complex ones, and (ii) we allow for mismatch
between the manifold described by the parameters and its polar approximation.
To quantify the improvements afforded by the proposed extensions, we evaluate
six algorithms for estimation of parameters in sparse translation-invariant
signals, exemplified with the time delay estimation problem. The evaluation is
based on three performance metrics: estimator precision, sampling rate and
computational complexity. We use compressive sensing with all the algorithms to
lower the necessary sampling rate and show that it is still possible to attain
good estimation precision and keep the computational complexity low. Our
numerical experiments show that the proposed algorithms outperform existing
approaches that either leverage polynomial interpolation or are based on a
conversion to a frequency-estimation problem followed by a super-resolution
algorithm. The algorithms studied here provide various tradeoffs between
computational complexity, estimation precision, and necessary sampling rate.
The work shows that compressive sensing for the class of sparse
translation-invariant signals allows for a decrease in sampling rate and that
the use of polar interpolation increases the estimation precision.Comment: 13 pages, 5 figures, to appear in IEEE Transactions on Signal
Processing; minor edits and correction
Non-Local Compressive Sensing Based SAR Tomography
Tomographic SAR (TomoSAR) inversion of urban areas is an inherently sparse
reconstruction problem and, hence, can be solved using compressive sensing (CS)
algorithms. This paper proposes solutions for two notorious problems in this
field: 1) TomoSAR requires a high number of data sets, which makes the
technique expensive. However, it can be shown that the number of acquisitions
and the signal-to-noise ratio (SNR) can be traded off against each other,
because it is asymptotically only the product of the number of acquisitions and
SNR that determines the reconstruction quality. We propose to increase SNR by
integrating non-local estimation into the inversion and show that a reasonable
reconstruction of buildings from only seven interferograms is feasible. 2)
CS-based inversion is computationally expensive and therefore barely suitable
for large-scale applications. We introduce a new fast and accurate algorithm
for solving the non-local L1-L2-minimization problem, central to CS-based
reconstruction algorithms. The applicability of the algorithm is demonstrated
using simulated data and TerraSAR-X high-resolution spotlight images over an
area in Munich, Germany.Comment: 10 page
Fast Sublinear Sparse Representation using Shallow Tree Matching Pursuit
Sparse approximations using highly over-complete dictionaries is a
state-of-the-art tool for many imaging applications including denoising,
super-resolution, compressive sensing, light-field analysis, and object
recognition. Unfortunately, the applicability of such methods is severely
hampered by the computational burden of sparse approximation: these algorithms
are linear or super-linear in both the data dimensionality and size of the
dictionary. We propose a framework for learning the hierarchical structure of
over-complete dictionaries that enables fast computation of sparse
representations. Our method builds on tree-based strategies for nearest
neighbor matching, and presents domain-specific enhancements that are highly
efficient for the analysis of image patches. Contrary to most popular methods
for building spatial data structures, out methods rely on shallow, balanced
trees with relatively few layers. We show an extensive array of experiments on
several applications such as image denoising/superresolution, compressive
video/light-field sensing where we practically achieve 100-1000x speedup (with
a less than 1dB loss in accuracy)
Generalized Inpainting Method for Hyperspectral Image Acquisition
A recently designed hyperspectral imaging device enables multiplexed
acquisition of an entire data volume in a single snapshot thanks to
monolithically-integrated spectral filters. Such an agile imaging technique
comes at the cost of a reduced spatial resolution and the need for a
demosaicing procedure on its interleaved data. In this work, we address both
issues and propose an approach inspired by recent developments in compressed
sensing and analysis sparse models. We formulate our superresolution and
demosaicing task as a 3-D generalized inpainting problem. Interestingly, the
target spatial resolution can be adjusted for mitigating the compression level
of our sensing. The reconstruction procedure uses a fast greedy method called
Pseudo-inverse IHT. We also show on simulations that a random arrangement of
the spectral filters on the sensor is preferable to regular mosaic layout as it
improves the quality of the reconstruction. The efficiency of our technique is
demonstrated through numerical experiments on both synthetic and real data as
acquired by the snapshot imager.Comment: Keywords: Hyperspectral, inpainting, iterative hard thresholding,
sparse models, CMOS, Fabry-P\'ero
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