838 research outputs found
Deriving RIP sensing matrices for sparsifying dictionaries
Compressive sensing involves the inversion of a mapping , where , is a sensing matrix, and is a sparisfying
dictionary. The restricted isometry property is a powerful sufficient condition
for the inversion that guarantees the recovery of high-dimensional sparse
vectors from their low-dimensional embedding into a Euclidean space via convex
optimization. However, determining whether has the restricted isometry
property for a given sparisfying dictionary is an NP-hard problem, hampering
the application of compressive sensing. This paper provides a novel approach to
resolving this problem. We demonstrate that it is possible to derive a sensing
matrix for any sparsifying dictionary with a high probability of retaining the
restricted isometry property. In numerical experiments with sensing matrices
for K-SVD, Parseval K-SVD, and wavelets, our recovery performance was
comparable to that of benchmarks obtained using Gaussian and Bernoulli random
sensing matrices for sparse vectors
Depth Extraction from a Single Image and Its Application
In this chapter, a method for the generation of depth map was presented. To generate the depth map from an image, the proposed approach involves application of a sequence of blurring and deblurring operations on a point to determine the depth of the point. The proposed method makes no assumptions with regard to the properties of the scene in resolving depth ambiguity in complex images. Since applications involving depth map manipulation can be achieved by obtaining all-in-focus images through a deblurring operation and then blurring the obtained images, we have presented methods to derive all-in-focus images from our depth maps. Furthermore, 2D to 3D conversion can also be achieved from the estimated depth map. Some demonstrations show the performance and applications of the estimated depth map in this chapter
Multi-Ridge Detection and Time-Frequency Reconstruction
International audienceThe ridges of the wavelet transform, the Gabor transform or any time-frequency representation of a signal contain crucial information on the characteristics of the signal. Indeed they mark the regions of the time-frequency plane where the signal concentrates most of its energy. We introduce a new algorithm to detect and identify these ridges.The procedure is based on an original form of Markov Chain Monte Carlo algorithm specially adapted to the present situation. We show that this detection algorithm is especially useful for noisy signals with multi-ridge transforms. It is a common practice among practitioners to reconstruct a signal from the skeleton of a transform of the signal (i.e. the restriction of the transform to the ridges). After reviewing several known procedures we introduce a new reconstruction algorithm and we illustrate its efficiency on speech signals
- …