Monday, August 17, 2009

CS: Content Based Retrieval, Bioluminescence Tomography, Recovering sparse signals with non-convex penalties and DC programming

Today, we have three new entries at the Rice Compressive Sensing repository, I haven't had time to read time, I'll do that during my break.
Image databases, medical records and geographical information systems contain data that is intrinsically correlated, i.e. elements within a single single record show a high degree of correlation. Content based retrieval is a common technique for querying such databases. The query specifies an image or components that the record is expected to contain or be similar to.We propose a technique for compact storage of such correlated data that is used for content based retrieval. Our method utilizes the machinery of compressive sensing, which allows an under determined system of equations to be approximately solved by l1-minimization if the data is a sparse linear combination of an appropriate set of basis vectors. Such sparsity is seen in these correlated databases. If the sparsity is high or if some distortion is permitted in the retrieved data, the data can be retrieved by a reconstruction operation with a constant storage cost independent of the number of records stored. If exact retrieval is needed, some additional storage is required for each record, much smaller than the size of the original record. We illustrate the performance of this method with a database of remote sensing images.

Through restoration of the light source information in small animals in vivo, optical molecular imaging, such as fluorescence molecular tomography (FMT) and bioluminescence tomography (BLT), can depict biological and physiological changes observed using molecular probes. A priori information plays an indispensable role in tomographic reconstruction. As a type of a priori information, the sparsity characteristic of the light source has not been sufficiently considered to date. In this paper, we introduce a compressed sensing method to develop a new tomographic algorithm for spectrally-resolved bioluminescence tomography. This method uses the nature of the source sparsity to improve the reconstruction quality with a regularization implementation. Based on verification of the inverse crime, the proposed algorithm is validated with Monte Carlo-based synthetic data and the popular Tikhonov regularization method. Testing with different noise levels and single/multiple source settings at different depths demonstrates the improved performance of this algorithm. Experimental reconstruction with a mouse-shaped phantom further shows the potential of the proposed algorithm.

This paper considers the problem of recovering a sparse signal representation according to a signal dictionary. This problem could be formalized as a penalized least-squares problem in which sparsity is usually induced by a ℓ1-norm penalty on the coefficients. Such an approach known as the Lasso or Basis Pursuit Denoising has been shown to perform reasonably well in some situations. However, it was also proved that non-convex penalties like the pseudo ℓq-norm with q \lt 1 or SCAD penalty are able to recover sparsity in a more efficient way than the Lasso. Several algorithms have been proposed for solving the resulting non-convex least-squares problem. This paper proposes a generic algorithm to address such a sparsity recovery problem for some class of non-convex penalties. Our main contribution is that the proposed methodology is based on an iterative algorithm which solves at each iteration a convex weighted Lasso problem. It relies on the family of non-convex penalties which can be decomposed as a difference of convex functions. This allows us to apply difference of convex functions programming which is a generic and principled way for solving non-smooth and non-convex optimization problem. We also show that several algorithms in the literature dealing with non-convex penalties are particular instances of our algorithm. Experimental results demonstrate the effectiveness of the proposed generic framework compared to existing algorithms, including iterative reweighted least-squares methods.

Credit: NASA / JPL / SSI, Shadow on Saturn's ring thanks to the equinox.

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