In the CS world, we have :Dimensionality reduction using compressed sensing and its application to a large-scale visual recognition task by Son Lam Phung, Fok Hing Chi Tivive, Abdesselam Bouzerdoumz, Jie Yang. The abstract reads:
This paper presents a novel algorithm for the dimensionality reduction which employs compressed sensing (CS) to improve the generalization capability of a classifier, especially for large-scale data. Compared to traditional dimensionality reduction methods, the proposed algorithm makes no use of the problem-dependent parameters, nor does it require additional computation for the eigenvalue decomposition like PCA or LDA. Mathematically, the derived algorithm regards the input features as the dictionary in CS, and selects the features that minimize the residual output error iteratively, thus the resulting features have a direct correspondence to the performance requirements of the given problem. Furthermore, the proposed algorithm can be regarded as a sparse classifier, which selects discriminative features and classifies the training data simultaneously. Experimentally, the CS-based algorithm is tested with a hierarchical visual pattern recognition architecture. The simulation results show that not only does the proposed method utilize only 25% of full features while achieving the test accuracy of the original full architecture, but also its performance is competitive when compared to existing dimensionality reduction methods.
Also, Gabriel Peyre let me know of a series of presentations in honor of Yves Meyer at ENS Cachan. I just found a presentation by Zainul Charbiwala entitled Recovering Lost Sensor Data through Compressed Sensing and behind a paywall, we also have: Prior estimate-based compressed sensing in parallel MRI. by Wu B, Millane RP, Watts R, Bones PJ. The abstract reads:
Two improved compressed sensing (CS)-based image reconstruction methods for MRI are proposed: prior estimate-based compressed sensing (PECS) and sensitivity encoding-based compressed sensing (SENSECS). PECS allows prior knowledge of the underlying image to be intrinsically incorporated in the image recovery process, extending the use of data sorting as first proposed by Adluru and DiBella (Int J Biomed Imaging 2008: 341648). It does so by rearranging the elements in the underlying image based on the magnitude information gathered from a prior image estimate, so that the underlying image can be recovered in a new form that exhibits a higher level of sparsity. SENSECS is an application of PECS in parallel imaging. In SENSECS, image reconstruction is carried out in two stages: SENSE and PECS, with the SENSE reconstruction being used as a image prior estimate in the following PECS reconstruction. SENSECS bypasses the conflict of sampling pattern design in directly applying CS recovery in multicoil data sets and exploits the complementary characteristics of SENSE-type and CS-type reconstructions, hence achieving better image reconstructions than using SENSE or CS alone. The characteristics of PECS and SENSECS are investigated using experimental data.
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