Pressure algometry is widely used to assess deep tissue sensitivity. In this study the relation between pressure-induced pain in humans and stress/strain distribution within the deep tissue is evaluated. A three-dimensional finite-element computer model was used to describe the stress/strain distribution in tissues of the lower leg during pressure stimulation. The computer model was validated based on data recorded by computer-controlled pressure-induced muscle pain in eight subjects. An indentation of 7 mm was painful for all subjects and at this level data were extracted from each simulation. Simulations were performed with different stimulation sites (muscle, near-bone), probe diameters (5, 10, 15 mm), and probe designs (flat, rounded). The principal stress peaked in the skin and was reduced to about 10% in the underlying muscle tissue. The principal strain peaked in adipose tissue and was reduced in muscle tissue to 80% with the 15 mm probe and 66% with the 5mm probe. The large diameter probe evoked a strain peak in adipose tissue at 0.12 (flat probe) and 0.24 (rounded probe); in muscle tissue 0.10 and 0.20 respectively. The human pressure pain thresholds with the rounded probe were significantly lower compared with the flat probe (p<0.05). The results suggest that pressure-induced muscle pain is mainly related to muscle strain and most efficiently induced by large rounded probes, while smaller and flat ones mainly activate superficial structures. The relatively low stress in the deep tissue suggests that the mechanosensitivity of nociceptors in the deep tissue is lower compared with nociceptors in the superficial tissue.

Abstract.A series of recent results shows that if a signal admits a sufficiently sparse representation (in terms of the number of nonzero coefficients) in an "incoherent" dictionary, this solution is unique and can be recovered as the unique solution of a linear programming problem. We generalize these results to a large class of sparsity measures which includes the p -sparsity measures for 0 ≤ p ≤ 1. We give sufficient conditions on a signal such that the simple solution of a linear programming problem simultaneously solves all the non-convex (and generally hard combinatorial) problems of sparsest representation w.r.t. arbitrary admissible sparsity measures. Our results should have a practical impact on source separation methods based on sparse decompositions, since they indicate that a large class of sparse priors can be efficiently replaced with a Laplacian prior without changing the resulting solution.

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Signal compression is gaining importance in biomedical engineering due to the potential applications in telemedicine. In this work, we propose a novel scheme of signal compression based on signal-dependent wavelets. To adapt the mother wavelet to the signal for the purpose of compression, it is necessary to define (1) a family of wavelets that depend on a set of parameters and (2) a quality criterion for wavelet selection (i.e., wavelet parameter optimization). We propose the use of an unconstrained parameterization of the wavelet for wavelet optimization. A natural performance criterion for compression is the minimization of the signal distortion rate given the desired compression rate. For coding the wavelet coefficients, we adopted the embedded zerotree wavelet coding algorithm, although any coding scheme may be used with the proposed wavelet optimization. As a representative example of application, the coding/encoding scheme was applied to surface electromyographic signals recorded from ten subjects. The distortion rate strongly depended on the mother wavelet (for example, for 50% compression rate, optimal wavelet, mean+/-SD, 5.46+/-1.01%; worst wavelet 12.76+/-2.73%). Thus, optimization significantly improved performance with respect to previous approaches based on classic wavelets. The algorithm can be applied to any signal type since the optimal wavelet is selected on a signal-by-signal basis. Examples of application to ECG and EEG signals are also reported.

International audienceTen years ago, Mallat and Zhang proposed the Matching Pursuit algorithm : since then, the dictionary approach to signal processing has been a very active field. In this paper, we try to give an overview of a series of recent results in the field of sparse decompositions and nonlinear approximation with redundant dictionaries. We discuss sufficient conditions on a decomposition to be the unique and simultaneous sparsest \ell^\tau expansion for all \tau,0 \leq \tau \leq 1. In particular, we prove that any decomposition has this nice property if the number of its nonzero coefficients does not exceed a quantity which we call the spread of the dictionary. After a brief discussion of the interplay between sparse decompositions and nonlinear approximation with various families of algorithms, we review several recent results that provide sufficient conditions for the Matching Pursuit, Orthonormal Matching Pursuit, and Basis Pursuit algorithms to have good recovery properties. The most general conditions are not straightforward to check, but weaker estimates based on the notions of coherence of the dictionary are recalled, and we discuss how these results can be applied to approximation and sparse decompositions with highly redundant incoherent dictionaries built by taking the union of several orthonormal bases. Eventually, based on Bernstein inequalities, we discuss how much approximation power can be gained by replacing a single basis with such redundant dictionaries