Sparse Signal Recovery under Poisson Statistics

We are motivated by problems that arise in a number of applications such as Online Marketing and explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random variable whose mean is a sparse linear superposition of known patterns. Unlike many conventional problems observations here are not identically distributed since they are associated with different sensing modalities. We analyze the performance of a Maximum Likelihood (ML) decoder, which for our Poisson setting involves a non-linear optimization but yet is computationally tractable. We derive fundamental sample complexity bounds for sparse recovery when the measurements are contaminated with Poisson noise. In contrast to the least-squares linear regression setting with Gaussian noise, we observe that in addition to sparsity, the scale of the parameters also fundamentally impacts sample complexity. We introduce a novel notion of Restricted Likelihood Perturbation (RLP), to jointly account for scale and sparsity. We derive sample complexity bounds for $\ell_1$ regularized ML estimators in terms of RLP and further specialize these results for deterministic and random sensing matrix designs.Comment: 13 pages, 11 figures, 2 tables, submitted to IEEE Transactions on Signal Processin

Selective classification via one-sided prediction

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Differing myocardial response to a single session of hemodialysis in end-stage renal disease with and without type 2 diabetes mellitus and coronary artery disease

BACKGROUND: Though hemodialysis (HD) acutely improves cardiac function, the impact of background diseases like coronary artery disease (CAD) and Type 2 diabetes (DM) in the setting of end-stage renal disease (ESRD) is not known. Tissue velocity echocardiography (TVE) offers a fast choice to follow changes in myocardial function after HD in ESRD with concomitant DM and /or CAD. METHODS: 46 subjects (17 with ESRD, Group 1; 15 with DM, Group 2; 14 with DM+CAD, Group 3) underwent standard and TVE prior to and shortly after HD. Besides standard Doppler variables, regional myocardial systolic and diastolic velocities, as well as systolic strain rate were post processed. RESULTS: Compared with pre-HD, post-HD body weight (kg) significantly decreased in all the three groups (51 ± 9 vs. 48 ± 8, 62 ± 10 vs.59 ± 10, and 61 ± 9 vs. 58 ± 9 respectively; all p < 0.01). Left ventricular end diastolic dimensions (mm) also decreased post- HD (46 ± 5 vs. 42 ± 7, 53 ± 7 vs. 50 ± 7, 51 ± 7 vs. 47 ± 8 respectively; all p < 0.01). Regional longitudinal peak systolic velocity in septum (cm/s) significantly increased post-HD in Group 1(5.7 ± 1.6 vs. 7.2 ± 2.3; p < 0.001) while remained unchanged in the other two groups. Similar trends were noted in other left ventricular walls. When the myocardial velocities (cm/s) were computed globally, the improvement was seen only in Group 1 (6.3 ± 1.5 vs. 7.9 ± 2.0; p < 0.001). Global early regional diastolic velocity (cm/s) improved in Group 1, remained unchanged in Group 2, while significantly decreased in Group 3(-5.9 ± 1.3 vs. -4.1 ± 1.8; p < 0.01). Global systolic strain rate (1/sec) increased in the first 2 Groups but remained unchanged (-0.87 ± 0.4 vs. -0.94 ± 0.3; p = ns) in Group 3. CONCLUSION: A single HD session improves LV function only in ESRD without coexistent DM and/or CAD. The present data suggest that not only dialysis-dependent changes in loading conditions but also co-existent background diseases determine the myocardial response to HD