Semi-orthogonal wavelet packet bases for parallel least-squares approximation

AbstractA generalization to the wavelet packet case of the semi-orthogonal wavelets given by C.K. Chui is presented and a simple numerical algorithm for their practical evaluation is developed. To provide a motivation, it is shown how, using these new bases, the least-squares approximation problem in a multiresolution space can easily be solved by means of an efficient parallel algorithm

Wavelet analysis and parallel numerical algorithms

Multiresolution wavelet and wavelet packet decomposition has recently found a wide range of application fields. In this work we show that its localization property in the frequency domain together with the corresponding orthogonal splitting of the multiresolution spaces can be used to build up new parallel algorithms. It is then shown that with the construction of semiorthogonal wavelets and wavelet packet packets, which in some cases can be $adapted$ to certain differential and integral operator, the corresponding numerical problems split into indipendet subproblems according to the orthogonality of the multiresolution spaces. Parallelism is therefore inherent in this basis change: the solutions of the subproblems obtained concurrently by different processors are defined on the whole physical domain but are local in the frequency domain ad they correspond to different frequency bands. The final solution, which is global in both frequency and physical spaces, is then easily obtained by means of the usual wavelet packet reconstruction algorithm

Blind cluster structured sparse signal recovery: A nonconvex approach

open3noWe consider the problem of recovering a sparse signal when its nonzero coefficients tend to cluster into blocks, whose number, dimension and position are unknown. We refer to this problem as {it blind cluster structured sparse recovery}. For its solution, differently from the existing methods that consider the problem in a statistical context, we propose a deterministic neighborhood based approach characterized by the use both of a nonconvex, nonseparable sparsity inducing function and of a penalized version of the iterative $ell_1$ reweighted method. Despite the high nonconvexity of the approach, a suitable integration of these building elements led to the development of MB-NFCS ({it Model Based Nonlinear Filtering for Compressed Sensing}), an iterative fast, self-adaptive, and efficient algorithm that, without requiring any information on the sparsity pattern, adjusts at each iteration the action of the sparsity inducing function in order to strongly encourage the emerging cluster structure. The effectiveness of the proposed approach is demonstrated by a large set of numerical experiments that show the superior performance of MB-NFCS to the state-of-the-art algorithms.This work was supported by Miur, R.F.O. projects.openDamiana Lazzaro;Laura B. Montefusco;Serena PapiDamiana Lazzaro;Laura B. Montefusco;Serena Pap

A fast algorithm for nonconvex approaches to sparse recovery problems

This paper addresses the problem of sparse signal recovery from a lower number of measurements than those requested by the classical compressed sensing theory. This problem is formalized as a constrained minimization problem, where the objective function is nonconvex and singular at the origin. Several algorithms have been recently proposed, which rely on iterative reweighting schemes, that produce better estimates at each new minimization step. Two such methods are iterative reweighted l2 and l1 minimization that have been shown to be effective and general, but very computationally demanding. The main contribution of this paper is the proposal of the algorithm WNFCS, where the reweighted schemes represent the core of a penalized approach to the solution of the constrained nonconvex minimization problem. The algorithm is fast, and succeeds in exactly recovering a sparse signal from a smaller number of measurements than the l1 minimization and in a shorter time. WNFCS is very general, since it represents an algorithmic framework that can easily be adapted to different reweighting strategies and nonconvex objective functions. Several numerical experiments and comparisons with some of the most recent nonconvex minimization algorithms confirm the capabilities of the proposed algorithm

Distribution of cardiovascular disease and retinopathy in patients with type 2 diabetes according to different classification systems for chronic kidney disease: a cross-sectional analysis of the renal insufficiency and cardiovascular events (RIACE) Italian multicenter study.

Background: The National Kidney Foundation's Kidney Disease Outcomes Quality Initiative (NKF's KDOQI) staging system for chronic kidney disease (CKD) is based primarily on estimated GFR (eGFR). This study aimed at assessing whether reclassification of subjects with type 2 diabetes using two recent classifications based on both eGFR and albuminuria, the Alberta Kidney Disease Network (AKDN) and the Kidney Disease: Improving Global Outcomes (KDIGO), provides a better definition of burden from cardiovascular disease (CVD) and diabetic retinopathy (DR) than the NKF's KDOQI classification. Methods: This is a cross-sectional analysis of patients with type 2 diabetes (n = 15,773) from the Renal Insufficiency And Cardiovascular Events Italian Multicenter Study, consecutively visiting 19 Diabetes Clinics throughout Italy in years 2007-2008. Exclusion criteria were dialysis or renal transplantation. CKD was defined based on eGFR, as calculated from serum creatinine by the simplified Modification of Diet in Renal Disease Study equation, and albuminuria, as measured by immunonephelometry or immunoturbidimetry. DR was assessed by dilated fundoscopy. Prevalent CVD, total and by vascular bed, was assessed from medical history by recording previous documented major acute events. Results: Though prevalence of complications increased with increasing CKD severity with all three classifications, it differed significantly between NKF's KDOQI stages and AKDN or KDIGO risk categories. The AKDN and KDIGO systems resulted in appropriate reclassification of uncomplicated patients in the lowest risk categories and a more graded independent association with CVD and DR than the NKF's KDOQI classification. However, CVD, but not DR prevalence was higher in the lowest risk categories of the new classifications than in the lowest stages of the NKF's KDOQI, due to the inclusion of subjects with reduced eGFR without albuminuria. CVD prevalence differed also among eGFR and albuminuria categories grouped into AKDN and KDIGO risk category 1 and moderate, respectively, and to a lesser extent into higher risk categories. Conclusions: Though the new systems perform better than the NKF's KDOQI in grading complications and identifying diabetic subjects without complications, they might underestimate CVD burden in patients assigned to lower risk categories and should be tested in large prospective studies

Familial aggregation of MATRICS Consensus Cognitive Battery scores in a large sample of outpatients with schizophrenia and their unaffected relatives

Background: The increased use of the MATRICS Consensus Cognitive Battery (MCCB) to investigate cognitive dysfunctions in schizophrenia fostered interest in its sensitivity in the context of family studies. As various measures of the same cognitive domains may have different power to distinguish between unaffected relatives of patients and controls, the relative sensitivity of MCCB tests for relativeâ\u80\u93control differences has to be established. We compared MCCB scores of 852 outpatients with schizophrenia (SCZ) with those of 342 unaffected relatives (REL) and a normative Italian sample of 774 healthy subjects (HCS). We examined familial aggregation of cognitive impairment by investigating within-family prediction of MCCB scores based on probandsâ\u80\u99 scores. Methods: Multivariate analysis of variance was used to analyze group differences in adjusted MCCB scores. Weighted least-squares analysis was used to investigate whether probandsâ\u80\u99 MCCB scores predicted REL neurocognitive performance. Results: SCZ were significantly impaired on all MCCB domains. REL had intermediate scores between SCZ and HCS, showing a similar pattern of impairment, except for social cognition. Proband's scores significantly predicted REL MCCB scores on all domains except for visual learning. Conclusions: In a large sample of stable patients with schizophrenia, living in the community, and in their unaffected relatives, MCCB demonstrated sensitivity to cognitive deficits in both groups. Our findings of significant within-family prediction of MCCB scores might reflect disease-related genetic or environmental factors