Total Variation Blind Deconvolution: The Devil Is in the Details

In this paper we study the problem of blind deconvolution. Our analysis is based on the algorithm of Chan and Wong [2] which popularized the use of sparse gradient priors via total variation. We use this algorithm because many methods in the literature are essentially adaptations of this framework. Such algorithm is an iterative alternating energy minimization where at each step either the sharp image or the blur function are reconstructed. Recent work of Levin et al. [14] showed that any algorithm that tries to minimize that same energy would fail, as the desired solution has a higher energy than the no-blur solution, where the sharp image is the blurry input and the blur is a Dirac delta. However, experimentally one can observe that Chan and Wong's algorithm converges to the desired solution even when initialized with the no-blur one. We provide both analysis and experiments to resolve this paradoxical conundrum. We find that both claims are right. The key to understanding how this is possible lies in the details of Chan and Wong's implementation and in how seemingly harmless choices result in dramatic effects. Our analysis reveals that the delayed scaling (normalization) in the iterative step of the blur kernel is fundamental to the convergence of the algorithm. This then results in a procedure that eludes the no-blur solution, despite it being a global minimum of the original energy. We introduce an adaptation of this algorithm and show that, in spite of its extreme simplicity, it is very robust and achieves a performance comparable to the state of the art.

Synovial sarcomas usually metastasize after >5 years: a multicenter retrospective analysis with minimum follow-up of 10 years for survivors

Synovial sarcoma (SS) is a malignant soft tissue sarcoma with a poor prognosis because of late local recurrence and distant metastases. To our knowledge, no studies have minimum follow-up of 10 years that evaluate long-term outcomes for survivors.

Effects of isoflurane upon minimum alveolar concentration and cerebral cortex depression in pigs and goats: an interspecies comparison

This study compared the effects of isoflurane in pigs (n=10 Yorkshire-Landrace cross) and dairy goats (n=10) by evaluation of electroencephalographic (EEG) burst suppression thresholds (BST) in the cerebral cortex and minimum alveolar concentration (MAC) values in the spinal cord. The study also investigated whether individual MAC values can predict the effects of isoflurane on the cerebral cortex. MAC values and BST/MAC ratios were significantly different between species. Inhibition of movement by isoflurane may be less effective in pigs than in goats. No significant correlation was found between individual MAC and BST values, indicating that in single animals the individual MAC poorly reflects the cerebrocortical depressant effect of isoflurane in pigs and goats.

The effects of isoflurane minimum alveolar concentration on withdrawal reflex activity evoked by repeated transcutaneous electrical stimulation in ponies

The aim of this study was to quantify the effects of isoflurane at approximately the minimum alveolar concentration (peri-MAC) on the temporal summation (TS) of reflex activity in ponies. TS was evoked by repeated electrical stimulations applied at 5 Hz for 2 s on the digital nerve of the left forelimb of seven ponies. Surface electromyographic activity was recorded from the deltoid and common digital extensor muscles. TS thresholds and amplitude of response to stimulations of increasing intensities were assessed during anaesthesia at 0.85, 0.95 and 1.05 times the individual MAC, and after anaesthesia in standing animals. Under isoflurane anaesthesia, TS thresholds increased significantly in a concentration-dependent fashion and at each isoflurane MAC, the responses increased significantly for increasing stimulation intensities. A concentration-dependent depression of evoked reflexes with a reduction in the slopes of the stimulus-response function was observed for both muscles. The results demonstrated that with this model it is possible to describe and quantify the effects of anaesthetics on spinal sensory-motor processing in ponies.

Evaluation of administration of isoflurane at approximately the minimum alveolar concentration on depression of a nociceptive withdrawal reflex evoked by transcutaneous electrical stimulation in ponies

OBJECTIVE: To investigate effects of isoflurane at approximately the minimum alveolar concentration (MAC) on the nociceptive withdrawal reflex (NWR) of the forelimb of ponies as a method for quantifying anesthetic potency. ANIMALS: 7 healthy adult Shetland ponies. PROCEDURE: Individual MAC (iMAC) for isoflurane was determined for each pony. Then, effects of isoflurane administered at 0.85, 0.95, and 1.05 iMAC on the NWR were assessed. At each concentration, the NWR threshold was defined electromyographically for the common digital extensor and deltoid muscles by stimulating the digital nerve; additional electrical stimulations (3, 5, 10, 20, 30, and 40 mA) were delivered, and the evoked activity was recorded and analyzed. After the end of anesthesia, the NWR threshold was assessed in standing ponies. RESULTS: Mean +/- SD MAC of isoflurane was 1.0 +/- 0.2%. The NWR thresholds for both muscles increased significantly in a concentration-dependent manner during anesthesia, whereas they decreased in awake ponies. Significantly higher thresholds were found for the deltoid muscle, compared with thresholds for the common digital extensor muscle, in anesthetized ponies. At each iMAC tested, amplitudes of the reflex responses from both muscles increased as stimulus intensities increased from 3 to 40 mA. A concentration-dependent depression of evoked reflexes with reduction in slopes of the stimulus-response functions was detected. CONCLUSIONS AND CLINICAL RELEVANCE: Anesthetic-induced changes in sensory-motor processing in ponies anesthetized with isoflurane at concentrations of approximately 1.0 MAC can be detected by assessment of NWR. This method will permit comparison of effects of inhaled anesthetics or anesthetic combinations on spinal processing in equids.

Prediction of hypertensive crisis based on average, variability and approximate entropy of 24-h ambulatory blood pressure monitoring

Approximate entropy (ApEn) of blood pressure (BP) can be easily measured based on software analysing 24-h ambulatory BP monitoring (ABPM), but the clinical value of this measure is unknown. In a prospective study we investigated whether ApEn of BP predicts, in addition to average and variability of BP, the risk of hypertensive crisis. In 57 patients with known hypertension we measured ApEn, average and variability of systolic and diastolic BP based on 24-h ABPM. Eight of these fifty-seven patients developed hypertensive crisis during follow-up (mean follow-up duration 726 days). In bivariate regression analysis, ApEn of systolic BP (P<0.01), average of systolic BP (P=0.02) and average of diastolic BP (P=0.03) were significant predictors of hypertensive crisis. The incidence rate ratio of hypertensive crisis was 14.0 (95% confidence interval (CI) 1.8, 631.5; P<0.01) for high ApEn of systolic BP as compared to low values. In multivariable regression analysis, ApEn of systolic (P=0.01) and average of diastolic BP (P<0.01) were independent predictors of hypertensive crisis. A combination of these two measures had a positive predictive value of 75%, and a negative predictive value of 91%, respectively. ApEn, combined with other measures of 24-h ABPM, is a potentially powerful predictor of hypertensive crisis. If confirmed in independent samples, these findings have major clinical implications since measures predicting the risk of hypertensive crisis define patients requiring intensive follow-up and intensified therapy.