Most of the signal processing that we will study in this course involves local operations on a signal, namely transforming the signal by applying linear combinations of values in the neighborhood of each sample point. You are familiar with such operations from Calculus, namely, taking derivatives and you are also familiar with this from optics namely blurring a signal. We will be looking at sampled signals only. Let's start with a few basic examples. Local difference Suppose we have a 1D image and we take the local difference of intensities, DI(x) = 1 2 (I(x + 1) − I(x − 1)) which give a discrete approximation to a partial derivative. (We compute this for each x in the image.) What is the effect of such a transformation? One key idea is that such a derivative would be useful for marking positions where the intensity changes. Such a change is called an edge. It is important to detect edges in images because they often mark locations at which object properties change. These can include changes in illumination along a surface due to a shadow boundary, or a material (pigment) change, or a change in depth as when one object ends and another begins. The computational problem of finding intensity edges in images is called edge detection. We could look for positions at which DI(x) has a large negative or positive value. Large positive values indicate an edge that goes from low to high intensity, and large negative values indicate an edge that goes from high to low intensity. Example Suppose the image consists of a single (slightly sloped) edge:

http://ieeexplore.ieee.org/iel5/5/31307/01456462.pdf

Linear systems

Previous studies have shown that chronic dietary deficiency of calcium can result in more rapid orthodontic tooth movement. The purposes of this study were to confirm that finding in a calcium-deficient, lactating rat model and to quantify the degree to which the area of root surface resorption is affected by these conditions. Thirty-five adult female Sprague-Dawley rats were divided into two groups: (1) nonlactating animals on a control diet and (2) lactating animals on a calcium-deficient diet. A 60-gm orthodontic force designed to tip maxillary molars mesially was applied for varying times. At sacrifice, tooth movement was quantified by measuring the space created between maxillary molars; percent bone ash was measured for each humerus, and root surface resorption was estimated by means of a morphometric technique to measure the area of cratering on the mesial roots of first molars. Both groups showed a typical two-phased tooth movement cycle lasting for 10 days, although the magnitude of movement was significantly greater (p less than 0.001) in the test animals. The "humerus" test from animals exhibited a significantly decreased (p less than 0.001) fat-free dry weight, ash, and percent ash weight. The test group also displayed a significantly reduced percent area of root surface resorption (p less than 0.05) by 7 and 10 days following appliance activation. These findings confirm earlier observations that lactation, coupled with calcium deficiency, will produce decreased bone density which is consistent with increased parathyroid hormone secretion.(ABSTRACT TRUNCATED AT 250 WORDS)

Root resorption and tooth movement in orthodontically treated calcium deficient and lactating rats

Objective: To evaluate the effectiveness of interventions on accelerating orthodontic tooth movement. Materials and Methods: We searched the databases of PubMed, Embase, Science Citation Index, CENTRAL, and SIGLE from January 1990 to August 2011 for randomized or quasirandomized controlled trials that assessed the effectiveness of interventions on accelerating orthodontic tooth movement. The processes of study search, selection, and quality assessment were conducted independently in duplicate by two review authors. Original outcome data, if possible, underwent statistical pooling by using Review Manager 5. Results: Through a predefined search strategy, we finally included nine eligible studies. Among them, five interventions were studied (ie, low-level laser therapy, corticotomy, electrical current, pulsed electromagnetic fields, and dentoalveolar or periodontal distraction). Six outcomes were evaluated in these studies (ie, accumulative moved distance or movement rate, time required to move tooth to its destination, anchorage loss, periodontal health, pulp vitality, and root resorption). Conclusion: Among the five interventions, corticotomy is effective and safe to accelerate orthodontic tooth movement, low-level laser therapy was unable to accelerate orthodontic tooth movement, current evidence does not reveal whether electrical current and pulsed electromagnetic fields are effective in accelerating orthodontic tooth movement, and dentoalveolar or periodontal distraction is promising in accelerating orthodontic tooth movement but lacks convincing evidence. (Angle Orthod. 2013;83:164–171.)

/pdf/interventions-for-accelerating-orthodontic-tooth-movement-a-1tsiib6l8c.pdf

Interventions for accelerating orthodontic tooth movement: a systematic review.

Effectiveness of non-conventional methods for accelerated orthodontic tooth movement: a systematic review and meta-analysis.

This prospective 3-arm parallel-group randomized clinical trial investigated the effect of supplemental vibrational force on rate of orthodontic tooth alignment with fixed appliances. Eighty-one subjects (40 males, 41 females; mean age, 14.1 y) undergoing first premolar extraction-based fixed appliance treatment were randomly allocated to treatment supplemented with daily use (20 min) of a removable intraoral vibrational device (AcceleDent; OrthoAccel Technologies Inc.; n = 29), an identical nonfunctional (sham) device (n = 25), or fixed appliances only (n = 27). Mandibular study casts were taken at baseline (treatment start: placement of 0.014-in. nickel-titanium arch wire), initial alignment (0.018-in. nickel-titanium arch wire), and final alignment (0.019 x 0.025-in. stainless steel arch wire). Overall mean irregularity index in the mandibular arch at baseline was 8.5 ± 3.8 mm (95% CI, 7.6 to 9.3) with no significant difference between groups (P = 0.73). For the total sample, mean irregularity index at initial alignment was 2.7 ± 2.8 mm (95% CI, 2.2 to 3.4) with no significant difference between groups (P = 0.40). Mean time from baseline to initial alignment was 59 ± 25 d (95% CI, 54.5 to 65.6); from initial to final alignment, 150 ± 62.5 d (95% CI, 136 to 165); and baseline to final alignment, 209 ± 65 d (95% CI, 195 to 224). Kaplan-Meier analysis demonstrated that patterns of alignment were not significantly different among the 3 groups (P = 0.66). Multivariate linear regression for initial and overall alignment rates using initial irregularity index as the covariate showed no significant differences among groups. The most important influence on both initial and overall rates of alignment was initial irregularity (P = 0.1 × 10(-4)). This prospective randomized clinical trial found no evidence that supplemental vibrational force can significantly increase the rate of initial tooth movement or reduce the amount of time required to achieve final alignment when used in conjunction with a preadjusted edgewise fixed appliance (ClinicalTrials.gov NCT02314975).

Supplemental Vibrational Force During Orthodontic Alignment: A Randomized Trial

Aim: Accelerating the speed of orthodontic tooth movement should contribute to the shortening of the treatment period. This study was designed to determine whether a pulsed electromagnetic field (PEMF) affects orthodontic tooth movement. Methods: The canines of one side of 10 patients (mean age 23.0 ± 3.3 years) who needed canine retraction were exposed to a PEMF; the canines on the contralateral sides of the same patients were not similarly exposed. After extraction of the maxillary first premolars, both canines were retracted with coil springs. A circuit and a watch battery were used to generate a PEMF (1 Hz). The generator was embedded in a removable appliance. Foil was used to obstruct the contol group from PEMF exposure. Patients were instructed to use the device from the commencement of canine retraction, and it was removed when Class I canine relationship was achieved in either of the canines after 5.0 ± 0.6 months. The changes in the space between the maxillary canine and first molar were measured to indicate the amount of tooth movement. The canine retraction distances were compared by paired t test. Afterward, the treatment plan was continued. Results: With exposure to a PEMF, canine retraction was 1.57 ± 0.83 mm more than the control group (P < .001). Conclusion: These findings suggest that application of a PEMF can accelerate orthodontic tooth movement. World J Orthod 2010;11:e52‐e56.

The effect of pulsed electromagnetic fields on the acceleration of tooth movement.

Securing state reconstruction under sensor and actuator attacks: Theory and design

Data privacy is an important concern in machine learning, and is fundamentally at odds with the task of training useful learning models, which typically require acquisition of large amounts of private user data. One possible way of fulfilling the machine learning task while preserving user privacy is to train the model on a transformed, noisy version of the data, which does not reveal the data itself directly to the training procedure. In this work, we analyze the privacy-utility tradeoff of two such schemes for the problem of linear regression: additive noise, and random projections. In contrast to previous work, we consider a recently proposed notion of differential privacy that is based on conditional mutual information (MI-DP), which is stronger than the conventional $(\varepsilon,\delta)$ -differential privacy, and use relative objective error as the utility metric. We find that projecting the data to a lower-dimensional subspace before adding noise attains a better trade-off in general. We also make a connection between privacy problem and (non-coherent) SIMO, which has been extensively studied in wireless communication, and use tools from there for the analysis. We present numerical results demonstrating the performance of the schemes.

/pdf/privacy-utility-trade-off-of-linear-regression-under-random-1qi47b8dui.pdf

Privacy-Utility Trade-off of Linear Regression under Random Projections and Additive Noise

This paper addresses the problem of state estimation of a linear time-invariant system when some of the sensors or/and actuators are under adversarial attack. In our set-up, the adversarial agent attacks a sensor (actuator) by manipulating its measurement (input), and we impose no constraint on how the measurements (inputs) are corrupted. We introduce the notion of “sparse strong observability” to characterize systems for which the state estimation is possible, given bounds on the number of attacked sensors and actuators. Furthermore, we develop a secure state estimator based on Satisfiability Modulo Theory (SMT) solvers.

https://par.nsf.gov/servlets/purl/10065992

An SMT-based approach to secure state estimation under sensor and actuator attacks

We consider the problem of system identification of linear time invariant systems when some of the sensor measurements are changed by a malicious adversary. We treat adversaries as omniscient and impose no restrictions (statistical or otherwise) on how they can alter the measurements of the sensors under attack. Given a bound on the number of attacked sensors, and under a certain observability condition, we show that we can construct models that are useful for certain control purposes, e.g., stabilization. We also provide a precise characterization of the equivalence relation that identifies which models cannot be distinguished in the presence of attacks.

Mehrdad Showkatbakhsh

Papers

The effect of pulsed electromagnetic fields on the acceleration of tooth movement.

Securing state reconstruction under sensor and actuator attacks: Theory and design

Privacy-Utility Trade-off of Linear Regression under Random Projections and Additive Noise

An SMT-based approach to secure state estimation under sensor and actuator attacks

System identification in the presence of adversarial outputs