Calibration Using Matrix Completion with Application to Ultrasound Tomography

We study the calibration process in circular ultrasound tomography devices where the sensor positions deviate from the circumference of a perfect circle. This problem arises in a variety of applications in signal processing ranging from breast imaging to sensor network localization. We introduce a novel method of calibration/localization based on the time-of-flight (ToF) measurements between sensors when the enclosed medium is homogeneous. In the presence of all the pairwise ToFs, one can easily estimate the sensor positions using multi-dimensional scaling (MDS) method. In practice however, due to the transitional behaviour of the sensors and the beam form of the transducers, the ToF measurements for close-by sensors are unavailable. Further, random malfunctioning of the sensors leads to random missing ToF measurements. On top of the missing entries, in practice an unknown time delay is also added to the measurements. In this work, we incorporate the fact that a matrix defined from all the ToF measurements is of rank at most four. In order to estimate the missing ToFs, we apply a state-of-the-art low-rank matrix completion algorithm, OPTSPACE . To find the correct positions of the sensors (our ultimate goal) we then apply MDS. We show analytic bounds on the overall error of the whole process in the presence of noise and hence deduce its robustness. Finally, we confirm the functionality of our method in practice by simulations mimicking the measurements of a circular ultrasound tomography device.Comment: submitted to IEEE Transaction on Signal Processin

Euclidean Distance Matrices: Essential Theory, Algorithms and Applications

Euclidean distance matrices (EDM) are matrices of squared distances between points. The definition is deceivingly simple: thanks to their many useful properties they have found applications in psychometrics, crystallography, machine learning, wireless sensor networks, acoustics, and more. Despite the usefulness of EDMs, they seem to be insufficiently known in the signal processing community. Our goal is to rectify this mishap in a concise tutorial. We review the fundamental properties of EDMs, such as rank or (non)definiteness. We show how various EDM properties can be used to design algorithms for completing and denoising distance data. Along the way, we demonstrate applications to microphone position calibration, ultrasound tomography, room reconstruction from echoes and phase retrieval. By spelling out the essential algorithms, we hope to fast-track the readers in applying EDMs to their own problems. Matlab code for all the described algorithms, and to generate the figures in the paper, is available online. Finally, we suggest directions for further research.Comment: - 17 pages, 12 figures, to appear in IEEE Signal Processing Magazine - change of title in the last revisio

Ricketts Analysis Using Conventional and DolphinTM Generated CBCT Lateral Cephs

Purpose: The aim of this study was to evaluate the difference between Ricketts analysis measurements made on Sirona Orthophos XG Plus (Sirona Dental Systems, Charlotte,NC) lateral cephalograms, and DolphinTM generated perspective and orthogonal lateral cephalograms from CBCT (NewTom 5G; QR srl, Verona, Italy). Materials and Methods: A Sirona digital lateral cephalogram and DophinTM synthesized CBCT lateral cephalograms of a radiographic phantom in orthogonal and perspective projections were created. Horizontal and vertical measurements were made in multiple planes on the radiographic phantom to compare each imaging modality. Twenty-five lateral cephalometric radiographs were selected retrospectively from the records of patients of the LLUSD Graduate Orthodontic Clinic who had both CBCT and Sirona digital lateral cephalograms. Radiographs were excluded from the study if they displayed significant occlusal plane discrepancy (\u3e2 mm), or missing first molars. All lateral cephalograms were digitized into DolphinTM (version 11.8; Dolphin Imaging & Management Solutions, Chatsworth, Calif) and traced using Ricketts cephalometric analysis in addition to measurements from Nasion to Menton and Nasion to Basion. Eight linear and nine angular measurements from each imaging modality were compared and analyzed using one sample Wilcoxon signed rank test and pairwise comparison. Results: Statistically significant differences were found in percent magnification of horizontal and vertical measurements between the scanned grid and the various imaging modalities. No significant single plane perspective distortion (SPPD) was detected in the vertical and horizontal directions. Multiplane perspective distortion (MPPD) was only noted in Sirona images. Ricketts Analysis linear measurements were all statistically different except for lower lip to E-plane (P =0.544). The Ricketts Analysis angular measurements were not statistically different (P \u3c0.05) with the exception of facial axis (P =0.004) and maxillary depth (P =0.025). DolphinTM generated CBCT lateral cephalograms with orthogonal projection, adjusted to 101% magnification had the closest agreement to Sirona images. Conclusions: No clinically significant perspective distortion was found in the vertical and horizontal direction in the three modalities that were studied. DophinTM synthesized CBCT lateral cephalogram in perspective projection does not produce perspective images. CBCT Lateral cephalograms generated by DophinTM in orthogonal projection at 101% magnification is compatible with images from Sirona for clinical evaluation

Ad Hoc Microphone Array Calibration: Euclidean Distance Matrix Completion Algorithm and Theoretical Guarantees

This paper addresses the problem of ad hoc microphone array calibration where only partial information about the distances between microphones is available. We construct a matrix consisting of the pairwise distances and propose to estimate the missing entries based on a novel Euclidean distance matrix completion algorithm by alternative low-rank matrix completion and projection onto the Euclidean distance space. This approach confines the recovered matrix to the EDM cone at each iteration of the matrix completion algorithm. The theoretical guarantees of the calibration performance are obtained considering the random and locally structured missing entries as well as the measurement noise on the known distances. This study elucidates the links between the calibration error and the number of microphones along with the noise level and the ratio of missing distances. Thorough experiments on real data recordings and simulated setups are conducted to demonstrate these theoretical insights. A significant improvement is achieved by the proposed Euclidean distance matrix completion algorithm over the state-of-the-art techniques for ad hoc microphone array calibration.Comment: In Press, available online, August 1, 2014. http://www.sciencedirect.com/science/article/pii/S0165168414003508, Signal Processing, 201

Pulp Vitality Preservation of an Involved Tooth in a Large Radicular Cyst: A Case Report with 4-Year Recall

The current case study presents the surgical endodontic retreatment of a central incisor with a large periapical cyst that had extended to the adjacent lateral incisor. After anaesthesia, a full mucoperiosteal flap was carefully incised and completely reflected. Then, the cyst was cautiously excised without performing curettage of the apical region of the adjacent tooth. A 3-mm deep root-end cavity on tooth #21 was prepared, filled and sealed with calcium-enriched mixture cement. At 6-month and 4-year follow-ups, tooth #21 was fully functional and exhibited no clinical signs/symptoms, and complete periapical healing was evident. This report indicates the importance of proper diagnosis as well as a careful surgical approach in the successful management of comparable cases without the overtreatment of involved teeth

Pivotal Local Drug Delivery Systems in Endodontics; A Review of Literature

Endodontic pathosis is preliminary caused by bacteria and their by-products that interact with pulpal and periradicular host tissues. The purge of the root canal system (RCS) from bacteria is a necessity for successful endodontic treatment. Different approaches have been considered to reduce the number of microorganisms and confront microbiota in the radicular area; namely chemomechanical preparation and intracanal medication. However, various studies have shown that, due to the intricate anatomy of RCS, bacteria can persist in distant areas and significantly decrease the degree of success in endodontic ministrations. Thereby, elimination of bacteria remains a challenge, specifically from the infectious root canals. In recent years, local drug delivery systems (LDDS), loaded with drugs and/or antibacterial agents, have been deliberated for the removal of microorganisms or as a medicinal adjunct to mechanical instrumentation. Owing to the resistant species and complexities in the structure of root canals, it seems that LDDS may be able to closely affect microorganisms and improve the success rate of endodontic treatment. Furthermore, they are capable of limiting drugs to RCS, and can achieve a more effective therapeutic dose/concentration in the target site. Furthermore, and due to successful outcomes, administration of LDDS has also been given great attention for regenerative purposes. Micro/nanoparticles, liposomes, nanofibers, sealers and so forth represent typical delivery systems used for endodontic treatments. This study addresses pivotal LDDS used in endodontics and their applications.Keywords: Bacteria; Endodontics; Local Drug Delivery; Microorganism; Root Canal Syste

Supplementary health benefits of linoleic acid by improvement of vaginal cornification of ovariectomized rats

Purpose: This study aimed to evaluate the possible estrogenic activity of some ingredients of Nigella sativa including Linoleic acid and Gama-Linolenic acid by vaginal cornification assay. Methods: Forty ovariectomized (OVX) rats, aged 16 weeks were allotted randomly to five groups: negative control (taking 1 ml olive oil/ day); positive control (taking 0.2 mg/kg/day Conjucated Equine Estrogen-CEE); experimental groups (taking 50 mg/kg/day Linoleic acid or 10 mg/kg/day Gamma Linolenic acid or 15mg/kg/day Thymoquinone ). All of supplements administered via intragastric gavage for 21 consecutive days. To assess estrogen like activity, vaginal smear was examined daily and serum estradiol was measured at baseline, after 10 days and at the end of experiment. Results: The significant occurrence of vaginal cornification cell (p<0.05) after Linoleic acid supplementation indicated estrogenic activity of Linoleic acid which was in consistency with serum estradiol level, but this effect was not as much as CEE. Gama-Linolenic acid also exist a few cornified cell in smear which was not significantly differ from those control group. Conclusion: Linoleic acid showed the beneficial effects on OVX rats’ reproductive performance, thereby indicating its beneficial role in the treatment of the postmenopausal symptoms

How to Perform Descemet's Membrane Endothelial Keratoplasty: A Step by Step Guide

Descemet's Membrane Endothelial Keratoplasty (DMEK) is a type of lamellar (partial thickness) corneal transplantation in which the endothelium, along with Descemet's membrane, is transferred. This technique has gained increased popularity in recent years and is expected to become more prominent and widely used among the various types of corneal transplantation. This review article provides a step-by-step guide for corneal surgeons on conducting DMEK. Like any other surgical procedure, gaining experience and completing consecutive surgeries can improve the delicate and precise execution of this procedure. Watching videos, observing live surgeries performed by experienced surgeons who have sufficient expertise in this procedure, and ultimately performing the surgery under the guidance of experienced individuals are factors that contribute to better surgical outcomes. This text serves solely as a guide for performing the continuous stages of DMEK