As always being a giant company in the publishing industry, Adobe had a great head start advantage over Microsoft in terms of number of content available as well as number of readers being able to display or print PDF format. Numbers speak, as for year 2000, there are over 100,000 eBooks available in Adobe PDF format while there are only dozens available to any other formats. By having 200 million downloads, Adobe Acrobat readers also significantly outnumbered Microsoft with Microsoft reader in the market.

We design optimal 2 × N (2 < N ) matrices, with unit columns, so that the maximum condition number of all the submatrices comprising 3 columns is minimized. The problem has two applications. When estimating a 2-dimensional signal by using only three of N observations at a given time, this minimizes the worst-case achievable estimation error. It also captures the problem of optimum sensor placement for monitoring a source located in a plane, when only a minimum number of required sensors are active at any given time. For arbitrary N ≥ 3, we derive the optimal matrices which minimize the maximum condition number of all the submatrices of three columns. Surprisingly, a uniform distribution of the columns is not the optimal design for odd N ≥ 7.

We consider the problem of designing optimal M × N (M ≤ N ) sensing matrices which minimize the maximum condition number of all the submatrices of K columns. Such matrices minimize the worst-case estimation errors when only K sensors out of N sensors are available for sensing at a given time. For M = 2 and matrices with unit-normed columns, this problem is equivalent to the problem of maximizing the minimum singular value among all the submatrices of K columns. For M = 2, we are able to give a closed form formula for the condition number of the submatrices. When M = 2 and K = 3, for an arbitrary N ≥ 3, we derive the optimal matrices which minimize the maximum condition number of all the submatrices of K columns. Surprisingly, a uniformly distributed design is often not the optimal design minimizing the maximum condition number.

—This paper presents a novel method to detect three types of abnormal Red Blood Cells (RBCs) called Poikilocytes in Iron deficient blood smears. Classification and counting the number of Poikilocyte cells is considered as an important step for the automatic detection of Iron Deficiency Anemia (IDA) disease. Dacrocyte, Elliptocyte and Schistocyte cells are three essential Poikilocyte cells that are prevalent in IDA. The suggested cell recognition approach includes preprocessing, segmentation, feature extraction and classification steps. Classification is done by using three distinct classifiers including Neural Network (NNET), Support Vector Machine (SVM) and K-Nearest Neighbor (KNN) classifiers. Finally, the output of all of the three classifiers are used via Maximum Voting theory to choose the proper class. In maximum voting theory, the class that receives the maximum number of votes is chosen as the final predicted class of a sample cell. In this paper, the accuracy of the proposed method is %99, %97 and %100 for detecting Dacrocyte cells, Elliptocyte cells and Schistocyte cells, respectively.

In this paper we present a new algorithm for compressive sensing that makes use of binary measurement matrices and achieves exact recovery of ultra sparse vectors, in a single pass and without any iterations. Due to its noniterative nature, our algorithm is hundreds of times faster than 1-norm minimization, and methods based on expander graphs, both of which require multiple iterations. Our algorithm can accommodate nearly sparse vectors, in which case it recovers index set of the largest components, and can also accommodate burst noise measurements. Compared to compressed sensing methods that are guaranteed to achieve exact recovery of all sparse vectors, our method requires fewer measurements. However, methods that achieve statistical recovery, that is, recovery of almost all but not all sparse vectors, can require fewer measurements than our method.

In this paper, we study the problem of compressed sensing using binary measurement matrices and 1-norm minimization (basis pursuit) as the recovery algorithm. We derive new upper and lower bounds on the number of measurements to achieve robust sparse recovery with binary matrices. We establish sufficient conditions for a column-regular binary matrix to satisfy the robust null space property (RNSP) and show that the associated sufficient conditions for robust sparse recovery obtained using the RNSP are better by a factor of (3 √ 3)/2 ≈ 2.6 compared to the sufficient conditions obtained using the restricted isometry property (RIP). Next we derive universal lower bounds on the number of measurements that any binary matrix needs to have in order to satisfy the weaker sufficient condition based on the RNSP and show that bipartite graphs of girth six are optimal. Then we display two classes of binary matrices, namely parity check matrices of array codes and Euler squares, which have girth six and are nearly optimal in the sense of almost satisfying the lower bound. In principle, randomly generated Gaussian measurement matrices are "order-optimal." So we compare the phase transition behavior of the basis pursuit formulation using binary array codes and Gaussian matrices and show that (i) there is essentially no difference between the phase transition boundaries in the two cases and (ii) the CPU time of basis pursuit with binary matrices is hundreds of times faster than with Gaussian matrices and the storage requirements are less. Therefore it is suggested that binary matrices are a viable alternative to Gaussian matrices for compressed sensing using basis pursuit.

Compressive sensing refers to the reconstruction of high dimensional but low-complexity objects from relatively few measurements. Examples of such objects include: high dimensional but sparse vectors, large images with very few sharp edges, and high-dimensional matrices of low rank. One of the most popular methods for reconstruction is to solve a suitably constrained \(\ell _1\)-norm minimization problem, otherwise known as basis pursuit (BP). In this approach, a key role is played by the measurement matrix, which converts the high dimensional but sparse vector (for example) into a low-dimensional real-valued measurement vector. The widely used sufficient conditions for guaranteeing that BP recovers the unknown vector are the restricted isometry property (RIP), and the robust null space property (RNSP). It has recently been shown that the RIP implies the RNSP. There are two approaches for generating matrices that satisfy the RIP, namely, probabilistic and deterministic. Probabilisti...