Sharif Digital Repository

Feature coding has received great attention in recent years as a building block of many image processing algorithms. In particular, the importance of the locality assumption in coding approaches has been studied in many previous works. We review this assumption and claim that using the similarity of data points to a more global set of anchor points does not necessarily weaken the coding method, as long as the underlying structure of the anchor points is considered. We propose to capture the underlying structure by assuming a random walker over the anchor points. We also show that our method is a fast approximation to the diffusion map kernel. Experiments on various data sets show that with a... 

This paper studies detecting matrices in random dense and sparse Code Division Multiple Access (CDMA) systems. Detecting matrices were originally introduced in the coin weighing problem. Such matrices can be used in CDMA systems in over-loaded scheme where the number of users is greater than the number of chips. We drive some conditions in the large system limit for binary and bipolar random CDMA systems to ensure that any random matrix is a detecting matrix. Furthermore, we extend our results to sparse random ternary matrices that have been using in the sparse CDMA literature. Finally, a construction method for the sparse detecting matrices is introduced  

In this work we present a sparse dictionary learning method, specifically tuned to solve the tracking problem. Recently, sparse representation has drawn much attention because of its genuineness and strong mathematical background. In this paper we present an online method for dictionary learning which is desirable for problems such as tracking. Online learning methods are preferable because the whole data are not available at the current time. The presented method tries to use the advantages of the generative and discriminative models to achieve better performance. The experimental results show our method can overcome many tracking challenges  

In this paper, an algorithm for ECG denoising and compression based on a sparse separable 2-dimensional transform for both complete and overcomplete dictionaries is studied. For overcomplete dictionary we have used the combination of two complete dictionaries. The experimental results obtained by the algorithm for both complete and overcomplete transforms are compared to soft thresholding (for denoising) and wavelet db9/7 (for compression). It is experimentally shown that the algorithm outperforms soft thresholding for about 4dB or more and also outperforms Extended Kalman Smoother filtering for about 2dB in higher input SNRs. The idea of the algorithm is also studied for ECG compression,... 

The purpose of dictionary learning problem is to learn a dictionary D from a training data matrix Y such that Y ≈ DX and the coefficient matrix X is sparse. Many algorithms have been introduced to this aim, which minimize the representation error subject to a sparseness constraint on X. However, the dictionary learning problem is non-convex with respect to the pair (D,X). In a previous work [Sadeghi et al., 2013], a convex approximation to the non-convex term DX has been introduced which makes the whole DL problem convex. This approach can be almost applied to any existing DL algorithm and obtain better algorithms. In the current paper, it is shown that a simple modification on that approach... 

In this paper, we prove the existence of capacity achieving linear codes with random binary sparse generating matrices over the Binary Symmetric Channel (BSC). The results on the existence of capacity achieving linear codes in the literature are limited to the random binary codes with equal probability generating matrix elements and sparse parity-check matrices. Moreover, the codes with sparse generating matrices reported in the literature are not proved to be capacity achieving for channels other than Binary Erasure Channel. As opposed to the existing results in the literature, which are based on optimal maximum a posteriori decoders, the proposed approach is based on a different decoder... 

In this paper, we consider sparse decomposition (SD) of two-dimensional (2D) signals on overcomplete dictionaries with separable atoms. Although, this problem can be solved by converting it to the SD of one-dimensional (1D) signals, this approach requires a tremendous amount of memory and computational cost. Moreover, the uniqueness constraint obtained by this approach is too restricted. Then in the paper, we present an algorithm to be used directly for sparse decomposition of 2D signals on dictionaries with separable atoms. Moreover, we will state another uniqueness constraint for this class of decomposition. Our algorithm is obtained by modifying the Smoothed L0 (SL0) algorithm, and hence... 

In dictionary learning, a desirable property for the dictionary is to be of low mutual and average coherences. Mutual coherence is defined as the maximum absolute correlation between distinct atoms of the dictionary, whereas the average coherence is a measure of the average correlations. In this paper, we consider a dictionary learning problem regularized with the average coherence and constrained by an upper-bound on the mutual coherence of the dictionary. Our main contribution is then to propose an algorithm for solving the resulting problem based on convexly approximating the cost function over the dictionary. Experimental results demonstrate that the proposed approach has higher... 

This paper introduces a novel coding scheme based on the diffusion map framework. The idea is to run a t-step random walk on the data graph to capture the similarity of a data point to the codebook atoms. By doing this we exploit local similarities extracted from the data structure to obtain a global similarity which takes into account the nonlinear structure of the data. Unlike the locality-based and sparse coding methods, the proposed coding varies smoothly with respect to the underlying manifold. We extend the above transductive approach to an inductive variant which is of great interest for large scale datasets. We also present a method for codebook generation by coarse graining the data... 

Image registration is a basic task in medical image processing applications like group analysis and atlas construction. Similarity measure is a critical ingredient of image registration. Intensity distortion of medical images is not considered in most previous similarity measures. Therefore, in the presence of bias field distortions, they do not generate an acceptable registration. In this paper, we propose a sparse based similarity measure for mono-modal images that considers non-stationary intensity and spatially-varying distortions. The main idea behind this measure is that the aligned image is constructed by an analysis dictionary trained using the image patches. For this purpose, we use...