In this paper, dependence of storage capacity of an analogue associative memory model using nonmonotonic neurons on static synaptic noise and static threshold noise is shown. This dependence is analytically calculated by means of the self-consistent signal-to-noise analysis (SCSNA) proposed by Shiino and Fukai. It is known that the storage capacity of an associative memory model can be improved markedly by replacing the usual sigmoid neurons with nonmonotonic ones, and the Hopfield model has theoretically been shown to be fairly robust against introducing the static synaptic noise. In this paper, it is shown that when the monotonicity of neuron is high, the storage capacity decreases rapidly according to an increase of the static synaptic noise. It is also shown that the reduction of the storage capacity is more sensitive to an increase in the static threshold noise than to the increase in the static synaptic noise.

An associative memory model with a forgetting process a la Mezard et al. is investigated for a piecewise nonmonotonic output function by the SCSNA proposed by Shiino and Fukai. Similar to the formal monotonic two-state model analyzed by Mezard et al. , the discussed nonmonotonic model is also free from a catastrophic deterioration of memory due to overloading. We theoretically obtain a relationship between the storage capacity and the forgetting rate, and find that there is an optimal value of forgetting rate, at which the storage capacity is maximized for the given nonmonotonicity. The maximal storage capacity and capacity ratio (a ratio of the storage capacity for the conventional correlation learning rule to the maximal storage capacity) increase with nonmonotonicity, whereas the optimal forgetting rate decreases with nonmonotonicity.

The main target of compressed sensing is recovery of one-dimensional signals, because signals more than two-dimension can also be treated as one-dimensional ones by raster scan, which makes the sensing matrix huge. This is unavoidable for general sensing processes. In separable cases like discrete Fourier transform (DFT) or standard wavelet transforms, however, the corresponding sensing process can be formulated using two matrices which are multiplied from both sides of the target two-dimensional signals. We propose an approximate message passing (AMP) algorithm for the separable sensing process. Typically, we suppose DFT for the sensing process, in which the measurements are complex numbers. Therefore, the formulation includes cases in which both target signal and measurements are complex. We show the effectiveness of the proposed algorithm by computer simulations.

Shape matching with local descriptors is an underlying scheme in shape analysis. We can visually confirm the matching results and also assess them for shape classification. Generally, shape matching is implemented by determining the correspondence between shapes that are represented by their respective sets of sampled points. Some matching methods have already been proposed; the main difference between them lies in their choice of matching cost function. This function measures the dissimilarity between the local distribution of sampled points around a focusing point of one shape and the local distribution of sampled points around a referring point of another shape. A local descriptor is used to describe the distribution of sampled points around the point of the shape. In this paper, we propose an extended scheme for shape matching that can compensate for errors in existing local descriptors. It is convenient for local descriptors to adopt our scheme because it does not require the local descriptors to be modified. The main idea of our scheme is to consider the correspondence of neighboring sampled points to a focusing point when determining the correspondence of the focusing point. This is useful because it increases the chance of finding a suitable correspondence. However, considering the correspondence of neighboring points causes a problem regarding computational feasibility, because there is a substantial increase in the number of possible correspondences that need to be considered in shape matching. We solve this problem using a branch-and-bound algorithm, for efficient approximation. Using several shape datasets, we demonstrate that our scheme yields a more suitable matching than the conventional scheme that does not consider the correspondence of neighboring sampled points, even though our scheme requires only a small increase in execution time.

The main contribution of this paper is a non-trivial expression, that is called dual expression, of the posterior values for non-adaptive group testing problems. The dual expression is useful for exact bitwise MAP estimation. We assume a simplest non-adaptive group testing scenario including N-objects with binary status and M-tests. If a group contains one or more positive object, the test result for the group is assumed to be one; otherwise, the test result becomes zero. Our inference problem is to evaluate the posterior probabilities of the objects from the observation of M-test results and the prior probabilities for objects. The derivation of the dual expression of posterior values can be naturally described based on a holographic transformation to the normal factor graph (NFG) representing the inference problem. In order to handle OR constraints in the NFG, we introduce a novel holographic transformation that converts an OR function to a function similar to an EQUAL function.

We propose a novel algorithm for the recovery of non-sparse, but compressible signals from linear undersampled measurements. The algorithm proposed in this paper consists of two steps. The first step recovers the signal by the l1-norm minimization. Then, the second step decomposes the l1 reconstruction into major and minor components. By using the major components, measurements for the minor components of the target signal are estimated. The minor components are further estimated using the estimated measurements exploiting a maximum a posterior (MAP) estimation, which leads to a ridge regression with the regularization parameter determined using the error bound for the estimated measurements. After a slight modification to the major components, the final estimate is obtained by combining the two estimates. Computational cost of the proposed algorithm is mostly the same as the l1-nom minimization. Simulation results for one-dimensional computer generated signals show that the proposed algorithm gives 11.8% better results on average than the l1-norm minimization and the lasso estimator. Simulations using standard images also show that the proposed algorithm outperforms those conventional methods.