In this paper, we investigate the convergence speed of the Arimoto-Blahut algorithm. For many channel matrices, the convergence speed is exponential, but for some channel matrices it is slower than exponential. By analyzing the Taylor expansion of the defining function of the Arimoto-Blahut algorithm, we will make the conditions clear for the exponential or slower convergence. The analysis of the slow convergence in this paper is new. Based on this analysis, we will compare the convergence speeds of the Arimoto-Blahut algorithm numerically with the values obtained in our theorems for several channel matrices. The purpose of this paper is to obtain a complete understanding of the convergence speed of the Arimoto-Blahut algorithm.

In this paper, we investigate the convergence speed of the Arimoto algorithm. By analyzing the Taylor expansion of the defining function of the Arimoto algorithm, we will clarify the conditions for the exponential or 1=N order convergence and calculate the convergence speed. We show that the convergence speed of the 1=N order is evaluated by the derivatives of the Kullback-Leibler divergence with respect to the input probabilities. The analysis for the convergence of the 1=N order is new in this paper. Based on the analysis, we will compare the convergence speed of the Arimoto algorithm with the theoretical values obtained in our theorems.

In this paper, an effective implementation of the allpass-based orthonormal symmetric wavelets is proposed for image compression. Since the orthonormal symmetric wavelets are used, it can be expected to get better compression performance than biorthogonal wavelets. Firstly, the implementation of irreversible real-to-real wavelets is presented and its decomposition process is shown by using allpass filters. Then, the realization of the reversible integer-to-integer wavelets is given by utilizing the invertible implementation of allpass filters. Finally, the coding performance of the orthonormal symmetric wavelets is evaluated and compared with the D-9/7 and D-5/3 wavelets. It is shown from the experimental results that the allpass-based orthonormal symmetric wavelets can achieve better compression performance than the D-9/7 and D-5/3 wavelets.

The lifting scheme is well-known to be an efficient tool for constructing second generation wavelets and is often used to design a class of biorthogonal wavelet filter banks. For its efficiency, the lifting implementation has been also adopted in the international standard JPEG2000. It is known that the orthogonality of wavelets is an important property for many applications. This paper presents how to implement two band IIR orthogonal wavelet filter banks according to the lifting scheme. It is shown that a class of IIR orthogonal wavelet filter banks can be realized by using allpass filters in the lifting steps. Thus, the proposed filter banks have approximate linear phase responses. Finally, the proposed IIR orthogonal wavelet filter banks are applied to image lossless compression and the coding performance is investigated.

An explicit study of min-wise independent permutation families, together with their variants --- k-restricted, approximate, etc. --- was initiated by Broder, et al[4]. In this paper, we give a lower bound for the size of k-restricted min-wise independent permutation family. A family F of permutations on [0,n-1]=(0,1,...,n-1) is said to be k-restricted min-wise independent if for any subset X ⊆ [0,n-1] with |X| ≤ k and any x ∈ X, Pr[min(π(X))=π(x)] = 1/|X|, when π is randomly chosen from F according to a probability distribution D on the family F. For the minimum size of a family of k-restricted min-wise independent permutations, upper bounds of O(nk) for any fixed k have been shown for uniform and biased probability distributions on F. We show that if a family F of permutations on [0,n-1] is k-restricted min-wise independent, then |F| ≥ m(n-1,k-1), where m(n,d) = ∑i=0d/2(ni) if d is even; m(n,d)= ∑i=0(d-1)/2(ni) + (n-1(d-1)/2) otherwise. The lower bound for the size of F still holds when we allow an arbitrary probability distribution on F. Our proof technique is based on linear algebra methods, and can be regarded as a generalization of the result by Alon, Babai, and Itai[1], i.e., if random variables X1,X2,...,Xn: Ω → (0,1) are k-wise independent and Pr[Xi=1] = pi is neither 0 nor 1, then |Ω| ≥ m(n,k). By applying our proof technique, we also derive lower bounds for the sample size of the related notions, e.g., k-wise symmetrically independent distributions, k-rankwise independent permutation families, etc.

In this paper, the observation technique on the micro environments with a real-time virtual reality camera system, which is constructed with a dynamic focusing lens and a smart vision sensor using the "depth from focus" criteria, is discussed. However, one drawback opt the all-in-focus image is that there is no information about the depth of objects. Then, it is also important to reconstruct a micro 3D environment in real-time to actuate objects in the micro virtual environments. Important factors to realize real-time system with the "depth from focus" criteria, which can obtain the all in-focus image and micro 3D reconstruction, simultaneously, are discussed. Finally, the real-time system is constructed by a dynamic focusing lens, which can change the focus in high frequency, and a smart vision system which is capable in capturing and processing the image data in high speed with SIMD architecture.

In this paper, a real-time observation technique for the tele-micro-operation has been proposed with a dynamic focusing lens and a smart vision sensor using the "depth from focus" criteria. On the operation of micro objects, such as the microsurgery, DNA operation and etc., the small depth of a focus on the microscope makes bad observability. For example, if the focus is on the object, the actuator could not be seen with the microscope. On the other hand, if the focus is on the actuator, the object could not be observed. The "all-in-focus image" is useful to observe the micro environments with the microscope. However, one drawback on the all-in-focus image is that there is no information about the depth of objects. It is also important to reconstruct the micro 3D environments, in real-time to actuate the micro objects in the micro virtual environments. This paper discusses, firstly, the criteria of "depth from focus" to achieve the all-in-focus image and the micro 3D environments' reconstruction, simultaneously. Then, a real-time VR micro camera system has been proposed to achieve the micro VR environments with the "depth from focus" criteria, i.e. the combination of the all-in-focus image and the micro 3D construction. This system is constructed with a dynamic focusing lens, which could change the focal distance of lens in high frequency, and a smart vision system, which is capable in capturing and processing the image data in high speed with SIMD architecture.