We propose a deep convolutional neural network architecture codenamed Inception that achieves the new state of the art for classification and detection in the ImageNet Large-Scale Visual Recognition Challenge 2014 (ILSVRC14). The main hallmark of this architecture is the improved utilization of the computing resources inside the network. By a carefully crafted design, we increased the depth and width of the network while keeping the computational budget constant. To optimize quality, the architectural decisions were based on the Hebbian principle and the intuition of multi-scale processing. One particular incarnation used in our submission for ILSVRC14 is called GoogLeNet, a 22 layers deep network, the quality of which is assessed in the context of classification and detection.

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Going deeper with convolutions

There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

计量经济分析 = Econometric analysis

We propose to generate a library of median pyramidal decompositions organized as a tree. It is shown that the best decomposition on this tree can be chosen using the techniques developed in wavelet theory. Based on the tree of decompositions, a denoising algorithm is introduced. Numerical simulations have shown that the proposed algorithm is more effective for signal denoising than the method based on the traditional median pyramidal transform.

A tree of median pyramidal decompositions with an application to signal denoising

This paper is devoted to the theoretical analysis of the fitness function in genetic algorithms using wavelet packet (WP) transforms. More specifically, WP transforms are used to calculate the average fitness value of a schema. Based on this one can decide whether a certain function is easy or hard for a genetic algorithm. The result is an extension of Bethke's (1980) work who discovered an efficient method for calculating schema average fitness values using the Walsh transform.

Wavelet packets and genetic algorithms

Impulsive noise filtering is an important problem of image processing. The problem of noise elimination is closely connected with the problem of maximal preservation of image edges. The requirement of maximal preservation of edges is especially important for images corrupted by impulsive noise with a low corruption rate. To avoid smoothing of the image during filtering, all noisy pixels must be detected. Then only these detected pixels must be corrected. We present in this paper two solutions to the edge preservation problem. The first one is an impulse detector. This detector is based on a comparison of signal samples within a narrow rank window. It is quite efficient for precise detection of impulses in images corrupted by impulsive noise with a low corruption rate. The second solution is based on threshold Boolean filtering, when the binary slices of an image, obtained by the threshold decomposition, are processed by original Boolean functions.

Effective detection and elimination of impulsive noise with a minimal image smoothing

This paper studies the problem of full reference visual quality assessment of denoised images with a special emphasis on images with low contrast and noise-like texture. Denoising of such images together with noise removal often results in image details loss or smoothing. A new test image database, FLT, containing 75 noise-free "reference" images and 300 filtered ("distorted") images is developed. Each reference image, corrupted by an additive white Gaussian noise, is denoised by the BM3D filter with four different values of threshold parameter (four levels of noise suppression). After carrying out a perceptual quality assessment of distorted images, the mean opinion scores (MOS) are obtained and compared with the values of known full reference quality metrics. As a result, the Spearman Rank Order Correlation Coefficient (SROCC) between PSNR values and MOS has a value close to zero, and SROCC between values of known full-reference image visual quality metrics and MOS does not exceed 0.82 (which is reached by a new visual quality metric proposed in this paper). The FLT dataset is more complex than earlier datasets used for assessment of visual quality for image denoising. Thus, it can be effectively used to design new image visual quality metrics for image denoising.

Statistical evaluation of visual quality metrics for image denoising

The Hadamard transform of Sylvester's type, which is also known as the Walsh-Hadamard transform, is widely used in signal processing and communication. Note that the Walsh-Hadamard transform operates only with vectors whose length AT is a power of 2. If N is not a power of two, then in order to compute the Walsh-Hadamard spectrum of the vector one has to either discard components or pad zeros up to the next power of two. In the first case we have an information loss and in the second case extra computations are needed. Thus, construction of fast Hadamard transforms of different orders is important problem. In this paper we develop fast Hadamard transforms based on special classes of Hadamard matrices, namely, the Williamson type Hadamard matrices.

Karen Egiazarian

Papers

A tree of median pyramidal decompositions with an application to signal denoising

Wavelet packets and genetic algorithms

Effective detection and elimination of impulsive noise with a minimal image smoothing

Statistical evaluation of visual quality metrics for image denoising

On fast hadamard transforms of Williamson type