# Haar Wavelet-Based Classification Method for Visual Information Processing Systems
## 1 Introduction  
The application field of visual information processing systems and/or non-stationary periodic signals is actively expanding at present [1; 2; 3; 4; 5]. For example, such systems are in demand in technical diagnostics, in quality management, in traffic control, in many military fields, in fields related to decision support in medicine, security, and so on. Visual information processing in such systems investigates physical processes and phenomena that are unambiguously described by random signals or images. In particular, this applies to the tasks of remote parameter control of stationary and moving control objects [3], as well as the remote sensing and tracking of objects in different backgrounds [4], object counting, and product manufacturing control [5]. The modern approach to the creation of such systems involves extensive use of computer information technology (IT). The implementation of such an approach involvesadaptation to a specific application of existing IT. Such an adaptation is based on a pragmatic approach; that is, an effort to achieve the goal with the minimum values of the procedures parameters sufficient to make the right decision. An important computational procedure in the above systems is the classification procedure [6]. The development of actual IT often requires training the classifier on new datasets. Such datasets may have a small volume; clusters of data may overlap in the feature space [2; 6; 7]. In addition, when a system is functioning, the data for classification may be distorted in shape (scale, shift, rotation) and with an increased level of noise due to changes in capture conditions [1; 2; 4; 5]. In such a situation, the quality and/or efficiency of decisions made in the system may decrease [4]. However, increasing the dataset for training the classifier by measurements (e.g., when researching new drug methods in medicine, security methods in military applications, etc.) can reduce the speed of training such systems. Increasing the set of images and/or signals under study based on known augmentation methods [8; 9] with unknown parameters of noise distribution laws and/or shape distortions may not acheive the required values of quality and efficiency of such systems within the limits of acceptable resource intensity. In such cases, it is necessary to choose a classification method and its parameters. However, when making such a choice for a particular applied task, it is often difficult to implement a systematic pragmatic approach, taking into account the information sufficiency. Such an approach, as a rule, requires a quantitative assessment of the effectiveness and/or quality of the investigated classifiers variants. For most classification methods, the implementation of such an approach requires a large number of experiments, i.e., up to a complete enumeration of parameter variants. Classification training enables us to calculate the coefficients that determine the shape of the surfaces and separate classes in the feature space. Tasks traditionally solved in the system (pattern recognition, clustering, and finding informative features) often differ in the fact that their solution algorithms contain objective functions defined implicitly by measuring their parameters. The classification problem also belongs to this category of problems. Classifier training is often complicated by the high level of noise in the training sample data. The quality functional is not explicitly known and may have a multi-extremal surface (this is due to the complex shape of clusters) and be noisy, especially when the analysis is performed on small datasets. The existing classification methods in systems for visual information processing are usually based on optimization techniques, determining the direction of search for an extremum of the objective function using the first derivative. Such methods include the following: steepest descent, gradient, Gauss-Seidel, Rosenbrock, Powell, and Southwell [10].