In this monograph, the novel promising trends in adaptive digital processing of multidimensional 1D-3D signals with different applications to radio physics, radio engineering, and medicine are considered. The monograph consists of three parts. The first part (chapters 1-4) is devoted to the atomic functions (AF) and their applications, such as the novel wavelet systems (WA). This part includes the definition of the atomic functions, their properties, possible applications in signal and image processing, and the construction of novel wavelets based on the AF. The synthesis of novel weighting functions (windows) based on the AF and applications of the novel windows are discussed in the next chapters. In chapter 4, the basic principles of the wavelet analysis are considered in detail. Here, the Kotelnikov-Shannon and the Meyer wavelets as well as the wavelets based on the atomic functions are discussed. The second part of the book (chapters 5-9) is devoted to the multidimensional signal enhancement. Models of the image-and-noise and objective-and-subjective criteria are discussed in the fifth chapter. Chapter 6 introduces different types of statistical estimators (M, R, L, and RM) and their properties. Chapter 7 gives a review of the linear and nonlinear filtering techniques. Some commonly used models of multichannel (color) images are presented there. A novel approach of the vectorial order statistics to multichannel and video processing is presented in chapter 8. The vector median ordering and filtering, the adaptive multichannel non-filtering, the Vector Directional filter with a double window, etc. are explained. Elements of fuzzy logics theory and novel filtering techniques, such as 3D ultrasound, 3D vector, and fuzzy 3D vectorial filters, are discussed there. Chapter 9 exposes different implementations of processing techniques on the DSP and FPGA platforms. Some important problems are resolved: applications of the AF and wavelets based on the AF (WA) for compression-windowing in radar systems, compression algorithms for medical applications, and neural-network classification procedures in the mammography analysis. The analysis of the transversal FIR filter structure along with some of its most widely used adaptive algorithms is presented in the tenth chapter. In chapter 11, the fast Fourier transform is used for performing the convolution and correlation required in applications reducing the computational complexity. The adaptive infinite impulse response can provide the computational complexity with a much smaller number of filter coefficients. Some problems such as slow convergence, possible filter instability, and error function with multiple local minima, are discussed in chapter 12. The echo canceling procedures are described in chapter 13. The inter symbol interference reduction applying efficient equalizer algorithms are discussed in the final, fourteenth chapter of this book. The monograph is recommended for scientists, engineers, students, and post-graduates specializing in radio physics, radio engineering, computational mathematics, computational physics, and medicine applications.