Sparse Signal Representation using Overlapping Frames
نویسنده
چکیده
Signal expansions using frames may be considered as generalizations of signal representations based on transforms and filter banks. Frames for sparse signal representations may be designed using an iterative method with two main steps: (1) Frame vector selection and expansion coefficient determination for signals in a training set, – selected to be representative of the signals for which compact representations are desired, using the frame designed in the previous iteration. (2) Update of frame vectors with the objective of improving the representation of step (1). In this thesis we solve step (2) of the general frame design problem using the compact notation of linear algebra. This makes the solution both conceptually and computationally easy, especially for the non-block-oriented frames, – for short overlapping frames, that may be viewed as generalizations of critically sampled filter banks. Also, the solution is more general than those presented earlier, facilitating the imposition of constraints, such as symmetry, on the designed frame vectors. We also take a closer look at step (1) in the design method. Some of the available vector selection algorithms are reviewed, and adaptations to some of these are given. These adaptations make the algorithms better suited for both the frame design method and the sparse representation of signals problem, both for block-oriented and overlapping frames. The performances of the improved frame design method are shown in extensive experiments. The sparse representation capabilities are illustrated both for one-dimensional and two-dimensional signals, and in both cases the new possibilities in frame design give better results. Also a new method for texture classification, denoted Frame Texture Classification Method (FTCM), is presented. The main idea is that a frame trained for making sparse representations of a certain class of signals is a model for this signal class. The FTCM is applied to nine test images, yielding excellent overall performance, for many test images the number of wrongly classified pixels is more than halved, in comparison to state of the art texture classification methods presented in [59].
منابع مشابه
Speech Enhancement using Adaptive Data-Based Dictionary Learning
In this paper, a speech enhancement method based on sparse representation of data frames has been presented. Speech enhancement is one of the most applicable areas in different signal processing fields. The objective of a speech enhancement system is improvement of either intelligibility or quality of the speech signals. This process is carried out using the speech signal processing techniques ...
متن کاملA Simple Design of Sparse Signal Representations Using Overlapping Frames
The use of frames and matching pursuits for signal representation are receiving increased attention due to their perceived potential in various signal processing applications. Good design algorithms for block oriented frames have recently been published. Viewing these block oriented frames as generalizations of block oriented transforms, it is natural to seek corresponding generalizations of cr...
متن کاملVoice-based Age and Gender Recognition using Training Generative Sparse Model
Abstract: Gender recognition and age detection are important problems in telephone speech processing to investigate the identity of an individual using voice characteristics. In this paper a new gender and age recognition system is introduced based on generative incoherent models learned using sparse non-negative matrix factorization and atom correction post-processing method. Similar to genera...
متن کاملGeneral design algorithm for sparse frame expansions
Signal expansions using frames may be considered as generalizations of signal representations based on transforms and filter banks. Frames, or dictionaries, for sparse signal representations may be designed using an iterative algorithm with two main steps: (1) Frame vector selection and expansion coefficient determination for signals in a training set, selected to be representative of the signa...
متن کاملFrames for compressed sensing using coherence
We give some new results on sparse signal recovery in the presence of noise, for weighted spaces. Traditionally, were used dictionaries that have the norm equal to 1, but, for random dictionaries this condition is rarely satised. Moreover, we give better estimations then the ones given recently by Cai, Wang and Xu.
متن کامل