We suggest a new approach to optimize the learning of sparse features under the constraints of explicit transformation symmetries imposed on the set of feature vectors. Given a set of basis feature vectors and invariance transformations, from each basis feature a family of transformed features is generated. We then optimize the basis features for optimal sparse reconstruction of the input patte...

We have developed convolutional sparse coding (CSC) to attenuate noise in seismic data. CSC gives a data-driven set of basis functions whose coefficients form distribution. The attenuation method by can be divided into the training and denoising phases. Seismic data with relatively high signal-to-noise ratio are chosen for get learned functions. Then, we use all (or subset) random or coherent N...

Sparse representation of information provides a powerful means to perform feature extraction on high-dimensional data and is of broad interest for applications in signal processing, computer vision, object recognition and neurobiology. Sparse coding is also believed to be a key mechanism by which biological neural systems can efficiently process a large amount of complex sensory data while cons...