Multiscale directional transforms based on cosine-sine modulated filter banks for sparse directional image representation

This paper proposes multiscale directional transforms (MDTs) based on cosine-sine modulated filter banks (CSMFBs). Sparse image representation by directional transforms is necessary for image analysis and processing tasks and has been extensively studied. Conventionally, cosine-sine modulated filter banks (CSMFBs) have been proposed as one of separable directional transforms (SepDTs). Their computational cost is much lower than non-SepDTs, and they can work better than other SepDTs, e.g., dual-tree complex wavelet transforms (DTCWTs) in image processing applications. One drawback of CSMFBs is a lack of multiscale directional selectivity, i.e., it cannot provide multiple scale directional atoms as in the DTCWT frame, and thus flexible image representation cannot be achieved. In this work, we show a design method of multiscale CSMFBs by extending modulated lapped transforms, which are a subclass of CSMFBs. We confirm its effectiveness in nonlinear approximation and image denoising as a practical application.