This paper proposes an extension of total variation (TV) image deconvolution technique that enhances image quality over classical TV while preserving algorithm speed. Enhancement is achieved by altering the regularization term to include directional decompositions before the gradient operator. Such decompositions select areas of the image with characteristics that are more suitable for a certain type of gradient than another. Speed is guaranteed by the use of the augmented Lagrangian approach as basis for the algorithm. Experimental evidence that the proposed approach improves TV deconvolution is provided, as well as an outline for a future work aiming to support and substantiate the proposed method.

This paper studies the issue of which filters should be used for feature point detection. Classical feature point detection methods, e.g., SIFT, are based on the scale-space theory in which Gaussian filters are proven to be optimal under the scale-space axiom. However, the recent method SURF demonstrates empirically that a box filter can also achieve good performance even though it violates the scale-space axiom. This leads to the question: Is Gaussian filters necessary for feature point detection? Based on the analysis using filter bank and detection theory, we show that theoretically it is possible for a box filter to perform better than the Gaussian filter. Additionally, we show that a new filter, pyramid filter, performs better than both box and Gaussian filters in some situations.

This paper addresses the problem of two-layer out-of-focus blur removal from a single image, in which either the foreground or the background is in focus while the other is out of focus. To recover details from the blurry parts, the existing blind deconvolution algorithms are insufficient as the problem is spatially variant. The proposed method exploits the invariant structure of the problem by first predicting the occluded background. Then a blind deconvolution algorithm is applied to estimate the blur kernel and a coarse estimate of the image is found as a side product. Finally, the blurred region is recovered using total variation minimization, and fused with the sharp region to produce the final deblurred image.