Ko [26] and Bruschi [11] independently showed that, in some relativized world, PSPACE (in fact, ⊕P) contains a set that is immune to the polynomial hierarchy (PH). In this paper, we study and settle the question of relativized separations with immunity for PH and the counting classes PP, $\mathrm{C}=\mathrm{P}$, and ⊕P in all possible pairwise combinations. Our main result is that there is an oracle A relative to which $\mathrm{C}=\mathrm{P}$ contains a set that is immune BPP⊕P. In particular, this ${\mathrm{C}=\mathrm{P}}^A$ set is immune to PHA and to ⊕PA. Strengthening...

Image denoising is a fundamental problem in image processing operations. In this paper, we present a two-phase scheme for the impulse noise removal. In the first phase, noise candidates are identified by the adaptive median filter (AMF) for salt-and-pepper noise. In the second phase, a new hybrid conjugate gradient method is used to minimize an edge-preserving regularization functional. The second phase of our algorithm inherits advantages of both Dai-Yuan (DY) and Hager-Zhang (HZ) conjugate gradient...