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deblatting.py
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deblatting.py
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import numpy as np
from numpy.fft import fft2, ifft2
import scipy.sparse.linalg
from scipy import sparse
from utils import *
from vis import *
class Params:
def __init__(self): ## Parameters with which users can experiment are marked by #!
## universal parameters
self.loop_maxiter = 200 #! max number of (F,M)/H blind loop alternations
self.maxiter = 50 #! max number of outer iterations
self.cg_maxiter = 25 # max number of inner CG iterations ('h' subproblem)
self.cg_tol = 1e-5 # tolerance for relative residual of inner CG iterations
self.rel_tol_h = 9e-3 # relative between iterations difference for outer ADMM loop
self.rel_tol_f = 1e-4 # relative between iterations difference for outer ADMM loop
self.lp = 1 # exponent of the Lp regularizer sum |h|^p or TV |Df|^p, allowed values are 0, 1
self.gamma = 1.0 # data term weight
## parameters for H estimation
self.alpha_h = 1.0 # Lp regularizer weight
self.beta_h = 1e3*self.alpha_h
self.sum1 = True # force sum(H)=1 constraint (via beta_h), takes precedence over lp
self.do_fit = True #! applying psffit
## parameters for F,M estimation
self.alpha_f = 2**(-12) #! F,M total variation regularizer weight, for strong influence use at least 2e-4
self.lambda_T = 1e-3 #! template L2 term weight, influence: 1e-3 soft, 1e-2 strong, 1e-1 very strong
self.lambda_R = 1e-2 #! mask rotation symmetry weight term, lambda_R*|R*m-m|^2 where R is approx rotational averaging, similar values as *_T
self.beta_fm = 1e-3 # splitting vf=f and vm=m due to (F,M) in C constraint where C is prescribed convex set given by positivity and F-M relation, penalty weight
self.beta_f = 10*self.alpha_f # splitting vx/vy=Df due to the TV regularizer
self.pyramid_eps = 1 # inverse slope of the f<=m/eps constraing for each channel. eps=0 means no constraint (only m in [0,1], f>0), eps=1 means f<=m etc
## parameters for sub-frame F,M estimation
self.alpha_cross_f = 2**(-13) #! cross-image (in 3-dim) image TV regularizer weight
self.beta_cross_f = 10*self.alpha_cross_f # splitting vc=D_cross*f due to cross-image TV regularizer
## visualization parameters
self.verbose = True #!
self.do_cost = False #!
self.visualize = True #!
def estimateFMH(I,B,M=None,F=None,Hmask=None,params=None):
## Estimate F,M,H in FMO equation I = H*F + (1 - H*M)B, where * is convolution
if params is None:
params = Params()
if I.shape != B.shape:
raise Exception('Shapes must be equal!')
if M is None:
M = np.ones(I.shape[:2])
if F is None:
F = np.ones((M.shape[0],M.shape[1],I.shape[2]))
if Hmask is None:
Hmask = np.ones(I.shape[:2]).astype(bool)
Hmask_small = Hmask
else: ## speed-up by padding and ROI
pads = np.ceil( (np.array(M.shape)-1)/2 ).astype(int)
rmin, rmax, cmin, cmax = boundingBox(Hmask, pads)
I = I[rmin:rmax,cmin:cmax,:]
B = B[rmin:rmax,cmin:cmax,:]
Hmask_small = Hmask[rmin:rmax,cmin:cmax]
H = np.zeros(I.shape[:2])
params.maxiter = 1
rel_tol2 = params.rel_tol_h**2
stateh = StateH()
statefm = StateFM()
## blind loop, iterate over estimateFM and estimateH
for iter in range(params.loop_maxiter):
H_old = H
H, stateh = estimateH(I, B, M, F, Hmask=Hmask_small, state=stateh, params=params)
F, M, statefm = estimateFM(I, B, H, M, F, state=statefm, params=params)
reldiff2 = np.sum((H_old - H)**2) / np.sum(H**2)
if params.visualize:
imshow_nodestroy(get_visim(H,F,M,I), 600/np.max(I.shape))
if params.verbose:
print("FMH: iter={}, reldiff_h={}".format(iter+1, np.sqrt(reldiff2)))
if reldiff2 < rel_tol2:
break
if params.do_fit:
H = psffit(H)
params.maxiter = 50
F, M = estimateFM(I, B, H, M, F, params=params)
He = np.zeros(Hmask.shape[:2])
He[Hmask] = H[Hmask_small]
return He, F, M
def psffit(H,returnpars=False):
## very simple version of PSF fitting
## there are more sophisticated ways to do it with RANSAC
bH = (H/np.max(H) > 0.4)
x, y = np.nonzero(bH)
res1 = np.polyfit(x, y, 3, full=True)
res2 = np.polyfit(y, x, 3, full=True)
if res2[1].shape[0] == 0 or (res1[1].shape[0] != 0 and res1[1][0] < res2[1][0]):
coeffs = res1[0]
xs = [np.min(x), np.max(x)]
poly1d_fn = np.poly1d(coeffs)
ys = poly1d_fn(xs)
else:
coeffs = res2[0]
ys = [np.min(y), np.max(y)]
poly1d_fn = np.poly1d(coeffs)
xs = poly1d_fn(ys)
pars = np.array([[xs[0], ys[0]], [xs[1]-xs[0], ys[1]-ys[0]]]).T
Hf = renderTraj(pars, np.zeros(H.shape))
Hf /= np.sum(Hf)
if returnpars:
return Hf, pars
return Hf
def estimateFM(I, B, H, M=None, F=None, F_T=None, M_T=None, state=None, params=None):
## Estimate F,M in FMO equation I = H*F + (1 - H*M)B, where * is convolution
## M is suggested to be specified to know approximate object size, at least as am array of zeros, for speed-up
## F_T, M_T - template for F and M
if params is None:
params = Params()
if M is None:
if F is not None:
M = np.zeros(F.shape[:2])
else:
M = np.zeros(I.shape[:2])
if F is None:
F = np.zeros((M.shape[0],M.shape[1],3))
Fshape = F.shape
f = vec3(F)
m = M.flatten('F')
if F_T is not None:
F_T = vec3(F_T)
if M_T is not None:
M_T = M_T.flatten('F')
Me = np.zeros(I.shape[:2])
Fe = np.zeros(I.shape)
idx_f, idy_f, idz_f = psfshift_idx(F.shape, I.shape)
idx_m, idy_m = psfshift_idx(M.shape, I.shape[:2])
## init
Dx = None
if state is not None:
Dx = state.Dx; Dy = state.Dy; DTD = state.DTD; Rn = state.Rn
vx = state.vx; vy = state.vy; ax = state.ax; ay = state.ay
vx_m = state.vx_m; vy_m = state.vy_m; ax_m = state.ax_m; ay_m = state.ay_m
vf = state.vf; af = state.af; vm = state.vm; am = state.am
if Dx is None:
Dx, Dy = createDerivatives0(Fshape)
DTD = (Dx.T @ Dx) + (Dy.T @ Dy)
vx = np.zeros((Dx.shape[0],Fshape[2]))
vy = np.zeros((Dy.shape[0],Fshape[2]))
ay = 0; ax = 0 ## v=Df splitting due to TV and its assoc. Lagr. mult.
vx_m = np.zeros((Dx.shape[0],1))
vy_m = np.zeros((Dy.shape[0],1))
ay_m = 0; ax_m = 0 ## v_m=Dm splitting due to TV (m-part) and its assoc. Lagr. mult.
af = 0; vf = 0 ## vf=f splitting due to positivity and f=0 outside mask constraint
am = 0; vm = 0 ## vm=m splitting due to mask between [0,1]
if params.lambda_R > 0:
RnA = createRnMatrix(Fshape[:2]).A
Rn = RnA.T @ RnA - RnA.T - RnA + np.eye(RnA.shape[0])
Rn = sparse.csc_matrix(Rn)
fH = fft2(H,axes=(0,1)) # precompute FT
HT = np.conj(fH)
HT3 = np.repeat(HT[:, :, np.newaxis], 3, axis=2)
## precompute const RHS for 'f/m' subproblem
rhs_f = np.real(ifft2(HT3*fft2(I-B,axes=(0,1)),axes=(0,1)))
rhs_f = params.gamma*np.reshape(rhs_f[idx_f,idy_f,idz_f], (-1,Fshape[2]),'F')
if params.lambda_T > 0 and F_T is not None:
rhs_f += (params.lambda_T*F_T) ## template matching term lambda_T*|F-F_T|
rhs_m = np.real(ifft2(HT*fft2(np.sum(B*(I-B),2),axes=(0,1)),axes=(0,1)))
rhs_m = -params.gamma*rhs_m[idx_m,idy_m]
if params.lambda_T > 0 and M_T is not None:
rhs_m += (params.lambda_T*M_T) ## template matching term lambda_T*|M-M_T|
beta_tv4 = np.repeat(params.beta_f, Fshape[2]+1)
rel_tol2 = params.rel_tol_f**2
## ADMM loop
for iter in range(params.maxiter):
fdx = Dx @ f; fdy = Dy @ f
mdx = Dx @ m; mdy = Dy @ m
f_old = f; m_old = m
## dual/auxiliary var updates, vx/vy minimization (splitting due to TV regularizer)
if params.alpha_f > 0 and params.beta_f > 0:
val_x = fdx + ax
val_y = fdy + ay
shrink_factor = lp_proximal_mapping(np.sqrt(val_x**2 + val_y**2), params.alpha_f/params.beta_f, params.lp) # isotropic "TV"
vx = val_x*shrink_factor
vy = val_y*shrink_factor
ax = ax + fdx - vx ## 'a' step
ay = ay + fdy - vy
## vx_m/vy_m minimization (splitting due to TV regularizer for the mask)
val_x = mdx + ax_m
val_y = mdy + ay_m
shrink_factor = lp_proximal_mapping(np.sqrt(val_x**2 + val_y**2), params.alpha_f/params.beta_f, params.lp)
vx_m = val_x*shrink_factor
vy_m = val_y*shrink_factor
ax_m = ax_m + mdx - vx_m
ay_m = ay_m + mdy - vy_m
## vf/vm minimization (positivity and and f-m relation so that F is not large where M is small, mostly means F<=M)
if params.beta_fm > 0:
vf = f + af
vm = m + am
if params.pyramid_eps > 0: # (m,f) constrained to convex pyramid-like shape to force f<=const*m where const = 1/eps
vm, vf = project2pyramid(vm, vf, params.pyramid_eps)
else: # just positivity and m in [0,1]
vf[vf < 0] = 0
vm[vm < 0] = 0
vm[vm > 1] = 1
# lagrange multiplier (dual var) update
af = af + f - vf
am = am + m - vm
## F,M step
rhs1 = rhs_f + params.beta_f*(Dx.T @ (vx-ax) + Dy.T @ (vy-ay)) + params.beta_fm*(vf-af) # f-part of RHS
rhs2 = rhs_m + params.beta_f*(Dx.T @ (vx_m-ax_m) + Dy.T @ (vy_m-ay_m)).flatten('F') + params.beta_fm*(vm-am) # m-part of RHS
def estimateFM_cg_Ax(fmfun0):
fmfun = np.reshape(fmfun0, (-1,4),'F')
xf = fmfun[:,:Fshape[2]]
xm = fmfun[:,-1]
Fe[idx_f,idy_f,idz_f] = xf.flatten('F')
Me[idx_m,idy_m] = xm
HF = fH[:,:,np.newaxis]*fft2(Fe,axes=(0,1))
bHM = B*(np.real(ifft2(fH*fft2(Me,axes=(0,1)),axes=(0,1)))[:,:,np.newaxis])
yf = np.real(ifft2(HT3*(HF - fft2(bHM,axes=(0,1))),axes=(0,1)))
yf = params.gamma*np.reshape(yf[idx_f,idy_f,idz_f],(-1,Fshape[2]),'F')
ym = np.real(ifft2(HT*fft2(np.sum(B*(bHM - np.real(ifft2(HF,axes=(0,1)))),2),axes=(0,1)),axes=(0,1)))
ym = params.gamma*ym[idx_m,idy_m]
if params.lambda_T > 0 and F_T is not None:
yf = yf + params.lambda_T*xf
if params.lambda_T > 0 and M_T is not None:
ym = ym + params.lambda_T*xm
if params.lambda_R > 0:
ym = ym + params.lambda_R*(Rn @ xm) # mask regularizers
res = np.c_[yf,ym] + beta_tv4*(DTD @ fmfun) + params.beta_fm*fmfun # common regularizers/identity terms
return res.flatten('F')
A = scipy.sparse.linalg.LinearOperator((4*f.shape[0],4*f.shape[0]), matvec=estimateFM_cg_Ax)
fm, info = scipy.sparse.linalg.cg(A, np.c_[rhs1,rhs2].flatten('F'), np.c_[f,m].flatten('F'), params.cg_tol, params.cg_maxiter)
fm = np.reshape(fm, (-1,4),'F')
f = fm[:, :Fshape[2]]
m = fm[:, -1]
if state is not None:
continue
ff = f.flatten()
df = ff-f_old.flatten()
dm = m-m_old
rel_diff2_f = (df @ df)/(ff @ ff)
rel_diff2_m = (dm @ dm)/(m @ m)
if params.visualize:
f_img = ivec3(f, Fshape); m_img = ivec3(m, Fshape[:2])
imshow_nodestroy(get_visim(H,f_img,m_img,I), 600/np.max(I.shape))
if params.verbose:
if params.do_cost: # not fully implemented for all terms, e.g. lambda_R
Fe[idx_f,idy_f,idz_f] = ff
Me[idx_m,idy_m] = m
err = np.sum(np.reshape(np.real(ifft2(fH[:,:,np.newaxis]*fft2(Fe,axes=(0,1)),axes=(0,1)))-B*np.real(ifft2(fH*fft2(Me)))[:,:,np.newaxis]-(I-B), (-1,1),'F')**2)
cost = (params.gamma/2)*err + params.alpha_f*np.sum(np.sqrt(fdx**2+fdy**2))
cost = cost + params.alpha_f*np.sum(np.sqrt(mdx**2+mdy**2))
if F_T is not None:
cost = cost + params.lambda_T*np.sum((f-F_T)**2)/2
if M_T is not None:
cost = cost + np.sum(params.lambda_T*(m-M_T)**2)/2
print("FM: iter={}, reldiff=({}, {}), err={}, cost={}".format(iter, np.sqrt(rel_diff2_f), np.sqrt(rel_diff2_m),err,cost))
else:
print("FM: iter={}, reldiff=({}, {})".format(iter, np.sqrt(rel_diff2_f), np.sqrt(rel_diff2_m)))
if rel_diff2_f < rel_tol2 and rel_diff2_m < rel_tol2:
break
f_img = ivec3(f, Fshape)
m_img = ivec3(m, Fshape[:2])
if state is None:
return f_img,m_img
else:
state.Dx = Dx; state.Dy = Dy; state.DTD = DTD; state.Rn = Rn
state.vx = vx; state.vy = vy; state.ax = ax; state.ay = ay
state.vx_m = vx_m; state.vy_m = vy_m; state.ax_m = ax_m; state.ay_m = ay_m
state.vf = vf; state.af = af; state.vm = vm; state.am = am
return f_img,m_img,state
def estimateH(I, B, M, F, Hmask=None, state=None, params=None):
## Estimate H in FMO equation I = H*F + (1 - H*M)B, where * is convolution
## Hmask represents a region in which computations are done
if params is None:
params = Params()
if Hmask is None:
Hmask = np.ones(I.shape[:2]).astype(bool)
Hmask_small = Hmask
else: ## speed-up by padding and ROI
if state is None:
pads = np.ceil( (np.array(M.shape)-1)/2 ).astype(int)
rmin, rmax, cmin, cmax = boundingBox(Hmask, pads)
I = I[rmin:rmax,cmin:cmax,:]
B = B[rmin:rmax,cmin:cmax,:]
Hmask_small = Hmask[rmin:rmax,cmin:cmax]
else:
Hmask_small = Hmask
H = None
if state is None:
v_lp = 0 ## init
a_lp = 0
else:
H = state.H
v_lp = state.v_lp
a_lp = state.a_lp
if H is None:
H = np.zeros((np.count_nonzero(Hmask_small),))
hsize = Hmask_small.shape
iF = fft2(psfshift(F, hsize),axes=(0,1))
iM = fft2(psfshift(M, hsize),axes=(0,1))
Fgb = fft2(I-B,axes=(0,1))
Fbgb = fft2(B*(I-B),axes=(0,1))
iM3 = np.repeat(iM[:, :, np.newaxis], 3, axis=2)
## precompute RHS for the 'h' subproblem
rhs_const = np.sum(np.real(ifft2(np.conj(iF)*Fgb-np.conj(iM3)*Fbgb,axes=(0,1))),2)
rhs_const = params.gamma*rhs_const[Hmask_small]
He = np.zeros(hsize)
rel_tol2 = params.rel_tol_h**2
## ADMM loop
for iter in range(params.maxiter):
H_old = H
if params.beta_h > 0: ## also forces positivity
v_lp = H + a_lp
if params.sum1:
v_lp = proj2simplex(v_lp)
elif params.lp == 1:
temp = v_lp < params.alpha_h/params.beta_h
v_lp[temp] = 0
v_lp[~temp] -= (params.alpha_h/params.beta_h)
elif params.lp == 0:
v_lp[v_lp <= np.sqrt(2*params.alpha_h/params.beta_h)] = 0
a_lp = a_lp + H - v_lp
rhs = rhs_const + params.beta_h*(v_lp-a_lp)
def estimateH_cg_Ax(hfun):
He[Hmask_small] = hfun
FH = fft2(He,axes=(0,1))
Fh = iF*np.repeat(FH[:, :, np.newaxis], 3, axis=2) ## apply forward conv (->RGB image, summation over angles)
BMh = B*np.repeat(np.real(ifft2(iM*FH,axes=(0,1)))[:, :, np.newaxis], 3, axis=2)
Fh_BMh = Fh - fft2(BMh,axes=(0,1))
res = np.sum(np.real(ifft2(np.conj(iF)*Fh_BMh - np.conj(iM3)*fft2(B*np.real(ifft2(Fh_BMh,axes=(0,1))),axes=(0,1)),axes=(0,1))),2)
res = params.gamma*res[Hmask_small] + (params.beta_h)*hfun
return res
A = scipy.sparse.linalg.LinearOperator((H.shape[0],H.shape[0]), matvec=estimateH_cg_Ax)
H, info = scipy.sparse.linalg.cg(A, rhs, H, params.cg_tol, params.cg_maxiter)
if state is not None:
continue
Diff = (H - H_old)
rel_diff2 = (Diff @ Diff)/(H @ H)
if params.visualize:
imshow_nodestroy(get_visim(He,F,M,I), 600/np.max(I.shape))
if params.verbose:
if params.do_cost:
FH = fft2(He,axes=(0,1))
FH3 = np.repeat(FH[:, :, np.newaxis], 3, axis=2)
Fh = iF*FH3
BMh = B*np.real(ifft2(iM3*FH3,axes=(0,1)));
err = np.sum((np.real(ifft2(Fh,axes=(0,1)))-BMh-(I-B))**2)
cost = params.gamma/2*err + params.alpha_h*np.sum(np.abs(H)**params.lp)
print("H: iter={}, reldiff={}, err={}, cost={}".format(iter, np.sqrt(rel_diff2), err, cost))
else:
print("H: iter={}, reldiff={}".format(iter, np.sqrt(rel_diff2)))
if rel_diff2 < rel_tol2:
break
oHe = np.zeros(Hmask.shape)
oHe[Hmask] = H
if state is None:
return oHe
else:
state.a_lp = a_lp
state.v_lp = v_lp
state.H = H
return oHe, state
def createDerivatives0(sz):
N_in = sz[0] * sz[1]
N_out = (sz[0]+1) * (sz[1]+1)
idx_in = np.reshape( range(N_in), sz[:2],'F')
idx_out = np.reshape( range(N_out), np.array(sz[:2])+1,'F')
## x direction
v1 = np.ones((sz[0], sz[1]-1))
v2 = np.ones((sz[0],1))
inds = idx_out[:-1,np.r_[:(idx_out.shape[1]-1), 1:idx_out.shape[1]]]
index = idx_in[:, np.r_[0,:(idx_in.shape[1]-1), 1:idx_in.shape[1], idx_in.shape[1]-1] ]
values = np.hstack((v2,-v1,v1,-v2))
Dx = sparse.csc_matrix((values.flatten('F'),(inds.flatten('F'),index.flatten('F'))), shape=(N_out, N_in))
## y direction
v1 = np.ones((sz[0]-1, sz[1]))
v2 = np.ones((1,sz[1]))
inds = idx_out[np.r_[:(idx_out.shape[0]-1), 1:idx_out.shape[0]], :-1]
index = idx_in[np.r_[0,:(idx_in.shape[0]-1), 1:idx_in.shape[0], idx_in.shape[0]-1],:]
values = np.vstack((v2,-v1,v1,-v2))
Dy = sparse.csc_matrix((values.flatten('F'),(inds.flatten('F'),index.flatten('F'))), shape=(N_out, N_in))
return Dx, Dy
def createRnMatrix(img_sz, angles=None):
if angles is None:
angles = np.array([16, 25, 78, 152])/180*np.pi # selected set of angles
img_sz = np.array(img_sz[:2])
idx2, idx1 = np.meshgrid(range(img_sz[1]), range(img_sz[0]))
offset = (img_sz + 1)/2 # offset between indices and coordinates
idx = np.c_[idx1.T.flatten('F')+1, idx2.T.flatten('F')+1] - offset
idx_out = np.zeros((0,)).astype(int)
idx_in = np.zeros((0,)).astype(int)
for ki in range(len(angles)): # no antialiasing, NN 'interpolation'
ca = np.cos(angles[ki])
sa = np.sin(angles[ki])
R = np.array([[ca, -sa], [sa, ca]]) # rotates by angle; R.' rotates by -angle
res = np.round(idx @ R + offset).astype(int) # input indices (rotated)
keep = np.all(np.logical_and(res >= 1, res <= img_sz),1) # crop to image dimensions
idx_out = np.r_[idx_out, np.nonzero(keep)[0]] # recalculate to linear indices
res -= 1
idx_in = np.r_[idx_in, res[keep,0]*img_sz[0] + res[keep,1] ]
values = np.repeat(1/len(angles),idx_in.shape[0])
R = sparse.csc_matrix((values,(idx_out,idx_in)), shape=(np.prod(img_sz), np.prod(img_sz)))
temp = np.sum(R,1)
ww = np.nonzero(temp > 0)[0]
R[ww,:] = R[ww,:] / temp[ww] # averaging
return R
def project2pyramid(m, f, eps):
## projection of (m,f) values to feasible "pyramid"-like intersection of convex sets (roughly all positive, m<=1, m>=f)
maxiter = 10 # number of whole cycles, 0=only positivity
onedimm = False
if len(m.shape) == 1:
onedimm = True
m = m[:,np.newaxis]
mf = np.concatenate((m,f),1)
N = mf.shape[1] # number of conv sets
Z = np.zeros((mf.shape[0],mf.shape[1],N)) # auxiliary vars (sth like projection residuals)
normal = np.array([-1,eps]) / np.sqrt(1 + eps**2) # dividing plane normal vector (for projection to oblique planes)
for iter in range(N*maxiter+1): # always end with projection to the first set
mf_old = mf
idx = np.mod(iter,N) # set index
if idx == 0: # projection to f>0, 0<m<1
mf += Z[:,:,0]
mf[mf < 0] = 0 # f,m > 0
mf[mf[:,0] > 1,0] = 1 # m < 1
else: # one of the oblique sets
mf += Z[:,:,idx]
W = mf[:,idx]*eps > mf[:,0] # points outside of C_idx
proj = (np.c_[mf[W,0],mf[W,idx]] @ normal) # projection to normal direction
mf[W,0] -= (normal[0] * proj)
mf[W,idx] -= (normal[1] * proj)
Z[:,:,idx] = mf_old + Z[:,:,idx] - mf # auxiliaries
if onedimm:
m = mf[:,0]
else:
m = mf[:,:1]
f = mf[:,1:]
return m, f
def lp_proximal_mapping(val_norm, amount, p):
## helper function for vector version of soft thresholding for l1 (lp) minimization
shrink_factor = np.zeros(val_norm.shape)
if p == 1: ## soft thresholding
nz = (val_norm > amount)
shrink_factor[nz] = (val_norm[nz]-amount) / val_norm[nz]
elif p == 1/2: # see eg "Computing the proximity operator of the lp norm..., Chen et al, IET Signal processing, 2016"
nz = val_norm > 3/2*(val_norm)**(2/3)
shrink_factor[nz] = (2/3*val_norm[nz]*(1+np.cos(2/3*np.acos(-3**(3/2)/4*amount*val_norm[nz]**(-3/2)))))/(val_norm[nz])
else:
raise Exception('not implemented!')
return shrink_factor
def proj2simplex(Y):
## euclidean projection of y (arbitrarily shaped but treated as a single vector) to a simplex defined as x>=0 and sum(x(:)) = 1
## based on "Projection onto the probability simplex: An efficient algorithm with a simple proof, and an application"; Weiran Wang et al; 2013 (arXiv:1309.1541)
Yf = Y.flatten('F')
X = -np.sort(-Yf) ## descend sort
temp = (np.cumsum(X)-1)/np.array(range(1,len(X)+1))
X = np.reshape(Yf - temp[np.nonzero(X > temp)[0][-1]], Y.shape,'F')
X[X < 0] = 0
return X
def psfshift(H, usize):
## PSFSHIFT Moves PSF center to origin and extends the PSF to be the same size as image (for use with FT). ipsfshift does the reverse.
hsize = H.shape
usize = usize[:2]
if len(hsize) > 3:
Hp = np.zeros((usize[0],usize[1],hsize[2],hsize[3]))
Hp[:hsize[0],:hsize[1],:,:] = H ## pad zeros
elif len(hsize) > 2:
Hp = np.zeros((usize[0],usize[1],hsize[2]))
Hp[:hsize[0],:hsize[1],:] = H ## pad zeros
else:
Hp = np.zeros((usize[0],usize[1]))
Hp[:hsize[0],:hsize[1]] = H ## pad zeros
shift = tuple((-np.ceil( (np.array(hsize[:2])+1)/2 )+1).astype(int))
Hr = np.roll(Hp, shift, axis=(0,1))
return Hr
def ipsfshift(H, hsize):
## IPSFSHIFT Performs the inverse of 'psfshift' + crops PSF to desired size.
shift = tuple((np.ceil((np.array(hsize[:2])+1)/2) - 1).astype(int))
Hr = np.roll(H, shift, axis=(0,1))
Hc = Hr[:hsize[0], :hsize[1], :]
return Hc
def psfshift_idx(small, sz_large):
## variant of psfshift intended for repeated use in a loop (subsequent calls are faster)
## determines index pairing between 'small' and 'large' images, i.e. if large = psfshift(small, sz_large) then large[idx,idy] = small[mask_small]
if type(small) == tuple: ## it is shape
temp = np.reshape(np.array(range(1, np.prod(small)+1)), small,'F').astype(int)
else: ## it is array
temp = np.zeros(small.shape).astype(int)
temp[small] = np.array(range(1, np.count_nonzero(small)+1))
temp = psfshift(temp, sz_large).astype(int)
if len(temp.shape) == 2:
idx,idy = np.nonzero(temp)
temp_idx = temp[idx,idy]
pos = np.zeros(temp_idx.shape).astype(int)
pos[temp_idx-1] = range(len(temp_idx))
idx = idx[pos]
idy = idy[pos]
return idx, idy
elif len(temp.shape) == 3:
idx,idy,idz = np.nonzero(temp)
temp_idx = temp[idx,idy,idz]
pos = np.zeros(temp_idx.shape).astype(int)
pos[temp_idx-1] = range(len(temp_idx))
idx = idx[pos]
idy = idy[pos]
idz = idz[pos]
return idx, idy, idz
elif len(temp.shape) == 4:
idx,idy,idz,idf = np.nonzero(temp)
temp_idx = temp[idx,idy,idz,idf]
pos = np.zeros(temp_idx.shape).astype(int)
pos[temp_idx-1] = range(len(temp_idx))
idx = idx[pos]
idy = idy[pos]
idz = idz[pos]
idf = idf[pos]
return idx, idy, idz, idf
def vec3(I):
return np.reshape(I, (I.shape[0]*I.shape[1], -1),'F')
def ivec3(I, ishape):
return np.reshape(I, ishape,'F')
class StateH:
def __init__(self):
self.H = None
self.a_lp = 0
self.v_lp = 0
self.rgnA = 0
self.device = None
class StateFM:
def __init__(self):
self.vx = 0
self.vy = 0
self.ax = 0
self.ay = 0
self.vx_m = 0
self.vy_m = 0
self.ax_m = 0
self.ay_m = 0
self.vf = 0
self.af = 0
self.vm = 0
self.am = 0
self.Dx = None
self.Dy = None
self.DTD = None
self.Rn = None
## for piece-wise
self.vc = 0
self.ac = 0
self.vc_m = 0
self.ac_m = 0
self.Mask4 = None
self.device = None