{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 1D Deconvolution with wavelets\n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "import pywt\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from context import samplers as samplers,utils\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Display $f =\\Phi u + w$ where $u$ is a piecewise constant signal, $\\Phi$ is a convolution operator, and $s$ is some random Gaussian noise.\n", "\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from skimage.util import random_noise\n", "import matplotlib.pyplot as plt\n", "from numpy.fft import fft, ifft\n", "\n", "p=1024 #signal length\n", "\n", "#define convolution operator\n", "s = 8\n", "h = utils.GaussianFilter(s,p)\n", "Phi = lambda x: np.real(ifft(fft(x)*fft(h))); \n", "Phi_s = lambda x: np.real(ifft(fft(x)*np.conjugate(fft(h))))\n", "\n", "\n", "#measurements\n", "t = np.linspace(-2.5, 2.5, p)\n", "x0 = np.piecewise(t, [t < -1.5, t >= 0,t>1], [-2, 4,-2])\n", "b = Phi(x0)\n", "\n", "# add noise\n", "sigma = .1;\n", "b = random_noise(b,mode='gaussian',var=sigma,clip=False)\n", "\n", "plt.plot(Phi_s(b))\n", "plt.show()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will consider the regularisation\n", "$$\n", "R_\\alpha(f) := \\mathrm{argmin}_u \\frac12 \\| \\Phi u - f\\|^2 + \\alpha\\|D W u\\|_1\n", "$$\n", "where $W$ is the discrete wavelet transform and $D$ is a diagonal matrix (giving higher weights to wavelets of higher frequency). Note that since $W^* = W^{-1}$, we can rewrite this as $R_\\alpha(f) = W^* D^{-1} z_\\alpha$ where\n", "$$\n", "z_\\alpha := \\mathrm{argmin}_z \\frac12 \\| A z - f\\|^2 + \\alpha\\|z\\|_1.\n", "$$\n", "where $A:= \\Phi\\circ W^* D^{-1}$.\n" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [], "source": [ "#define the operator A\n", "lev = int(np.log2(p))-1\n", "py_W, py_Ws, scaling_vec = utils.getWaveletTransforms(p,wavelet_type = \"haar\",level = lev,weight=.7)\n", "\n", "# A = Phi o W^{-1}\n", "A = lambda coeffs: Phi(py_Ws(scaling_vec*coeffs))\n", "\n", "# adjoint operator A^* = W o Phi \n", "As = lambda x: scaling_vec*py_W(Phi_s(x))\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute the MAP using FISTA" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Run FISTA\n", "prox = lambda x, tau: np.maximum(np.abs(x)-tau, np.zeros_like(x))*np.sign(x)\n", "\n", "lam = .2\n", "mfunc = lambda x: .5* np.linalg.norm(A(x)-b)**2 + lam*np.linalg.norm(x,ord=1)\n", "dG = lambda x: As(A(x) - b)\n", "proxF = lambda x,tau: prox(x,tau*lam)\n", "\n", "tau = 1\n", "nIter =1000\n", "xinit = As(b)\n", "x_mode,fval = utils.rFISTA(proxF, dG, tau, xinit,nIter,mfunc)\n", "plt.plot(x0,label='x0')\n", "\n", "plt.plot(Phi_s(b),label='observed')\n", "plt.plot(py_Ws(scaling_vec*x_mode),'k--',label='MAP')\n", "\n", "plt.legend()\n", "plt.show()\n", "\n", "plt.semilogy(fval-min(fval))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Run proximal langevin and Hadamard langevin" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "stepsize 0.01\n", "Running prox-l1 sampler ...\n", "\n" ] } ], "source": [ "#defined the gradient of Moreau-envelope of the density\n", "def soft(x,tau): \n", " return np.sign(x)*np.maximum(np.abs(x)-tau,0)\n", "\n", "#Run proximal langevin\n", "\n", "\n", "Lf = 10\n", "gamma = 1/Lf\n", "tau = gamma/5/(Lf*gamma+1)\n", "print('stepsize ',tau)\n", "\n", "grad_F = lambda x: dG(x) + (x - soft(x,lam*gamma))/gamma\n", "mfunc = lambda x: .5* np.linalg.norm(A(x)-b)**2 + lam*np.linalg.norm(x,ord=1)\n", "\n", "Iterate = lambda x: samplers.one_step_langevin(x,p, grad_F, tau,beta=5)\n", "\n", "xinit = np.random.randn(p,)\n", "n = int(1e5)\n", "burn_in = int(1e4)\n", "\n", "print('Running prox-l1 sampler ...\\n')\n", "samples_proxl1 = samplers.generate_samples_x(Iterate, xinit, n, burn_in)\n" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Running hadamard sampler ...\n", "\n" ] } ], "source": [ "uvinit = np.concatenate((np.abs( np.random.rand(p,)),np.random.randn(p,)))\n", "Iterate_uv = lambda x: samplers.one_step_hadamard(x, p,dG, tau, lam,beta=5)\n", "\n", "print('Running hadamard sampler ...\\n')\n", "samples_uv = samplers.generate_samples_x(Iterate_uv, uvinit, n, burn_in)" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "plt.plot(x0, 'k',label='x0', alpha=0.3)\n", "\n", "\n", "plt.plot(py_Ws(scaling_vec*np.mean(samples_proxl1,axis=0)), 'r', label='Prox-l1',linewidth=4.0,alpha=0.5)\n", "plt.plot(py_Ws(scaling_vec*np.mean(samples_uv[:,:p]*samples_uv[:,p:], axis=0)), 'g-',label='Hadamard',linewidth=2.0,alpha=0.5)\n", "\n", "plt.plot(py_Ws(scaling_vec*x_mode), 'y--', label='MAP')\n", "\n", "signal_samples = np.stack([py_Ws(scaling_vec*x) for x in samples_proxl1],axis=0)\n", "signal_samples_uv = np.stack([py_Ws(scaling_vec*x) for x in samples_uv[:,:p]*samples_uv[:,p:]],axis=0)\n", "\n", "plt.legend(fontsize=16)\n", "\n", "plt.savefig('results/Deconv_mean.pdf', bbox_inches='tight')\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Plot the difference between the 95 and 5 percentiles" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "# Calculate 90% credibility intervals (pixel-wise)\n", "lower_bound = np.percentile(signal_samples, 5, axis=0)\n", "upper_bound = np.percentile(signal_samples, 95, axis=0)\n", "plt.plot(np.log(upper_bound-lower_bound), 'r', alpha=0.8, label='Prox-l1')\n", "\n", "\n", "lower_bound = np.percentile(signal_samples_uv, 5, axis=0)\n", "upper_bound = np.percentile(signal_samples_uv, 95, axis=0)\n", "plt.plot(np.log(upper_bound-lower_bound), 'g-',alpha=0.4, label='Hadamard')\n", "plt.legend(fontsize=16)\n", "\n", "plt.savefig('results/Deconv_quantile.pdf', bbox_inches='tight')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check the effective sample size" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [], "source": [ "import arviz as az\n", "\n", "\n", "idata = az.convert_to_inference_data(np.expand_dims(signal_samples, 0))\n", "ess = az.ess(idata)\n", "\n", "\n", "idata_uv = az.convert_to_inference_data(np.expand_dims(signal_samples_uv, 0))\n", "ess_uv = az.ess(idata_uv)" ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.4188756738327672\n", "12.56526233782412\n", "[0]\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ess_values = (ess['x'].values).min()\n", "print(ess_values)\n", "width=0.2\n", "# x = np.arange(len(ess_values))\n", "x = np.arange(1)\n", "\n", "fig, ax = plt.subplots()\n", "\n", "\n", "\n", "ess_uv_values = (ess_uv['x'].values).min()\n", "print(ess_uv_values)\n", "width=0.2\n", "\n", "rects1 = ax.bar(x +width, ess_uv_values, width, label='Hadamard')\n", "print(x)\n", "ax.set_xticks([-width,width])\n", "ax.set_xticklabels(['Prox-l1', 'Hadamard'])\n", "rects1 = ax.bar(x -width, ess_values, width, label='Prox-l1')\n", "\n", "plt.savefig('results/Deconv_ESS_min.pdf', bbox_inches='tight')\n", "\n", "\n", "# plt.legend()" ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "width=0.2\n", "# x = np.arange(1)\n", "\n", "fig, ax = plt.subplots()\n", "\n", "\n", "\n", "\n", "ess_uv_values = (ess_uv['x'].values)\n", "\n", "x = np.arange(len(ess_uv_values))\n", "\n", "\n", "\n", "\n", "ess_values = (ess['x'].values)\n", "rects1 = ax.bar(x -width, ess_values,width, label='Prox-l1',color='r')\n", "rects1 = ax.bar(x +width, ess_uv_values, width, label='Hadamard',color='g')\n", "\n", "plt.legend(fontsize=16)\n", "plt.savefig('results/Deconv_ESS.pdf', bbox_inches='tight')\n" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(4.1324715813899795, 286433.6894248724)" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.exp(1.4188756738327672),np.exp(12.56526233782412)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.0" } }, "nbformat": 4, "nbformat_minor": 4 }